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The currents, winds and tides of northern Howe Sound Buckley, Joseph Roy 1977

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THE CURRENTS, WINDS AND TIDES OF NORTHERN HOWE SOUND by JOSEPH ROY BUCKLEY B. Sc. McMaster University, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOB THE DEGREE OF : -• DOCTOR OF PHILOSOPHY i n the Department of Physics and the In s t i t u t e of Oceanography • Se accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1977 copyright J. R. Buckley, 1977 In presenting th is thes is in p a r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wri t ten permission. Department of PHVQTPQ The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 4 March 1977 f r o n t i s p i e c e - Northern Howe Sound from 9.6km a l t i t u d e , August 7, 1972. (National Air Photo Library photoqraph) i i i ABSTRACT Studies were carried out to determine the c i r c u l a t i o n of water i n the northern basin of Howe Sound, a small f j o r d on the mainland coast of B r i t i s h Columbia, and to determine the extent of the influence of the winds, the tide and r i v e r runoff on the c i r c u l a t i o n . In one experiment, surface-layer drogues were tracked by radar f o r four periods each of approximately three days duration. Data sere recorded photographically, then d i g i t i z e d f or computer processing. Cubic spline interpolation was used to produce positions, v e l o c i t i e s and accelerations at one minute i n t e r v a l s along every drogue track. The interpolated data were averaged i n a suitable manner to produce pseudo-Eulerian estimates of vel o c i t y . Near the head of the f j o r d , both wind and tide appeared to cause temporal fluctuations in the surface current of magnitude s i m i l a r to the expected mean flow due to the r i v e r . The r i v e r was the cause of s p a t i a l inhomogeneity i n the flow, but did not appear to be a s i g n i f i c a n t source of temporal variations. Farther down the i n l e t , wind forcing was the dominant cause of temporal variations i n the surface-layer flow of about f i v e times the magnitude of the expected mean river-driven flow. At no distance along the fj o r d was the velocity observed to be l a t e r a l l y uniform. Lateral gradients of long-channel velocity were strong at the i n l e t head and decreased away from i t , i n d i c a t i n g t h a t the f r e s h water from the r i v e r was s l o w l y mixing a c r o s s the i n l e t . Another experiment u s i n g drogues at three depths i n the upper 6m of the water i n d i c a t e d that the v e l o c i t y s t r u c t u r e was not uniform, e i t h e r l a t e r a l l y or with depth. A n a l y s i s was done on data from s i x cu r r e n t meters moored i n the no r t h e r n b a s i n of Howe Sound. The mean c u r r e n t s from these meters showed a s u r f a c e - l a y e r outflow and a r e t u r n i n f l o w i n the waters j u s t below. A mean down-i n l e t c u r r e n t was seen at 150m, 80m below s i l l depth. Spectra of the c u r r e n t s showed dominant peaks a t d i u r n a l and s e m i - d i u r n a l p e r i o d s . The wind was coherent with the c u r r e n t s at 3m f o r p e r i o d s l o n g e r than 10 hours. Below t h i s depth, no c o n s i s t e n t r e l a t i o n s h i p was seen. In the d i u r n a l band, the c u r r e n t s were s t r o n g e s t at the s u r f a c e , i n d i c a t i v e of f o r c i n g from the s u r f a c e by the wind. In the s e m i - d i u r n a l band, the c u r r e n t s were s t r o n g e s t at 10m depth. , Both bands a l s o showed a phase v a r i a t i o n with depth i n d i c a t i v e o f a b a r o c l i n i c s t r u c t u r e . These r e s u l t s were compared with some models f o r s u r f a c e - l a y e r behaviour. The f i r s t model assumed t h a t the wind momentum input was d i s t r i b u t e d u niformly throughout the s u r f a c e l a y e r and t h a t the l a y e r was not f r i c t i o n a l l y c oupled t o the deeper waters. Drag c o e f f i c i e n t s c a l c u l a t e d from the wind s t r e s s and drogue a c c e l e r a t i o n gave values of 1 to 2 x 1 0 - 3 , s i m i l a r to values measured i n other ways. T h i s model was o n l y v a l i d f o r the f i r s t few hours a f t e r the onset of the wind. Another model, developed by Farmer (1972), V a n a l y s e d t h e b e h a v i o u r o f t h e s u r f a c e l a y e r o f a s e m i -i n f i n i t e c a n a l u n d e r t h e i n f l u e n c e o f a s t e a d y w i nd s t r e s s . I t p r e d i c t e d c o r r e c t l y t h e l e n g t h o f t i m e o f w i n d d o m i n a n c e o f t h e f l o w , t h e m a g n i t u d e o f t h e v e l o c i t y c h a n g e and t h e m a g n i t u d e o f t h e a c c e l e r a t i o n o f t h e w a t e r . A b a r o c l i n i c t i d a l m o d e l i n a t w o - l a y e r f j o r d , a d a p t e d f r o m R a t t r a y ( I 9 6 0 ) , c o r r e c t l y p r e d i c t e d t h e p h a s e o f t h e s u r f a c e -l a y e r c u r r e n t s n e a r t h e h e a d o f a f j o r d w i t h r e s p e c t t o t h e h e i g h t o f t h e t i d e . v i TABLE OF CONTENTS page A b s t r a c t -.........................v.. i i i L i s t of Tables . x L i s t o f F i g u r e s . ..^vvvyyvvvW x i i Acknowledgements xv Chapter I - I n t r o d u c t i o n 1 1.1 - Howe Sound - The F j o r d Under I n v e s t i g a t i o n .. 3 ••'1.2'- S i l t , C i r c u l a t i o n and F o r c i n g F u n c t i o n s ..... 9 I. 3 - A B r i e f Background of E s t u a r i n e Theory and Forced C i r c u l a t i o n Dynamics ,..yy-.-Vv.v*;vV«4<.vy v12 Chapter I I - Surface Layer Flow - Experiment and Data A n a l y s i s ' .vv:;y . v . . ' . y . vy?.--4 -y~,v-'y... 15 I I . 1 - A P r e l i m i n a r y Experiment .y..y..............15 11,2 - Main Experiment ...yy.y y y . . y y . . i ............ 20 I I . 2. 1 - •  Introduction- •.;.vvyy.y'y;yy--.y-'.v.... . . v . - . 20 I I . 2. 2 - The Drogues- 21 II.2.3 - The Base S t a t i o n - Radar and Cameras . . 2 5 II.2.4 - Vessels, Communications and L o g i s t i c s . 2 9 II. 3 - Analysis of the Drogue Data 31 II. 4 - Data Averaging - a Problem of Lagrangian Measurements . ... •. • i •..... . ;.«........ •. 42 Chapter III - Measurements of Bind, Tide, Biver Flos and Surface Layer structure - - • % ; ^ 4 v.ViV :»v •>•>•'••...... ,48 III . 1 - Wind Measurements .... 4 8 III.2 - Biver Discharge 54 I I I . 3 — The Tide . :»:»:•» •. . *•».»: • »*.•»»•» • ••••» »*.....-...• 57 III . 4 - Density Measurements ..v. v. .v 61 III . 5 - Comparison of the Drogue V e l o c i t i e s with the 3m Current Meter .........................:. ..',-66 Chapter IV - Results of the Surface Layer Experiment . ;70 IV. 1 - • Introduction ............................... 70 IV.2 - A General Surface C i r c u l a t i o n P a t t e r n . . . . . . 72 IV. 3 - A Synopsis of the Data Sets•>-:y^-v-yy^'yVVy'Vy. 76 IV. 3.1 - Technigues of Presentationv.iywiyVW. ..•; 76 IV. 3.2 - Week 1 - May 8-11, 1973 81 1^. 3. 3 - Seek 2 - May 15-18,1973^-^•v^^^'Mwv^vvSS IV.3.4 - Week 3 - June 26-29,1973 ... i .v. i . ..... 90 IV. 3. 5 - Week 4 - July 3-6,1973 ........... ...96 IV.3.6 - Summary of the Observations .....\.....101 IV.4 - Temporal and cross-channel Variations i n Surface Layer Flow- . . . . . . >y*yvy>>-y ; •> ' • • ' . *yy .y •> 102 IV.5 - Lat e r a l Homogeneity of the Velocit y and Acceleration Fields .............................111 IV.6 - Temporal Variations i n L a t e r a l l y Averaged V e l o c i t i e s and Accelerations ....................114 v i i i IV.7 - Cross-channel S t r u c t u r e 1 of the V e l o c i t y F i e l d .118 IV.8 - Ensemble Averaged V e l o c i t y G r a d i e n t s .......121 Chapter V - I n t e r l u d e - The Three L e v e l Drogue Experiment""-. vWv.-.v. v...vv> -.•v>:,--V;.->rv.^ .*>;:*>y:i-vv v> ... . ..125 Chapter VI - Subsurface C u r r e n t s 133 VI.1 - A D e s c r i p t i o n of the Subsurface Current Mo n i t o r i n g Programme .133 VI.2 - Time S e r i e s Records from the Current Meters 135 VI.3 - S p e c t r a l A n a l y s i s of the Currents .........,139 VI.4 - Techniques and Problems of A n a l y s i s ........14 0 VI.5 - R e l i a b i l i t y and S t a b i l i t y of Coherence Estimates ... 148 VI. 6 - • Mean Currents 153 VI. 7 - Spectra of the Wind and Currents 157 VI.8 - Coherence of the Wind and Currents ......... 163 VI. 9 - T i d a l I n f l u e n c e on the C u r r e n t s .169 VI. 10 - Changes i n Hydrographic P r o p e r t i e s as I n d i c a t o r s of C urrents ..........................174 Chapter VII - Summary o f R e s u l t s and Comparison with Theory •,vv.-.v/v-.>-,vvvvv.-.:v. .vy,v.v :vvv.^v-.-rv.v*v.S.^.;*8-0 VII. 1 - Summary of the Experimental R e s u l t s 180 VII.1.1 - The Surface Layer Experiment ...180 VII.1.2 - The Subsurface Current Experiment .... 182 VII.2 - Drag C o e f f i c i e n t C a l c u l a t i o n s .....184 VII.3 - Farmer's Model of a Wind-Driven Surf ace • L a y e r ...... -. v-.v>,;-.....yvi!*!*v*v••••=•• 189 VII.4 - T i d e s and a Normal-Mode F j o r d Model ......,198 i x VII. 5 - Summary of the aodel R e s u l t s .............. 207 BxfoXi.OQ£cip]iY « « * • • • • * • • • * • • • • • * * * * * • •»• * ••••**209 Appendix I - Behaviour Cf A Drogue In A V e r t i c a l Shear 213 Appendix I I - Computer Movie Generation 226 Appendix I I I on tape i n Special Collections X LIST OF TABLES Table page I: Average Float V e l o c i t i e s And Directions In the F i r s t Experiment . y v v . • . vvyiyvyyvv';. 1 8 I I : Comparison Of Squamish And Radar Site Winds 49 I I I : River Discharge And Resultant Surface-layer V©locx^ fcy #'*"#'*••• * • ••' ••"»• • • y • > •-••'•-'•-•'»•-'"'• • »;'"•!'»-":«•• ,.T'5 € IV: Equivalent Fresh Water Depth For Several Cross—inlet Sections .... •.... •••'•;.-.-.<:v:'. ^ •'••v.vv.-..'.: ••••*-. :63 V: A Summary Of Drogue Observation S t a t i s t i c s ...... 70 VI: Ensemble Averaged Acceleration Ratio And VsXoc.X'ty SiiSciirs .»»'='•"••:»• * •^''•'^•^•/-•^••'•^  121 VII: Coherence And Phase Estimates Between Wind And 5m Current With Different Degrees Of Freedom •-.......149 VIII: Ratios Of Mean Square Currents In The Diurnal Band To Those In The Semi-diurnal Band For A l l DepthS " . . - . . ' .v..<'>"'* . . . . . .':V;.':-:. ....... 1 6 1 IX: Coherence And Phase Between Wind And Currents X: Tid a l Constituents At Sguamish ... .-.y .y .......... 16 9 XI: Coherence And Phase Between The Currents in the Diurnal And Semi-diurnal Bands .............. 170 XII: Amplitude And Phase Of The Surface Layer Currents Calculated From The Normal-mode Model ..203 x i XIII: The Forces And Torques On A Drogue 216 XIV: Drogue Speed And T i l t Angle In A Homogeneous Current ..... .v. .'Vv. .-.vvvv.>v^ ..., .... 219 XV: Drogue Speed And T i l t In A Linear Shear ......... 220 XVI: Comparison Of Drogue, Mean And E.m.s. Vel o c i t i e s For Three Analytic Shears ....................... 223 x i i L I S T OF FIGURES F i g u r e page 1: The B a t h y m e t r y Of Howe Sound 4 2: A T y p i c a l S i g m a - t S e c t i o n Of Howe Sound 7 3: S g u a m i s h H a r b o u r S h o w i n g L o c a t i o n Of The P h o t o g r a p h i c S i t e And The F l o a t T r a c k s From The Fxxrsfc £ xp*s ir xonsn t • • • • : v v : « v * *• * • • *< , ^ 8 4: The B a s i c D e s i g n Of The S u r f a c e D r o g u e s U s e d . ..... 2 2 5: D e t a i l s I n Dro g u e C o n s t r u c t i o n . . . . . . . 2 5 6: Howe Sound S h o w i n g The F o u r R a d a r S i t e s And A T h r e e M i l e Range A b o u t E a c h One 2 7 7: A Sample R a d a r Image, The A n t e n n a R e s p o n s e P a t t e r n And The E c h o Of A Drogue 3 2 8: A F l o w C h a r t Of The Dro g u e T r a c k C r e a t i n g And C h e c k i n g Programmes ...................... v . . 4 1 9 : R i n d Rose F o r The E x p e r i m e n t S u p e r i m p o s e d On A C h a r t Of Howe Sound 5 2 1 0 : A C o m p a r i s o n Of The L o n g - c h a n n e l Wind Component From S g u a m i s h And The R a d a r S i t e 5 3 1 1 : D i s c h a r g e Of The S g u a m i s h R i v e r T h r o u g h o u t The E x p e r i m e n t .«... i«v :ri :« ,tVvviVfriV' :'i ••• • »;*'» ••.•-«•••••,••••,» . 5 6 1 2 : T i d a l H e i g h t F o r The E x p e r i m e n t As P r e d i c t e d F o r 1 3 : S a l i n i t y P r o f i l e s From Two C r o s s - i n l e t S e c t i o n s . . . 6 2 x i i i 14: A Comparison Between Rater V e l o c i t y As Measured By Drogue And By Current Meter •. . - ' . / v - . v . ; y . / V . v , ; . ,<67 • 15: P a t t e r n Of The C i r c u l a t i o n Of The Surface Layer . . 7 3 16: Correspondence Between The A c t u a l And "Squared" 17: A T y p i c a l Diagram From The Averaged Data Set ..... 78 18: T y p i c a l Three Hour Average V e l o c i t i e s P l o t t e d With Standard D e v i a t i o n E r r o r Bars .... 80 19: The week 1 Data Set 82 20: The Week 2 Data Set 86 21: The Week 3 Data Set 91 22: The Week 4 Data Set 97 23: L o c a t i o n Of The Averaging Regions 103 24: Contours Of Long-channel V e l o c i t y As A Fun c t i o n Of Cross-channel P o s i t i o n And Time ..................104 25: T o t a l V e l o c i t y As A Function Of Cross-channel P o s i t i o n And Time . • i ' i v : i , . f > > ^ > ; f t v v « v ? ^ > , « ^ V i ' V » ^ ; f ' « .110 26: V e l o c i t y And A c c e l e r a t i o n Vs. Time For Three C r o s s - i n l e t P o s i t i o n s In Week 1 .........w........ 113 27: L a t e r a l l y Averaged V e l o c i t y And A c c e l e r a t i o n Vs 28: Cross-channel S t r u c t u r e Of The V e l o c i t y F i e l d ....119 29: Three Layer Experiment - Shallow Drogue Tracks ... 128 30: Three Layer Experiment - Intermediate Drogue Tracks-' v-.-t^ .'.-v. ^*'V"."••"••V'*^.-v.'. *''"•/'.•'• * ..129 31: Three Layer Experiment - Deep Drogue Tracks 130 32: V e l o c i t y Contoured C r o s s - i n l e t S e c t i o n From The Three L e v e l Experiment . .. v..... *..,...'..>....*. 131 xiv 33: F i f t e e n Days Of Current Meter Records .........v..136 34: Onsmoothed And Smoothed Current Meter Records ....145 35: Smoothed And Unsmoothed 5m Current S p e c t r a .......147 36: The Mean Current P r o f i l e In Howe Sound , A p r i l -37: Spectra Of The Wind And Currents ................. 158 38: Coherence And Phase Between The Wind And Currents 164 39: Phasor Diagrams For The Semi-diurnal And D i u r n a l C u r r e n t s At D i f f e r e n t Depths '';.v;r:»>->444:y'.-.%vyi-v.!;./....173 40: Time S e r i e s P l o t Of Temperature Vs Depth At How 4 176 41: Temperature S e c t i o n s i n Howe Sound on 20 September and 13 November, 19.73 ............................177 42: C a l c u l a t e d "drag C o e f f i c i e n t s " For A l l Four Weeks 187 43: V e l o c i t y And A c c e l e r a t i o n From Farmer's Model .,..194 44: Geometry Of The Basin For A Normal-mode F j o r d 45: Amplitude And Phase Of The Surface Layer C u r r e n t s As C a l c u l a t e d From R a t t r a y ' s Model 205 46: The Forces On A Drogue 216 XV ACKNOWLEDGEMENTS The type of drogue study described in t h i s thesis requires a large amount of manpower to be performed sucessfully. During the course of the experiment; v i r t u a l l y a l l of the Physical Oceanography graduate students and many of the s t a f f members of the Ins t i t u t e of Oceanography, University of B r i t i s h Columbia volunteered t h e i r services. Much assistance came from Mr. David English, who helped to design the , drogues and to keep the f l e e t of vessels operating during the experiment, and provided technical expertise i n the project. Assistance i n t h i s experiment also came from the P a c i f i c Environment I n s t i t u t e , Sest Vancouver, B.C., which provided the E/V Active Lass, her skipper Mr. A. Matheson and the Sangstercraft; from the P a c i f i c B i o l o g i c a l Station, Nanaimo, B.C., which provided the R/V Caligus with Mr.,Eon Page, Dr. John Sibert and Dr. Robert Parker; from Construction Aggregates Ltd., which allowed us to use i t s property for the radar s i t e s at Britannia Beach and at Furry Creek and to Rayonier of Canada Ltd., Woodfibre D i v i s i o n , which allowed us to use i t s property for the radar s i t e at Woodfibre. To a l l these people and organizations, thank you. Without your help, i t would have been impossible to perform t h i s experiment. My thanks are also extended to the Coastal Zone Oceanography group at the Institute of Ocean Sciences, x v i P a t r i c i a Bay, B.C., who maintained the c u r r e n t meter s t r i n g s i n Howe Sound and t o Mr. W.H. B e l l of t h a t group who d i d a l l the p r e l i m i n a r y a n a l y s i s o f the c u r r e n t meter data and k i n d l y provided me with h i s r e s u l t s , and to Dr. P.B. Crean o f the Numerical M o d e l l i n g group of I.O.S. f o r p r o v i d i n g me with t i d a l data i n Howe Sound and r e s u l t s from h i s t i d a l model of t h e area. I would a l s o l i k e t o express my thanks t o my committee and to those other members of the I n s t i t u t e who d i s c u s s e d the many a s p e c t s of t h i s work with me. The work was supported mainly by c o n t r a c t s from the I n s t i t u t e of Ocean Scien c e s , P a t r i c i a Bay, with some a d d i t i o n a l support from the N a t i o n a l Research C o u n c i l of Canada, grant A 8301,,During my years at the U n i v e r s i t y of B r i t i s h Columbia, I have been p e r s o n a l l y supported by a Postgraduate S c h o l a r s h i p and a Postgraduate Bursary from the N a t i o n a l Research C o u n c i l of Canada, by a MacMillan Family F e l l o w s h i p from the U n i v e r s i t y of B r i t i s h Columbia, by a r e s e a r c h a s s i s t a n t s h i p provided i n the c o n t r a c t s and by s e v e r a l t e a c h i n g a s s i s t a n t s h i p s from the Department of P h y s i c s , U n i v e r s i t y of B r i t i s h Columbia. I have a l s o been helped through t h i s t h e s i s by my wife Eve, who, as we l l as t y p i n g the document and d r a f t i n g many of the f i g u r e s , c o n s t a n t l y provided the moral support necessary t o enable me to see t h i s p r o j e c t to completion. F i n a l l y , I would l i k e t o thank my r e s e a r c h s u p e r v i s o r , Dr. Stephen Pond, f o r the expert guidance, sage a d v i c e , enthusiasm, d e d i c a t i o n and support he has given me x v i i throughout the f i v e and one h a l f years of research work presented i n t h i s t h e s i s . 1 CHAPTER I INTRODUCTION T h i s t h e s i s d e s c r i b e s an i n v e s t i g a t i o n i n t o f l u c t u a t i o n s i n water movement i n a f j o r d and the s e v e r a l p o s s i b l e causes of these f l u c t u a t i o n s . The i n v e s t i g a t i o n , conducted i n Howe Sound, B r i t i s h Columbia, c o n s i s t e d of two main p a r t s . The f i r s t part was a s u r f a c e l a y e r experiment performed i n fou r p e r i o d s , each o f f o u r days d u r a t i o n , i n May, June and J u l y , 1973. A number of s u r f a c e drogues were t r a c k e d by radar t o o b t a i n a p i c t u r e of the s u r f a c e l a y e r flow f i e l d . The subsequent a n a l y s i s attempted to r e l a t e the v e l o c i t y and a c c e l e r a t i o n of the water to wind s t r e s s , to t i d a l f o r c i n g and to v a r i a t i o n s i n r i v e r flow. The second p a r t of the i n v e s t i g a t i o n c o n s i s t e d of the a n a l y s i s of data from a c u r r e n t meter s t r i n g moored i n the same f j o r d throughout 1973. T h i s c u r r e n t meter s t r i n g was maintained by the C o a s t a l Zone Oceanography group of the I n s t i t u t e of Ocean S c i e n c e s , P a t r i c i a Bay, B.C. T h i s a n a l y s i s attempted to r e l a t e the c u r r e n t s t o wind and t i d a l f o r c i n g . T h i s t h e s i s s t a r t s with a survey o f the b a s i c oceanography of Howe Sound and a b r i e f h i s t o r y o f previous s t u d i e s on the dynamics of water c i r c u l a t i o n i n f j o r d s . Chapter I I c o n t a i n s a d e s c r i p t i o n of the s u r f a c e l a y e r experiment and of the a n a l y s i s techniques used t o process 2 the data. Chapter III i s a description of the forcing functions of wind, r i v e r flow and t h e i r behaviour during the experiment. That chapter also contains a description of the measurements made to ascertain the v a l i d i t y of the concept of a "surface layer" in Howe Sound, and to determine the depth of t h i s layer. In chapter IV, the results of the surface-layer experiment, both q u a l i t a t i v e and quantitative, are described. Chapter V i s the description of a short but i n t e r e s t i n g experiment performed with the drag elements of the drogues suspended at d i f f e r e n t depths i n the near surface layer of Howe Sound. The results provide a bridge between the surface layer experiment described i n the previous chapters and the current meter experiment described i n chapter VI which contains the r e s u l t s obtained by spectral analysis of the currrent meter data. In the f i n a l chapter, the r e s u l t s of both experiments are examined i n the l i g h t of e x i s t i n g theories and some conclusions are drawn about the v a l i d i t y of these theories. Due to the c a l i b r a t i o n of the radar set, one unit of horizontal distance measurement used throughout t h i s thesis i s the B r i t i s h Nautical mile (about 1.85km). any reference to miles in t h i s thesis r e f e r s to t h i s unit. With the exception of the b a r o c l i n i c t i d a l model in chapter VII,--a l o c a l right-handed co-ordinate system i s used throughout t h i s t h e s i s , with the x axis directed up-inlet (nominally north), the y axis directed c r o s s - i n l e t (nominally east) and the z axis directed v e r t i c a l l y downward, u, v and w are the v e l o c i t i e s i n the x, y and z d i r e c t i o n respectively. 3 1. 1 Howe Sound The Fjord^CTnder^Investi.gation From Pt. Atkinson on the northern side of the entrance to Vancouver harbour to Sguamish, 4 3 km north, l i e s a body of water that has been known for almost 200 years as Howe Sound. From a 20km wide opening onto the S t r a i t of Georgia between Pt Atkinson and Gower Pt, Howe Sound narrows to about 3.5km at the Defence Islands 26km north. This triang u l a r southern basin i s f u l l of islands. I t s average depth i s about 200m, In the Pleistocene era there was a s i l l made of g l a c i a l t i l l near the south end of the basin separating the deep waters of the sound from those of the S t r a i t of Georgia. According to K.Bicker (unpublished manuscript), t h i s s i l l has since been breached by a f a u l t and subsequently eroded in the eastern channel between Passage Island and Bowen Island allowing free mixing of the waters of t h i s basin with those of the S t r a i t . Between the Defence Islands and Porteau Cove there i s a s i l l of g l a c i a l material that r i s e s to within no greater than 70m of the surface. Just north of t h i s s i l l , the channel achieves i t s maximum depth of 300m. The channel width from Porteau Cove to Sguamish i s a roughly constant 2.5km. The bathymetry and major features of Howe Sound are shown i n figure 1 . The Sguamish Biver flows into Howe Sound at the head of the i n l e t . It has an average annual discharge of 242 m3/s (Water Survey of Canada, 1974), one of the larger outflows i n the province. Its drainage basin of 2341 km2 i s i n the mountains and snowfields to the north of Sguamish. This Figure 1 Bathymetry and major features of Hcwe Sound. 5 r i v e r provides almost a l l of the fresh water input into the sound. In June 1792, during his explorations of the west coast of North America, Captain George Vancouver v i s i t e d Howe Sound and had these words to say about i t : Quitting point Atkinson and proceeding up the sound...we made a rapid progress, by the assistance of a fresh southerly gale, attended with dark gloomy weather that greatly added to the dreary prospect of the surrounding country. The low f e r t i l e shores we had been accustomed to see, though l a t e l y with some interuption, here no longer existed: t h e i r place was now occupied by the base of the stupendous snowy barrier, t h i n l y wooded and r i s i n g from the sea abruptly to the clouds; from whose f r i g i d summit, the dissolving snow i n foaming torrents rushed down the sides and chasms of i t s rugged surface, ex h i b i t i n g altogether a sublime, though gloomy spectacle, which animated nature seemed to have deserted. ... (We) f i n d i t to terminate in a round bason encompassed on every side by the dreary country already described... The water of the sound was here nearly fresh, and i n colour a few shades darker than milk; t h i s I attributed to the melting snow and i t s water passing over some chalky substance. ...We had scarcely finished our examinations when the wind became excessively boisterous from the southward attended with heavy sgualls and torrents of r a i n . ...At a distance of an hundred yards from shore, the bottom could not be reached with 60 fathoms of l i n e , nor had we been able to gain soundings i n many places since we had quitted point Atkinson with 80 and 100 fathoms, though i t was frequently attempted... Westward from Anvil island ...the colour of the water changed from being nearly milk white and almost fresh to that of oceanic and perfectly s a l t . ...About nine o'clock (we) landed for the night near the west point of entrance into the sound, which I distinguished by the name of Howe's Sound i n honor of Admiral Earl Howe. 6 During his short rainy v i s i t , Vancouver observed many of the basic f j o r d - l i k e c h a r a c t e r i s t i c s of Howe Sound, the depth, the steep side walls, the s i l t y fresh water input (although he mistakenly i d e n t i f i e d i t s source as a "chalky substance" instead of g l a c i a l " f l o u r " ) , and the strong winds. In the more recent past, Howe Sound was the subject of observation by Hutchinson and Lucas (1931) who examined the summer hydrographic properties of the surface 50yd (46m) at three locations i n the sound as part of a larger S t r a i t of Georgia surface layer study. Carter (1934) studied the hydrographic and chemical properties of the upper 50m several times throughout the year at the mouth and head of Howe Sound. In more recent years, Howe Sound has been v i s i t e d on occasion by personnel from the In s t i t u t e of Oceanography, University of B r i t i s h Columbia (IOUBC) as part of ongoing B r i t i s h Columbia i n l e t s studies. From 1957 to 1971 a t o t a l of 13 cruises were made., Temperature, s a l i n i t y and dissolved oxygen content were recorded at discrete depths from the surface to the bottom at several stations within the Sound on each of these cruises. As a result of some of these cruis e s , the basic oceanographic features of Howe Sound have been described by Packard (1961). Further sources of hydrographic data and description may be found i n Maries et a l . (1973) . A t y p i c a l sigma-t section of the northern basin of Howe Sound i s shown i n figure 2 . An obvious feature of t h i s Figure 2 - Sigma-t contours in upper Howe Sound 23 July 1973. C i r c l e s on the v e r t i c a l l i n e indicate locations of current meters discussed in chapter VI. 8 f i g u r e i s the e f f e c t of the s i l l on the continuity of the water masses. Inside the s i l l , below 150m, sigma-t i s a constant 23.70 within the precision of measurement, while outside the s i l l i t increases to values greater than 24.00, The upper layers both inside and outside the s i l l show the expected strong s t r a t i f i c a t i o n . A survey of the annual variation i n hydrographic properties was done as a baseline for t h i s thesis work. A series of 19 cruises were made from July 1972 to March 1974 measuring temperature, s a l i n i t y and dissolved oxygen content from bottle samples and making STD casts at seven stations from Anvil Island to Sguamish. This survey showed that, although the density structure of the upper waters throughout the i n l e t and the deeper waters outside the s i l l changed continuously on an annual basis, the deep waters behind the s i l l did not change measurably i n density. Analysis of temperature, s a l i n i t y and dissolved oxygen showed an occasional deep water replacement in t h i s inner basin.. The data from these cruises have been used by Pickard (1975) to show t h i s l a s t r e s u l t . S c i e n t i f i c i n t e r e s t i n the currents of Howe Sound i s recent., Strings of current meters were i n s t a l l e d and maintained by the Coastal Zone Oceanography section of the In s t i t u t e of Ocean Sciences, P a t r i c i a Bay B.C. from November 1971 to November 1972 just north of Anvil Island; from February 1972 to November 1972 south of Anvil Island and from November 1972 to February 19 74 i n the centre of the channel opposite Furry Creek. The basic data from these 9 meters have been published by B e l l (1975). These data show that the expected estuarine c i r c u l a t i o n i s indeed present i n Howe Sound. There was a seaward flow i n the surface layer and a return flow i n the deeper layers. There were, however, large variations about the mean. The f i n a l l o c a t i o n , shown i n figure 6, was chosen to complement the hydrographic study and the surface current study described i n t h i s t h e s i s . It i s the data from these meters that w i l l be discussed i n d e t a i l i n chapter VI. Thus the background of physical data already co l l e c t e d i n Howe Sound i s guite considerable as might be expected for an i n l e t so close to Vancouver. It was against t h i s background that the present investigation was set. 1.2 Silt-, C i r c u l a t i o n , ^ Functions The feature of the water flow i n Howe Sound most noticeable to the casual observer i s the s i l t pattern i n the surface layer. I t obviously comes from the r i v e r and appears to reveal a " r i v e r " of fresh water that meanders and eddies through the s a l t i e r water of the i n l e t u n t i l • i t f i n a l l y d i f f u s e s throughout the surface layer. A fine example of such a s i l t pattern i s shown in the frontispiece, A more ca r e f u l observation of these s i l t patterns w i l l show that the general shape of these patterns i s not fixed , but varies with a period of approximately one day. I t seems most probable that these variations i n s i l t patterns r e f l e c t variations in the t o t a l surface layer c i r c u l a t i o n . One main 10 objective of t h i s thesis was to discover the cause of these variations. Tugboat and fishboat operators on the B.C. coast refer to any current as a " t i d e " . Certainly the ti d e i s a l i k e l y candidate for the cause of the variations in surface currents i n Howe Sound. The tides i n Howe Sound are mixed semi-diurnal with a range of about 5m. The sum of the amplitudes of the diurnal constituents i s about the same as the sum of the semi-diurnal constituents and so some diurnal forcing by the t i d e must be expected. There are, however, other possible sources of the variations in the currents. The Sguamish River depends on the snow and ice f i e l d s i n the mountains north of Sguamish f o r i t s water supply. Maximum runoff i s i n the l a t e spring and early summer when snow melting i s at i t s peak. Since t h i s melting i s dependant on the warmth of the sun, runoff i s higher i n the daytime than at night. The d a i l y runoff peak w i l l of course be delayed by the length of time i t takes to t r a v e l from the snow f i e l d s to the i n l e t . These dai l y variations i n r i v e r runoff can be seen i n the gauge records, shown in figure 11, taken at Brackendale, just north of Sguamish. Since the r i v e r runoff i s the major driving force i n the gr a v i t a t i o n a l c i r c u l a t i o n i n the i n l e t , i t i s possible that variations i n t h i s force cause the variations i n the surface flow. Many coastal areas are subject to the phenomenon of land and sea breezes. These winds, caused by the temperature difference between adjacent land and water areas, have b a s i c a l l y the same p e r i o d i c i t y as the fluctuations i n land 11 temperature, which in turn are governed by the d a i l y cycle of i n s o l a t i o n . In an area l i k e Howe Sound, during summer days the land i s quite a b i t hotter than the water surface, so r i s i n g a i r over the land causes strong up-inlet winds. At night the land cools so the temperature difference between land and sea becomes very much smaller and the winds are weak and variable i n dir e c t i o n . The narrowing of the main channel of Howe Sound north of Porteau Cove tends to funnel the winds in from the wider areas both in the north and i n the south, so that in the region of in t e r e s t in t h i s study, the winds may be expected to be stronger than a simple temperature differnce model might indicate. The observations of Pickard and Eodgers (1959) have shown that the wind can have a large effect on the surface currents in a f j o r d . Therefore an investigation of the ef f e c t s of the wind must be included i n a search for the cause of apparent current fluctuations. Tide, wind and r i v e r runoff a l l appear to be possible causes of the observed fluctuations i n the position of the s i l t patterns on the surface of Howe Sound. The studies described i n t h i s t h e s i s attempt to r e l a t e these three factors to variations not just in the s i l t patterns, but also in the water currents, both i n the surface layer and deeper. 12 1.3 • • ••&/;;;Jrief---:&^  F o r c e d C i r c u l a t i o n Dynamics The h i s t o r y of the theory of water movement i n f j o r d s i s almost as long as the h i s t o r y of oceanographic o b s e r v a t i o n s i n the f j o r d s . The i n t e n s e s t r a t i f i c a t i o n i n many of the Scandanavian f j o r d s l e d to some work around the t u r n of the century on i n t e r n a l waves ( f o r example Ekman (1904)). T h e o r i e s were advanced to p r e d i c t the p e r i o d s of both s u r f a c e and i n t e r n a l s e i c h e s i n f j o r d s . : Z e i l o n (1913) used measurments made at Bor.no on the Gullmar f j o r d on the west c o a s t of Sweden to v e r i f y h i s s e i c h e t h e o r i e s . , S t u d i e s of c i r c u l a t i o n dynamics i n f j o r d s have developed along roughly the same l i n e s as have s t u d i e s of ocean dynamics. T r a d i t i o n a l l y , t h e o r i e s of e s t u a r i n e c i r c u l a t i o n based on a n a l y t i c a l models have tended to be s t e a d y - s t a t e and l a t e r a l l y homogeneous. The f i r s t such model came from Cameron (1951), whose model had constant eddy v i s c o s i t y and an imposed v e l o c i t y p r o f i l e . Stommel and Farmer (1952) developed a two-layer model p r i m a r i l y t o look a t s t e a d y - s t a t e u p p e r - l a y e r dynamics, R a t t r a y and Hansen (1962) d e s c r i b e d a s i m i l a r i t y s o l u t i o n f o r e s t u a r i n e c i r c u l a t i o n t h a t i n c l u d e d a steady wind s t r e s s i n the s u r f a c e boundary c o n d i t i o n s . R a t t r a y (1966) modified t h i s s o l u t i o n to f i t the s p e c i f i c case of f j o r d c i r c u l a t i o n . T h i s l a t t e r model allowed the eddy v i s c o s i t y t o vary as a f u n c t i o n of depth and d i s t a n c e along the f j o r d . More r e c e n t l y , Pearson and Winter (1975) have used the method of 13 weighted residuals to solve for modally decomposed velocity and density d i s t r i b u t i o n s i n a f j o r d . A comprehensive description of the basics of estuarine c i r c u l a t i o n i s given by Dyer (1 973) . Other dynamical descriptions based on detailed observations have indicated, as have many recent oceanic experiments (for example MODE, the Mid-Ocean Dynamics Experiment), that v a r i a t i o n s about the mean are much larger than the mean i t s e l f . Some of these observers have looked at changes i n the c i r c u l a t i o n caused mainly by the wind. Tully (1949) noticed that in Alberni In l e t , the surface layer depth could be increased by more than a factor of two during a period of up-inlet winds. He also remarked on the lack of l a t e r a l homogenity of the surface flow f i e l d near the head of the i n l e t . Johannessen (1968) performed a regession analysis between current meter data from Dr^bak Sound i n the Oslo f j o r d and the sguare of the wind speed there. Although his r e s u l t s showed that the winds were responsible f o r about 67% of the variations i n the current at one meter, they also showed that the correlation between the current and the wind 10 hours previously was about twice as good as that between the current and the wind with zero time lag. Farmer (1972) was able to reproduce variations in surface layer depth in Alberni Inlet with a l i n e a r model using the square of the measured windspeed with a constant drag c o e f f i c i e n t to model the surface wind stress. His r e s u l t s also showed large variations in surface layer depth as a function of time. 1 4 It has been said that, i n the deep ocean, the variations in mean flow contain about one hundred times the k i n e t i c energy of the mean flow (W.H. Hunk, 1 975) . Experiments over the l a s t few years have provided a wealth of data to back up t h i s statement, and now general models of oceanic c i r c u l a t i o n are being developed based on this idea (e.g. Stern (1975)) . C i r c u l a t i o n dynamics i n fjords may have a s i m i l a r r e l a t i o n s h i p between mean and variations although the d e t a i l s of both parts of the c i r c u l a t i o n are guite d i f f e r e n t from the oceanic case. However, studies i n f j o r d s have not progressed as far as those i n the deep ocean. In t h i s thesis I s h a l l examine current data for temporal and s p a t i a l variations and attempt to r e l a t e these to various factors. While i t would be premature to attempt to build a complete, consistent model of f j o r d c i r c u l a t i o n based on the available data, I w i l l try to j u s t i f y several e x i s t i n g models of fjord dynamics and attempt to coalesce them into a more consistent picture of the c i r c u l a t i o n dynamics of a f j o r d . 15 CHAPTER I I SURFACE LAYER FLOW - EXPERIMENT AND DATA ANALYSIS 11*1 A Preliminary Experiment A small scale experiment was performed May 25 - 26, 1972 to determine the f e a s i b i l i t y of tracking surface f l o a t s photographically. The s i t e chosen to take the photographs from was Stawamus Chief, a flat-topped mountain near the head of Howe Sound (shown i n figure 3). From the top of t h i s mountain, 610 m above Sguamish harbour, there i s a clear view of the entir e head of Howe Sound from the Sguamish r i v e r to Woodfibre. The f l o a t s used were of a standard design used f o r a e r i a l photography of water movement. They were as large and as brig h t l y coloured as was p r a c t i c a l , being made from coloured polyethylene sheets stretched over 4ft X 16ft frames of cedar. These f l o a t s proved to be extremely awkward to handle from a small boat and were almost impossible to launch or recover i f the wind was blowing with much strength. This design was deemed unsatisfactory for future experiments without substantial modification. The attempt to track these f l o a t s photographically was an almost t o t a l f a i l u r e . Several 35mm cameras were used with several types of colour f i l m including Infrared Ektachrome, 16 i n order to discover which f i l m , i f any, was the best. .It was necessary to use wide angle lenses i n order to get at leas t one shore feature i n each picture for absolute positioning of each f l o a t . The fl o a t s proved to be too small. At a range of 2km, they only subtended an angle of 8 min. In the most successful f i l m , using the wide angle lens, 1.2 km of actual distance was represented by 1 cm on the negative. On t h i s scale, each 5 m f l o a t was only 4 0 micrometers long. This length i s not much di f f e r e n t from the grain size of the f i l m , so there was not much hope of r e l i a b l y finding f l o a t s on the negatives under l e s s than i d e a l circumstances. Use of a much larger negative s i z e such as the size used in a e r i a l photography would of course have helped cure t h i s problem, but was not attempted because of other problems outlined below. The observing conditions were often l e s s than i d e a l . Sun r e f l e c t i o n s obscured the water surface most of the afternoon. The rest of the afternoon and most of the evening the surface was hidden underneath a thick blanket of "Woodfibre fog", i.e.,smoke from the pulp m i l l . Only p a r t i a l l y greater success was had at night, when each f l o a t c a r r i e d a flashing l i g h t . In one 10 minute time exposure a f a i n t streak that showed the position of one f l o a t could be found. The experiment was not a t o t a l l o s s however. Somewhat greater success was had i n tracking the f l o a t s with a t r a n s i t . In the period from 1553 to 2314 on Hay 25, a t o t a l of 5 f l o a t s were tracked. A plot of the f i v e f l o a t tracks i s 17 shown i n figure 3 . T h e i r average speeds and directions are shown i n table I . f l o a t s Y1, P1 and Y2 appeared to be caught Table I Average speed (cm/s) and direction (degrees true) of f l o a t s launched Hay 25,1972 i n Sguamish harbour. The f l o a t positions were measured with a t r a n s i t . The tracks of these f l o a t s are shown in figure 3. r x — - — : ~ J i time „. r„„._ _ i _ average 1 t f l o a t ! s t a r t t I f i n i s h speed I direction) r ! Y1 | 1556 I 1605 ! 36 1 50 j P1 I 1726 I 1913 ! 9 1 20 | Y2 | 1836 I 1938 I 5 1 105 | G ! 19U5 I 1947 I 24 I 175 | N | 2234 I 2315 | 17 1 210 ! 1 i... ' -i n a back eddy of the r i v e r going i n t o Sguamish harbour. Floats G and N were ca r r i e d along i n the main flow of the r i v e r . These data are too sparse to interpret the flow f i e l d i n the harbour from them alone. However, they are consistent with the f i e l d suggested by the s i l t patterns i n the water and with the subsequent measurements made i n the fourth week of the main experiment. Even though tracking by t r a n s i t proved to be marginally successful, i t did not f u l f i l l the basic c r i t e r i o n of 18 Figure 3 - Float tracks from the preliminary experiment. The l e t t e r in each f l o a t designation refers to f l o a t colour i . e . G-green, Y-yellow P-pink N (night tracked). Stawamus Chief (el. 610m) was the observation s i t e . 19 tracking up to 50 f l o a t s continuously f o r a few days. Although the r e s u l t s from th i s experiment were largely negative, they were useful i n designing the major surface layer experiment that i s described in the rest of t h i s chapter. 20 II.2 Main Experiment II,2.1 Introduction The major experimental e f f o r t took place in the spring and summer of 1973. The experience of the previous spring led to a complete redesign of the drogues to a form much more e a s i l y manageable from a small boat, much less affected by wind and more v i s i b l e . Since o p t i c a l tracking of the drogues had proven to be unreliable, they were tracked by a radar set mounted on the shore. Each drogue carried a radar r e f l e c t o r and was therefore v i s i b l e to the radar set through most obscuring atmospheric conditions. These drogues were also more o p t i c a l l y v i s i b l e than the previous design: depending on conditions they could be seen up to one mile away in either daylight or darkness, As many drogues as possible were deployed as simultaneously as possible i n the area of observation. A number of small vessels were used to deploy the drogues and to re t r i e v e those that had l e f t the area of observation. ,Data were recorded by photographing the Plan Position Indicator (PPI) screen of the radar set both with s t i l l and with movie cameras. The res u l t i n g s t i l l photographs were l a t e r d i g i t i z e d f o r further processing. Hadar tracking of drogues has been done before with some success, for example by Kenney (1972) , but the problems associated with attempting the experiment in a large, open 21 area with s w i f t c u r r e n t s l i k e Howe Sound, f o r such an extended l e n g t h of time, make t h i s experiment somewhat d i f f e r e n t from p r e v i o u s ones, A more complete d e s c r i p t i o n of t h e experiment f o l l o w s . II.2.2 The_Drogues The drogues t h a t were used i n t h i s experiment were designed and b u i l t at IOUBC s p e c i f i c a l l y to f i t the needs of t h i s p r o j e c t , The b a s i c design i s shown i n f i g u r e 4 . .. The drag element of the drogue was of the window b l i n d s t y l e as d e s c r i b e d i n Terhune (1968). His t e s t s of i t s performance showed t h a t t h i s type of drag element a l i g n s i t s e l f at r i g h t angles to the flow a f t e r t r a v e l l i n g two or t h r e e times i t s own l e n g t h and from then on maintains the same o r i e n t a t i o n ( w i t h i n about 10°) t o the flow. T h i s window b l i n d , a l s o r e f e r r e d t o as a s a i l , was 10ft wide by 6 f t deep (about 3m by 2m), c o n s t r u c t e d of Polyweave, a f l e x i b l e f a b r i c woven of p o l y e t h y l e n e f i b r e s laminated between t h i n sheets of p o l y e t h y l e n e . T h i s f a b r i c i s g u i t e tear r e s i s t a n t and durable. I t was s t a p l e d t o a f i r 2 X 2 (5cm by 5cm) on the top edge and had a 1in diameter s t e e l r e i n f o r c i n g rod sewn i n t o the bottom edge f o r b a l l a s t . The s a i l was attached t o the f l o a t pole by snap hooks that c l i p p e d i n t o nylon r i n g s i n the c e n t r e of the top and bottom b a r s . Short l e n g t h s of braided nylon cord t i e d onto the r e i n f o r c i n g rod were used as t i e s t o secure the s a i l i n t o a r o l l f o r s t o r a g e . 22 Soil Radar Reflector Flashing Light ~ 2 m Aluminum Top Pole Col lar Aluminum Bottom Pote Snap Hook and Ring n g f '2 m ^ I Reinforcing Rod 4 Figure 4 - Basic design of the drogues. 23 The v e r t i c a l support element, the f l o a t p o l e , was an aluminum pole 1,050in OD, 12ft long, s p l i t i n t o two p a r t s near the c e n t r e . A 1 f t long p i e c e of 1,350in OD aluminum tube was used as a c o l l a r to hold the two p i e c e s t o g e t h e r . A s w i v e l snap hook was b o l t e d to the bottom of the bottom pole t o connect with the bottom bar of the s a i l . The c o l l a r was pop r i v e t e d t o the t o p of the bottom pole. The top pole was h e l d i n the c o l l a r by a 0.125in X 2.5in c o t t e r p i n . Approximately 14in up the top pole from the h i g h e s t p o s i t i o n o f the c o l l a r was a machined aluminum c o l l a r placed to prevent the f l o a t from r i d i n g up the pole. At the top of the top p o l e , another c o l l a r o f 1,350in OD tube h e l d a 9 i n radar r e f l e c t o r . The r e f l e c t o r was mounted with one c o r n e r r e f l e c t o r p o i n t i n g v e r t i c a l l y . T h i s arrangement was suggested i n Wylie (1968) as being the way of mounting an o c t a h e d r a l c l u s t e r t h a t g i v e s the o p t imal response. There i s a l a r g e v a r i a t i o n i n the s t r e n g t h of radar echo as a f u n c t i o n of angle with the r e f l e c t o r mounted i n t h i s manner, as i s shown l a t e r i n f i g u r e 7, but the average response i s g r e a t e r than f o r any o t h e r o r i e n t a t i o n of the r e f l e c t o r . The f l o a t used was a 14in OD hollow v i n y l sphere with a h o l e through the middle, (brand name Viny, type 12B3). The bottom end of the t o p pole passed through t h i s h o l e before being pinned i n t o the c o l l a r . Thus the sphere was f i r m l y a t t a c h e d between the two s e c t i o n s of pole. A loop of braided nylon cord was placed around the f l o a t , h e l d i n p l a c e by the p o l e top and bottom, with a snap hook t i e d t o i t s c e n t r e . T h i s hook engaged the r i n g on the top of the s a i l . A 12ft 24 p i e c e of 1/4 i n c h diameter s i n g l e braided polypropylene rope with a l o o p i n each end was attached by one l o o p to the top snap hook. T h i s rope f l o a t e d on the water's s u r f a c e and pr o v i d e d a means t o recover the drogue without having t o b r i n g the v e s s e l too c l o s e . D e t a i l s o f the c o n s t r u c t i o n of the drogues are shown i n f i g u r e 5 . For ease of t r a n s p o r t a t i o n , the drogues were c a r r i e d i n f o u r s e c t i o n s ; the f l o a t , the top p o l e and r e f l e c t o r , the bottom pole and the r o l l e d s a i l . They were deployed by assembling the s e c t i o n s of p o l e , c l i p p i n g the bottom snaphook to the r i n g on the r e i n f o r c i n g rod of the s t i l l r o l l e d s a i l , then l o w e r i n g the drogue i n t o the water while u n r o l l i n g the s a i l and f i n a l l y c l i p p i n g the top snap hook i n t o the r i n g on the 2 X 2 j u s t before r e l e a s i n g the drogue i n t o the water. In t h i s way the l a r g e s u r f a c e area of t h e drogue was never exposed to the wind and hence was not too d i f f i c u l t t o handle. Recovery was the r e v e r s e procedure of i n s t a l l a t i o n . 11. 2.3 The_:-Base; S t a t i o n - Radar , And Ca roera s The base of o p e r a t i o n s f o r t h i s experiment c o n s i s t e d of the radar t r a n s c e i v e r and antenna, a s h e l t e r c o n t a i n i n g the r a d a r d i s p l a y , the cameras and a two-way r a d i o , and the necessary generators and l i v i n g q u a r t e r s . The radar set t h a t was used was a standard marine u n i t , a Decca RM916. The antenna was a v e r t i c a l l y p o l a r i z e d 6 f t l o n g , end-fed, s l o t t e d waveguide. I t was mounted together a . c o r n e r r e f l e c t o r Figure 5 - Details of droque construction. a. Attachment of the radar r e f l e c t o r . b. Top of the s a i l assembly. c. Float assembly. d. Bottom of the s a i l assembly. 26 with the t r a n s c e i v e r on an aluminum quadrupod with l e g s of a d j u s t a b l e l e n g t h t h a t kept the scanner 6 t o 15 f e e t above the ground. The d i s p l a y u n i t was a 9 i n PPI cathode-ray tube whose image was r e f r e s h e d every 2.14 seconds, i n s y n c r o n i z a t i o n with the r o t a t i o n of the scanner. The t r a n s m i t t e r sent out 850 p u l s e s per second at 10 GHz. The r e c e i v e r was a b l e t o d e t e c t the drogues r e l i a b l y to a range o f about 2.5 n a u t i c a l m i l e s and u s u a l l y out t o 3 miles. T h i s s h o r t range f o r c e d the experiment to be s p l i t i n t o f o u r s e c t i o n s , each one c o v e r i n g an area i n Howe Sound s i x miles l o n g . The f o u r s e c t i o n s are i d e n t i f i e d throughout the t h e s i s a s : week 1, based a t B r i t a n n i a Beach from May 8-11,1973; week 2, a t Woodfibre, May 15-18; week 3, at Furry Creek June 26-29 and week 4 north of Watts Pt. J u l y 3-6. These s e c t i o n s are shown i n f i g u r e 6 . T h e antenna had a h o r i z o n t a l beam width of 1.2° t o the h a l f power p o i n t s y i e l d i n g a minimum spot width on the PPI screen of 120m at t h r e e miles. The 0.75 microsecond p u l s e l e n g t h y i e l d e d a spot l e n g t h of 225m. The r e s u l t a n t a b s o l u t e accuracy of the drogue p o s i t i o n s w i l l be d i s c u s s e d i n the data a n a l y s i s s e c t i o n . Based on p r e l i m i n a r y t e s t s i t was expected t h a t each drogue would not n e c e s s a r i l y p a i n t a spot on the screen on each r o t a t i o n of the scanner. T h i s e x p e c t a t i o n was borne out, e s p e c i a l l y at long range. To reduce the chance of m i s s i n g a drogue when photographing the screen, approximately s i x sweeps of the radar scanner were i n c l u d e d i n each frame by l e a v i n g the camera s h u t t e r s open f o r 12 seconds. The l e n s a p e r t u r e s were s e t by t r i a l and e r r o r ; the 27 2 Figure 6 - The location of the four weeks of radar s i t e s , the current, meters and the amemometer in Squamish. The small c i r c l e s with numbers are the radar s i t e s , the larqe c i r c u l a r sections are 3 mile ranges about each one. 28 s t i l l camera u s u a l l y t o f11 and the movie camera u s u a l l y t o f 16. The s t i l l photographs were taken with a Hass e l b l a d 500C 70mm camera with a 100mm l e n s and a closeup r i n q . Kodak Plus-X Pan f i l m was used i n 12 exposure r o l l s . P i c t u r e s were taken manually by h o l d i n g the s h u t t e r open f o r about s i x sweeps approximately every 20 minutes whenever the radar screen was as unobscured as p o s s i b l e by r a i n or other i n t e r f e r e n c e . When the movie camera f a i l e d l a t e i n the experiment, s t i l l p i c t u r e s were taken every f i v e minutes. Movies were taken with a Bolex H16 Re f l e x 16 mm camera using Kodak T r i - X R e v e r s a l f i l m . One 12 second exposure was made every 30 seconds i n the f i r s t two weeks and every 15 seconds i n the l a s t two weeks of the experiment. T h i s seguence was c o n t r o l l e d by a mechanical t i m e r and a s o l e n o i d d r i v i n g the remote c a b l e r e l e a s e of the camera. There was a watch taped to the radar s c r e e n to r e c o r d on each negative the time of the photograph . Exposure q u a l i t y was c o n t r o l l e d by shooting at l e a s t one t e s t r o l l of f i l m a day on the s t i l l camera using v a r i o u s aperture s e t t i n g s , developing i t a t the radar s i t e and then s e t t i n g the a p e r t u r e t o the s e t t i n g t h a t produced the best c o n t r a s t on the t e s t r o l l . The movie camera aperture was determined from t h i s t e s t r o l l a l s o . I t was s e t t o the s t i l l camera value plus some o f f s e t t h a t was determined by sh o o t i n g a movie t e s t s t r i p once or twice a week. 29 I I . 2. 4 y§s§g;lgj^£p^;a-aniea-t;4Q^s And L o g i s t i c s Due to the s m a l l experimental area and the sometimes l a r g e water v e l o c i t i e s , i t was necessary t o keep at l e a s t one v e s s e l at work at a l l times. In a l l , four d i f f e r e n t v e s s e l s were used i n the experiment. The main v e s s e l used was the " A c t i v e Lass", a 42 f o o t long converted f i s h i n g boat p r o v i d e d t o us with her s k i p p e r , Mr. Sandy Matheson, f o r a l l f o u r weeks of the experiment by the P a c i f i c Environment I n s t i t u t e , West Vancouver, B.C. They a l s o provided us with a 2 3 f t s t e r n d r i v e S a n g s t e r c r a f t f o r the e n t i r e experiment. IOUBC provided a 21ft outboard-powered s k i f f . The P a c i f i c B i o l o g i c a l S t a t i o n of the F i s h e r i e s Research Board, Nanaimo, B.C. provided the " C a l i g u s " with her skipper> Mr. Ron Page, f o r the f i n a l week of the experiment. Dr. John S i b e r t and Dr. Robert Parker o f PBS took p a r t d u r i n g t h i s week on C a l i g u s . An e x t r a s k i p p e r was h i r e d f o r the A c t i v e Lass to enable her to be run f o r two s h i f t s a day. The v e s s e l s operated i n staggered 8 hour s h i f t s , the A c t i v e Lass on both n i g h t s h i f t s s i n c e she was eguipped with r a d a r to t r a c k drogues and av o i d f l o a t i n g l o g s , and the S a n g s t e r c r a f t , S k i f f and C a l i g u s at v a r i o u s times dur i n g d a y l i g h t . With the e x c e p t i o n of the t h r e e s k i p p e r s and the PBS s c i e n t i s t s noted, the v e s s e l s were manned e n t i r e l y with IOUBC p e r s o n n e l . In the f o u r weeks of the experiment, v i r t u a l l y a l l the P h y s i c a l Oceanography graduate students and t e c h n i c i a n s saw s e r v i c e e i t h e r on the v e s s e l s or a t the r a d a r s i t e . 30 Each s e c t i o n of the experiment was scheduled to take p l a c e i n a f i v e day week. The f i r s t day was spent moving eguipment to the radar s i t e , assembling the radar s t a t i o n and l o a d i n g the v e s s e l s with drogues. The a c t u a l o p e r a t i o n began i n the morning of the second day. The radar operator i n s t r u c t e d each v e s s e l to p l a c e drogues spaced about 1/4 mile a p a r t a c r o s s the i n l e t . These c r o s s - i n l e t l i n e s were spaced about 1/2 mile a p a r t along the i n l e t . About 20 drogues were i n i t i a l l y deployed i n t h i s manner. As the drogues moved with the flow, the v e s s e l s were d i s p a t c h e d by the radar operator to r e t r i e v e the drogues whose images were about to l e a v e the r a d a r screen and to i n s t a l l more drogues i n gaps i n the a r r a y as seen on the radar screen. The o p e r a t o r attempted to keep as many drogues i n the water as p o s s i b l e . T h i s process continued u n t i l the morning of the l a s t day when a f i n a l cleanup of drogues commenced. Thus a t o t a l of 72 hours of continuous measurements per week were p o s s i b l e . Of c o u r s e ; i n p r a c t i c e the o p e r a t i o n d i d not go n e a r l y t h i s smoothly, as i s mentioned b r i e f l y i n chapter IV, but t h i s d e s c r i p t i o n i s the b a s i c plan by which each week of the experiment was run. 31 II . 3 A n a l y s i s Of The Drogue Data The computer a n a l y s i s of the s t i l l photographs of the radar screen was a complex procedure t h a t can be broken down i n t o two major p a r t s ; the c a l c u l a t i o n of the drogue t r a c k s and the subseguent Lagrahgian and E u l e r i a n a n a l y s i s of the data. In the f o l l o w i n g paragraphs, the problems o f a n a l y s i s i n each p a r t w i l l be d i s c u s s e d as w e l l as the computer programmes used to s o l v e them. The H a s s e l b l a d photographs formed a r e c o r d of 829 p i c t u r e s each of which contained the radar images of boats, barges, f l o a t i n g l o g s and t r e e s , g u l l s , a eroplanes, waves and r a i n as w e l l as drogues. A sample p i c t u r e from the radar screen i s shewn i n f i g u r e 7 . I t was necessary to d i f f e r e n t i a t e between the images wanted and those not wanted. There was, of course, no way to t e l l one drogue from another i n each p i c t u r e except by p a t t e r n s i m i l a r i t y from one p i c t u r e to the next. Repeated viewing o f the movies of the radar screen, although they were o f t e n underexposed and s l i g h t l y out of f o c u s , gave a good sense o f the g e n e r a l p a t t e r n of the c i r c u l a t i o n and was of great help i n f o l l o w i n g the drogues from one p i c t u r e to the next. The i n s t a l l e d p o s i t i o n o f each drogue as recorded i n the log sheets u s u a l l y i d e n t i f i e d i t i n the f i r s t p i c t u r e i n which i t appeared. T h i s was o f t e n s u f f i c i e n t i n f o r m a t i o n t o allow a drogue to be f o l l o w e d along i t s complete t r a c k once i t s p o s i t i o n s were d i g i t i z e d and i n a form compatible to the PDP-12 computer at IOUBC. 3 2 Objects in circles are Drogues Current Meter Buoys a Edge of Radar Shadow 360 180 F i g u r e 7 - a. T y p i c a l photograph of the radar screen from the week 1 data set a t 1246 May 10,1973. b. Shape of a drogue echo on the radar PPI screen i n d i c a t i n g expected l o c a t i o n of the drogue i n the echo. c. R e l a t i v e response of an o c t a h e d r a l c l u s t e r radar r e f l e c t o r as a f u n c t i o n of angle i n the h o r i z o n t a l plane (from Wylie (1968)), 33 The p i c t u r e s were d i g i t i z e d by p r o j e c t i n g each H a s s e l b l a d n e gative onto a 25in square sheet of graph paper and r e c o r d i n g , on a keypunch coding form, the p o s i t i o n of each o b j e c t t h a t might have been a drogue. The p o s i t i o n s of the radar s i t e and one other f i x e d p o i n t on the shore were a l s o d i g i t i z e d . The t r u e p o s i t i o n s o f these l a s t two p o i n t s were used i n subsequent programmes to s c a l e and o r i e n t each p i c t u r e . The accuracy o f the graph paper was checked by p l o t t i n g a 25.00in square on i t using a Calcomp i n c r e m e n t a l p l o t t e r . The p l o t t e r was reputed to be ac c u r a t e t o 0.01in. The eye c o u l d d e t e c t no d i f f e r e n c e between the 25in square r u l e d on the graph paper and t h a t p l o t t e d on i t by the Calcomp. D i s t o r t i o n i n the o p t i c a l system was checked by photographing the d i g i t i z a t i o n g r i d with the Hasselblad and p r o j e c t i n g the r e s u l t i n g n e g ative back onto the g r i d . No d i f f e r e n c e s between the g r i d s were found, hence t h e r e was no d e t e c t a b l e o p t i c a l d i s t o r t i o n i n the system. The p r o j e c t e d image of the radar screen approximately f i l l e d the 25in sguare making the s c a l e of d i g i t i z a t i o n 1.Oin = 0.24mi. Thus a t y p i c a l drogue echo of dimension 120m by 225m as d i s c u s s e d p r e v i o u s l y a c t u a l l y covered an area o f 0.27in X 0.51in. The assumed p o s i t i o n of the drogue i n t h i s echo was at the c e n t r e of a c i r c l e o f the same diameter as the spot width c e n t r e d at the radar s e t end of the echo. T h i s p o s i t i o n i s shown i n f i g u r e 7b. The expected accuracy of such a det e r m i n a t i o n i s about ±30m. T h i s was the po i n t t h a t was d i g i t i z e d as the drogue. Accuracy of the d i g i t i z a t i o n 3 4 o p e r a t i o n was about ±0.02in or 1/5 of the s m a l l e s t d i v i s i o n on the graph paper. T h i s corresponds to ±9m at the s c a l e mentioned above. Thus the major source o f e r r o r i n l o c a t i n g a drogue i s i n the l o c a t i o n o f the drogue w i t h i n i t s echo, not i n the a c t u a l d i g i t i z a t i o n of the chosen spot. Programme PRE12 on the IBM 370/168 took the d i g i t i z e d data s e t from each week and produced a f i l e of o b j e c t p o s i t i o n s arranged p i c t u r e by p i c t u r e on a magnetic tape i n a form s u i t a b l e f o r i n p u t to the PDP-12 a t I0DBC . T h i s output tape contained a d i g i t i z e d o u t l i n e of the shore i n the a p p r o p r i a t e area o f Howe Sound , followed by a number of re c o r d s each d e s c r i b i n g one d i g i t i z e d photograph. The shore was s c a l e d so t h a t the s i x mile radar image diameter j u s t f i l l e d the 512 by 512 u n i t CRT screen o f the PDP-12 . T h i s programme accepted as in p u t f o r each week the t r u e d i s t a n c e and d i r e c t i o n of the ve c t o r from the radar s i t e t o the c a l i b r a t i o n p o i n t . For each p i c t u r e a v e c t o r was c a l c u l a t e d from the radar s i t e to the c a l i b r a t i o n p o i n t on th a t p i c t u r e . The d i f f e r e n c e between these two v e c t o r s was used to determine the r o t a t i o n , t r a n s l a t i o n and s c a l i n g necessary t o c onvert the d i g i t i z e d image p o s i t i o n s to t r u e p o s i t i o n s . The t o t a l e r r o r i n each o b j e c t p o s i t i o n was t h e r e f o r e the sum of the e r r o r s i n determining the p o s i t i o n s of thr e e d i f f e r e n t p o i n t s , the radar s e t , the c a l i b r a t i o n p o i n t and the o b j e c t p o i n t . T h i s e r r o r amounts to a t most 3X30m=90m. These true p o s i t i o n s i n n a u t i c a l miles were then s c a l e d a g a i n by a f a c t o r o f 512/6 to place them i n screen c o o r d i n a t e s . A r e c o r d was w r i t t e n on magnetic tape 35 containing the r o l l and negative number of the picture, the time and date, the positions of the radar s i t e and of the c a l i b r a t i o n point (for transform v e r i f i c a t i o n purposes), the number of objects d i g i t i z e d and that number of four element sets each containing the X and Y coordinates of the object and two i d e n t i f i c a t i o n words (now blank because the objects were not yet i d e n t i f i e d on the computer). This tape, c a l l e d IS, was transported to the PDP-12 where i t was copied onto a data disk. This data disk was the input/output f i l e f o r programme MAPS which allowed a l l of the d i g i t i z e d objects to be i d e n t i f i e d . I t continuously displayed the shoreline on the CRT screen and also displayed, one at a time, each d i g i t i z e d picture. Each d i g i t i z e d object had two i d e n t i f i c a t i o n words associated with i t . The f i r s t was used to i d e n t i f y the general type of the object as either a drogue that could be p o s i t i v e l y i d e n t i f i e d , a drogue that could be i d e n t i f i e d only as part of a discontinuous track, or something that was not a drogue. This word also contained the drogue track status: i f t h i s was the f i r s t point on the track, the l a s t point or some intermediate point. The second i d e n t i f i c a t i o n word contained the drogue number. In the case of a p o s i t i v e l y i d e n t i f i e d drogue, i t was the drogue number recorded in the log book, In the case of a tentative i d e n t i f i c a t i o n ; i t was a number chosen to be unique to that track during the time i t could be followed. These words were accessed by the value of an externally controlled potentiometer on the PDP-12 that was used to construct the 3 6 a d d r e s s i n t h e c o m p u t e r memory o f t h e s e w o r d s . C h a n g i n g t h e p o t e n t i o m e t e r s e t t i n g a l l o w e d a l l i d e n t i f i c a t i o n l o c a t i o n s t o be e x a m i n e d , one a t a t i m e . When a d i g i t i z e d o b j e c t l o c a t i o n was s e l e c t e d by t h e p o t e n t i o m e t e r f o r e x a m i n a t i o n , t h a t o b j e c t was i n t e n s i f i e d on t h e s c r e e n and t h e c o n t e n t s o f i t s i d e n t i f i c a t i o n w o r d s were d i s p l a y e d , B o t h o f t h e s e i d e n t i f i c a t i o n w o r d s were s e t by commands f r o m t h e c o m p u t e r c o n s o l e k e y b o a r d when t h e p o i n t e r i n d i c a t e d t h a t o b j e c t . I n s u c h a f a s h i o n , i n f o r m a t i o n was t r a n s c r i b e d f r o m t h e l o g s h e e t s and t h e t r a c k s a l r e a d y i d e n t i f i e d o n t h e p r i n t s t o t h e c o m p u t e r . When i t seemed as i f a l l p o s s i b l e t r a c k s were i d e n t i f i e d , a m a g n e t i c t a p e c a l l e d 00T was w r i t t e n f r o m t h e d i s k f i l e and t a k e n b a c k t o t h e IBM 3 7 0 / 1 6 8 , t h e m a i n c o m p u t e r a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . The n e x t programme i n s e g u e n c e , c a l l e d POST , t o o k t h e i d e n t i f i e d p h o t o g r a p h s , d i s c a r d e d t h e n o n - d r o g u e s , s o r t e d t h e d r o g u e p o s i t i o n s i n t o a s e g u e n c e o f i n d i v i d u a l t r a c k s a n d s c a l e d t h e p o s i t i o n s b a c k t o m i l e s f rom s c r e e n u n i t s . T h i s o u t p u t f i l e o f d r o g u e t r a c k s was t h e i n p u t t o a programme c a l l e d SPLN1 t h a t t o o k e a c h t r a c k a n d f i t t e d i t by means o f a c u b i c s p l i n e i n t e r p o l a t i o n and s m o o t h i n g r o u t i n e . T h i s r o u t i n e , s u p p l i e d by t h e UBC C o m p u t i n g c e n t r e was m o d e l l e d a f t e r t h e one d e s c r i b e d i n E e i n s c h ( 1 9 6 7 ) . I n t h i s r o u t i n e t h e c a l c u l u s o f v a r i a t i o n s i s used t o c o n s t r u c t a f u n c t i o n g (t) t h a t m i n i m i z e s \ g " ( t ) 2 d t s u b j e c t t o t h e c o n d i t i o n t h a t ^° S ( ( g f t j - f ( t . ) ) /S f (t. ) ) • * < S (2.1) 37 where S f (t^ ) i s the expected e r r o r of the i ' t h i n p u t p o i n t ( t . j f t t ^ ) ) and S i s a p o s i t i v e d e f i n i t e q u a n t i t y chosen from the range n- J2n < S < n+ \ 2n\ The s o l u t i o n g Ct) i s then the smoothest f u n c t i o n t h a t s a t i s f i e s the t o t a l l e a s t square e r r o r c r i t e r i o n . The value chosen f o r S c o n t r o l s the t o t a l amount of d e v i a t i o n allowed from the input v a l u e s . The value of S f < t t ) c o n t r o l s the e f f e c t of a s i n g l e d e v i a t i o n . Since i n t h i s experiment a l l the 5 f ( t • ) ' s were chosen t o be the same s i z e , they have a s i m i l a r e f f e c t on the smoothness of the f i t as does S and hence the two c r i t e r i a i n t e r a c t s t r o n g l y , i . e. a s m a l l 6 f ( t - ) r e q u i r e s a l a r g e S f o r smoothness of the f i t and v i c e versa. The s o l u t i o n i s of the form g(t)=a.+b t (t-t.) +c . ( t - t L ) 2 + d^ ( t - t t )3 (2 .2) t < t < t-C o n d i t i o n s on t h i s s o l u t i o n are that g, g', and g" are continuous at t=t. but that g'" need not be. Using the values f o r a., b., c ; and d^ c a l c u l a t e d i n t h i s manner, values f o r g<t),g' (t) and g" (t) may be c a l c u l a t e d f o r t.< t < t. . T h i s r o u t i n e was used twice on each drogue t r a c k , once to f i t the x c o - o r d i n a t e of drogue p o s i t i o n as a f u n c t i o n of time and once to f i t the y c o - o r d i n a t e . Thus, i n the x co-o r d i n a t e f i t , x ( d i g i t i z e d p o s i t i o n ) =f (t) , x ( i n t e r -polated) =g (t) , u=g' (t) and a x=g"(t) . S i m i l a r l y , when y ( d i g i t i z e d ) =f (t) , y ( i n t e r p o l a t e d ) =g (t) , v=g* (t) and a =g w ( t ) . The i n t e r p o l a t e d r e s u l t s were recombined to 38 provide the smoothed drogue t r a c k s . The e r r o r s Sx and &y (equal to 8 f ( t L ) i n t h e i r r e s p e c t i v e f i t s ) necessary f o r the r o u t i n e s were chosen by t r i a l and e r r o r to be as s m a l l as p o s s i b l e and s t i l l produce smoothly v a r y i n g a c c e l e r a t i o n s . The r e s u l t i n g value f o r these e r r o r s o f ±0.05mi (±90m) was somewhat l a r g e r than the expected u n c e r t a i n t y of the data due to the r e s o l u t i o n * l i m i t s of the radar set and to d i g i t i z a t i o n e r r o r s . The value of S was chosen to be q u i t e s m a l l ( n- \ 2n') and so the e r r o r had to be l a r g e r than expected to allow a smooth f i t . The e r r o r amounted to about 1% of the t o t a l radar range. The s p l i n e f i t produced the p o s i t i o n s , v e l o c i t i e s and a c c e l e r a t i o n s f o r each drogue f o r each minute along i t s t r a c k . These data were w r i t t e n i n d i f f e r e n t forms on two d i f f e r e n t magnetic tapes.,The f i r s t , c a l l e d the.DATA1 tape, co n t a i n e d r e c o r d s o f drogue p o s i t i o n i n miles from the radar s i t e , v e l o c i t i e s i n m/s, a c c e l e r a t i o n s i n m/s 2 and time as they were generated i n programme SPLN1 . The second tape, the BRUSHPLOT tape, contained the same data but with the v a l u e s of p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n i n both co-o r d i n a t e s f o r each t r a c k s c a l e d t o e x a c t l y f i t the range of the d i g i t a l t o analogue c o n v e r t e r s on the PDP-12. The OBC Computing Centre programme *S0ET was used t o s o r t the data s e t on DATA1 i n t o temporal order and w r i t e i t onto a tape c a l l e d DATA2 . T h e programme MOVIE took t h i s s o r t e d data set and s e c t i o n e d i t i n t o one minute i n t e r v a l s . A l l the p o s i t i o n s i n each s e c t i o n were s c a l e d t o PDP-12 screen c o o r d i n a t e s . Another magnetic tape, c a l l e d MOVIET , was then 39 w r i t t e n f r o m t h e s e r e c o r d s i n a f o r m a t s i m i l a r t o t h a t u s e d f o r t h e o r i g i n a l i n p u t t o 8 A P 5 . T h u s t h i s t a p e c o n t a i n e d one " p i c t u r e " p e r m i n u t e t h r o u g h o u t t h e w h o l e e x p e r i m e n t . The two m a g n e t i c t a p e s , MOVIET and BEUSHPLOT , were b o t h b r o u g h t b a c k t o t h e PDP-12 . The s c a l e d d r o g u e t r a c k s w ere p l a y e d w i t h programme D-A o n t o a s i x c h a n n e l B r u s h c h a r t r e c o r d e r . E a c h o f t h e s i x c h a n n e l s on t h e r e c o r d e r d i s p l a y e d one o f x o r y p o s i t i o n , v e l o c i t y o r a c c e l e r a t i o n . H e r e a n y a b n o r m a l l y l a r g e a c c e l e r a t i o n s o r v e l o c i t i e s o r r a p i d c h a n g e s i n e i t h e r c o u l d be s e e n e a s i l y . The SOVIET t a p e was p l a y e d b a c k on t h e s c r e e n by means o f a s p e c i a l d i s p l a y mode o f programme MAP5 t h a t d i s p l a y e d s e v e r a l p i c t u r e s s i m u l t a n e o u s l y on t h e CRT s c r e e n . A f t e r h o l d i n g t h e f r a m e s t e a d y f o r a s h o r t t i m e , t h e o l d e s t p i c t u r e was d r o p p e d f r o m t h e s c r e e n and r e p l a c e d w i t h t h e p i c t u r e one m i n u t e l a t e r t h a n t h e l a t e s t one a l r e a d y on t h e s c r e e n . T h i s p r o c e d u r e was c a r r i e d o u t many t i m e s i n r a p i d s u c c e s s i o n u n t i l t h e i n p u t t a p e was c o m p l e t e l y r e a d . T h i s c r e a t e d t h e e f f e c t o f a mov i n g "worm" on t h e s c r e e n whose l e n g t h and o r i e n t a t i o n i n d i c a t e d t h e s p e e d a n d d i r e c t i o n o f d r o g u e m o t i o n s . Any l a r g e a n o m a l i e s i n t h e f l o w f i e l d c o u l d be d e t e c t e d by w a t c h i n g t h i s m o v i e . / Any e r r o r s d e t e c t e d by e i t h e r o f t h e s e - t e c h n i q u e s were t h e n c o r r e c t e d by l o o k i n g f o r m i s t a k e s i n d r o g u e i d e n t i f i c a t i o n i n t h e d a t a s e t m a n i p u l a t e d by MAP5 . When t h e s e e r r o r s were c o r r e c t e d , more a c c e l e r a t i o n p l o t s and a n o t h e r m o v i e were g e n e r a t e d and a g a i n c h e c k e d f o r e r r o r s . A few t i m e s t h r o u g h t h e l o o p o f e r r o r c h e c k i n g p r o d u c e d 40 f o r each week a c o n s i s t e n t and smoothly v a r y i n g flow f i e l d as determined by the drogue t r a c k s . I t i s of course p o s s i b l e t h a t t h i s s o r t of s u b j e c t i v e e r r o r f i n d i n g technique might smooth over seme t r u e d e t a i l s of the flow f i e l d . Small d e t a i l s such as these c o u l d only have been determined a c c u r a t e l y i f p i c t u r e s had been taken more f r e q u e n t l y . A flow c h a r t of t h i s data processing and v e r i f i c a t i o n procedure i s shown i n f i g u r e 8 . 41 Figure 8 - Flow chart of the data analysis and v e r i f i c a t i o n procedures. Boxes represent computer programmes or manual procedures. C i r c l e s represent magnetic tapes used to tr a n s f e r data between the d i f f e r e n t environments. 42 I I . 4 Data,Averaging - P r o b l e m - Of-La^ranglan Heasurenients The drogue t r a c k s t h a t r e s u l t e d from the p r e v i o u s l y mentioned s e r i e s o f computer programmes provide a data base f a r too l a r g e t o look a t on an i n d i v i d u a l t r a c k by t r a c k b a s i s . I t was necessary to average the data i n some meaningful way to reduce the 250,000 i n t e r p o l a t e d data p o i n t s t o a c o n s i s t e n t p i c t u r e of the flow f i e l d of the Sound. A problem a r i s e s i n determining what s o r t of averaging procedure should be used to best deduce the mean E u l e r i a n v e l o c i t y f i e l d from a Lagrangian data s e t . A n a l y t i c a veraging techniques that c o u l d be used a r e : temporal a v e r a g i n g , as d e f i n e d by: TP "u~L = (1/T) ^ u^dt (2.3) o and s p a t i a l averaging as d e f i n e d by: [ u u (1/X) ^ u d x (2.4) o where u L i s the observed Lagrangian v e l o c i t y . Under most circumstances, n e i t h e r o f these averages w i l l correspond to the t r u e E u l e r i a n mean f i e l d as may be seen by c o n s i d e r i n g the two f o l l o w i n g examples. H3 In the f i r s t case, the v e l o c i t y f i e l d i s homogeneous i n space but v a r y i n g i n time. Because o f the s p a t i a l homogeneity, the drogue v e l o c i t y shows the same time v a r i a t i o n as the E u l e r i a n v e l o c i t y and hence u t= U + u' (t) (2.5) where 0 i s the E u l e r i a n mean v e l o c i t y of the f i e l d and u« (t) i s the time v a r y i n g p a r t . For example, U l = 2 + s i n t (2.6) U L = (1/2-rr) ^(2 + s i n t ) d t = 2 X but C U L 1 = ( V X ) ^ (2+ s i n t) dx (2.7) o r S i n c e u=dx/dt , then dx = u u d t or x = ^ uclt + c so X = U T T a t o T=2tr . Thus, [ u L ]= (1/4 IT ) ^ ( 2 • s i n t)X dt (2.8) o = 2.25 In the second case, c o n s i d e r i n g an E u l e r i a n v e l o c i t y f i e l d dependent only on p o s i t i o n , the drogue v e l o c i t y w i l l 44 have the same s p a t i a l v a r i a t i o n as the E u l e r i a n v e l o c i t y and u L= U + u« (x) (2.9) For example U L = 2+sin x (2. 10) 7.TT £ u u ]=(1/2'n-) ^ (2 + s i n x)dx = 2 Si n c e u=dx/dt, then t= I dx t= \ (dx/(2 + s i n x)) (2. 11) r =2 A tan-*(tan(x/2) +l\~ tan~» 1 + n t r I S I V I T ' f ? J where n i s a number such t h a t (n-1)Tr < x < (n + 1)rr thus when x=2Tr ,t= 2fr / J T ' a n d 1 ^ udx/u So i n the f i r s t case V* 0 ' u C2..12) 45 and i n the second < 0 , [ U l ] = U (2. 13) Of course a g e o p h y s i c a l flow w i l l be n e i t h e r t o t a l l y time dependent nor space dependent, but, i n g e n e r a l , u L w i l l u s u a l l y underestimate the t r u e E u l e r i a n mean v e l o c i t y 0, and [ u ^ ] w i l l o verestimate i t . Data c o l l e c t e d i n the s t y l e of the experiment performed i n Howe Sound are recorded at const a n t i n t e r v a l s i n time. Therefore any averaging t h a t i s done w i l l be a form of time average and the r e s u l t s w i l l approximate u*L» : Thus mean v e l o c i t i e s c a l c u l a t e d from the data s e t without regard f o r i t s Lagrangian c h a r a c t e r w i l l probably underestimate the tr u e mean v e l o c i t y . A.J.Dyer (1973) attempted t o f i n d a g e n e r a l a n a l y t i c form of t r a n s f o r m a t i o n of Lagrangian averages i n t o E u l e r i a n averages, but i n examining a n a l y t i c d e s c r i p t i o n s of v a r i o u s Lagrangian f i e l d s , was o n l y a b l e t o f i n d a n a l y t i c t r a n s f o r m a t i o n s i n a few cases. He concluded t h a t i f a ge n e r a l a n a l y t i c t r a n s f o r m a t i o n e x i s t s , i t i s f a r from t r i v i a l . Webster and C u r t i n (1974), i n the process o f a n a l y s i n g a l a r g e Lagrangian data s et s i m i l a r i n c h a r a c t e r t o the Howe Sound data d e s c r i b e a form of approximate transform t h a t tends to minimize the d i f f e r e n c e between Lagrangian space and time means and hence produce a mean v e l o c i t y c l o s e r t o the E u l e r i a n mean. They d i v i d e d t h e i r e xperimental area i n t o a number of s m a l l "boxes" and averaged the data s e p a r a t e l y i n each box. The f i n a l average o f the data was then 46 c a l c u l a t e d as the average of the box averages without regard f o r the number of o b s e r v a t i o n s i n each box. T h i s process has some of t h e c h a r a c t e r of a time average and some of a space average and may be t h e r e f o r e be expected to y i e l d a value t h a t o v e restimates u L and underestimates [ u L ] . Since i t i s expected t h a t U L < 0 < £ U L ] (2. 14) the box average u B should be a reasonable estimate of U. The problem remains of choosing the " c o r r e c t " box s i z e t o o b t a i n a b e s t e s t i m a t e of U. The maximum s i z e the box can be i s the t o t a l experimental area. T h i s would y i e l d u ^ i f . As the box s i z e i s made s m a l l e r and the number of boxes i n c r e a s e d , u^ should i n c r e a s e up to the p o i n t where each box c o n t a i n s o n l y drogues of the same approximate ; v e l o c i t y . At t h i s p o i n t , f u r t h e r s u b d i v i s i o n should not a f f e c t the value o f u*R g r e a t l y . I f t h e box s i z e i s made too s m a l l however, t h e r e w i l l be ,on average, very few drogues i n each box, so t h a t s t a t i s t i c a l l y , each average w i l l not be very r e l i a b l e . Thus the o c c a s i o n a l anomalous value c o u l d a f f e c t the mean of the box averages more g r e a t l y . T h e r e f o r e the optimum box s i z e i s governed by the s c a l e of v a r i a b i l i t y i n the flow and the number of o b s e r v a t i o n s a v a i l a b l e . In order t o keep a l l the measurements i n each box r e l a t i v e l y the same s i z e , the box s i z e must be s m a l l enough so t h e r e w i l l be reasonably s m a l l v e l o c i t y d i f f e r e n c e s due t o g r a d i e n t s i n the box. The measurements t h a t w i l l be d i s c u s s e d i n l a t e r s e c t i o n s show the downstream component of 4 7 ve l o c i t y to change at a rate of between 11 and 18 cm/sec/km across channel and about 2.4 cm/sec/km down-channel. The approximate rate of change of velocity with time i s 3 cm/sec/hr. The maximum r.m.s, v e l o c i t i e s i n this experiment are about 30cm/s, so i f a change of 10% of t h i s or 3cm/s i s allowed across each dimension of each box, then a consistent s i z e for each box i s then 0.17 to 0.25 km across by 1.2 km down channel by 1 hour long. In practice what was used for a l l guantitative results was 1/10 channel width (this varied between 0.2 and 0.3 km per box depending on week), by 1.8 km along channel by 1 hour (since the wind information was available only i n one hour averages). This size i s close to a consistent box as just defined. For some of the more q u a l i t a t i v e r e s u l t s to follow, a larger box size i s used, up to 0.9 km by 0.9 km by 3 hours. In these cases, the v e l o c i t i e s shown may be expected to be smaller than the true Eulerian v e l o c i t i e s i n the area, but s t i l l may be considered to be a useful indicator of the r e l a t i v e speed and dir e c t i o n of the drogues i n the area at that time. 48 CHAPTER I I I MEASUREMENTS OF WIND, TIDE, RIVER FLOW AND SURFACE LAYER STRUCTURE To form any c o n c l u s i o n s from the r e s u l t s of t h i s experiment, knowledge of the b a s i c f o r c i n g f u n c t i o n s was as e s s e n t i a l as t h e knowledge of the flow f i e l d i t s e l f . In t h i s c h a pter the techniques of measurement o f the wind, the t i d a l h e i g h t and the r i v e r d i s c h a r g e are d i s c u s s e d . The r e s u l t s of these measurements i n the f o u r weeks of the experiment are a l s o presented. Another e s s e n t i a l set of measurements was of th e d e n s i t y s t r u c t u r e of the near s u r f a c e waters i n the i n l e t . These measurements and r e s u l t s are a l s o d i s c u s s e d i n t h i s chapter, I I I . 1 • Wind -/Measure-meats -Measurements of wind speed and d i r e c t i o n were made a t two l o c a t i o n s each week o f the experiment, A Lambrecht r e c o r d i n g anemometer was l o c a t e d at the radar s i t e each week and recorded the winds t h e r e f o r the d u r a t i o n of the experiment. I t had the disadvantage of being on shore and t h e r e f o r e o f being more or l e s s s h e l t e r e d from the winds i n the c e n t r e of the channel. The second source of wind measurements was the anemometer maintained by the Atmospheric Environment S e r v i c e at FMC Chemicals, l o c a t e d 4 9 mid-channel at the head of the i n l e t i n Squamish. . The disadvantage of t h i s l o c a t i o n was i t s d i s t a n c e from some of the radar s i t e s . An anemometer was a l s o mounted on the c u r r e n t meter buoy l o c a t e d i n the c e n t r e of the week 3 working area and would have been most u s e f u l i f i t had worked., The data from Squamish were r e p o r t e d by AES i n h o u r l y t o t a l wind run i n s t a t u t e miles and average d i r e c t i o n i n compass o c t a n t . For purposes of comparison with t h i s data s e t , the data from the Lambrecht anemometer at the radar s i t e were converted to t h i s format. A comparison of these data s e t s i s shown i n t a b l e I I . The shores of the northern b a s i n of Howe Sound are g u i t e steep, e f f e c t i v e l y c o n s t r a i n i n g the wind to blow only along the a x i s o f the channel. T h i s c o n s t r a i n i n g i m p l i e s t h a t the long-channel component of the wind i s r e l a t i v e l y uniform along the channel f o r p e r i o d s of f l u c t u a t i o n of g r e a t e r than one hour. The anemometer s i t e i n Squamish i s l o c a t e d approximately mid-channel and t h e r e f o r e should be a good i n d i c a t o r of the of the wind v e l o c i t y throughout the channel. The r a d a r s i t e anemometer l o c a t i o n s , being on the shore c l o s e to the s i d e w a l l s of the f j o r d , are more s h e l t e r e d . T h i s s h e l t e r i n g e f f e c t i s s u b s t a n t i a t e d by the l a s t row i n t a b l e I I which shows the percentage of the Squamish wind run t h a t i s seen at the radar s i t e . Even i n the best l o c a t i o n (week 1) the radar s i t e anemometer saw o n l y 15% of the wind at Sguamish .Weeks 2 and 4 i n d i c a t e d o n l y a very s m a l l response to the wind at the radar s i t e , 50 T a b l e I I - The t o t a l number of miles of wind from each compass o c t a n t t h a t passed the anemometers a t Sguamish (SQ) and a t the radar s i t e (ES) f o r each of the f o u r weeks. The t o t a l s are the t o t a l wind run f o r each week at each anemometer. The precentage i s the f r a c t i o n of the wind run a t Sguamish t h a t was sensed at the radar s i t e . r t o t a l r — week 1 SQ RS 328 j 247 75 week 2 J SQ N I 46 | 24 48 f 6 21 ! 78 NE I 7 j 5 ! 3 1 0 | •'0- I 1 E I 0 i 0 ! 0 | 1 ! 0 i 2 SE I 3 | 31 0 | 30 I 0- j 65 S i i 7 t i 13 I 155 f 8' ! 107 | 301 SW I 95 • | 167 ! 214 } • 1 i 624 | 0 w J 0 I 1 i 0 | 59 | 0 I 0 NW J 6 | • 6 i 7 | 7 ! 10 I 0 BS 427 | 112 26 week 3 SQ~1 BS ;_4 week 4 ] i SQ } 1 ES J j 0 I 0 1 0 | 0 ! 0 1 0 J 0 | 1 1 134 | 6 f 589 | 227 | 0 | 2 ! 0 | 0 j —4-762 1 447 | 723 | 235 — — i .—_j ,„ , i, . 59 I 33 showing t h a t they were p a r t i c u l a r l y w ell s h e l t e r e d . Thus i t seems as i f the wind as measured at Sguamish may be a b e t t e r i n d i c a t o r of the wind s t r e n g t h i n mid-channel than t h a t measured much c l o s e r to the area of experiment but on the shore. Since the winds are predominantly of a land-sea breeze nature, the winds at the head of the i n l e t should be expected t o be somewhat s t r o n g e r than they are f a r t h e r downchannel. Thus some of the apparent r e d u c t i o n i n wind s t r e n g t h from Sguamish to the radar s i t e s may be r e a l . Table I I a l s o shows t h a t the wind i s predominantly b i -d i r e c t i o n a l as expected. The winds measured i n Sguamish never blow from the e a s t or west. With the e x c e p t i o n of week 51 2, the same i s mainly t r u e o f the radar s i t e winds. A rose o f the percent of the t o t a l wind run i n each o c t a n t throughout the e n t i r e experiment i s shown i n f i g u r e 9 . I t shows t h a t over 93% of the t o t a l wind comes from e i t h e r south or southwest and the remainder from the n o r t h , n o r t h e a s t or northwest. In an area of c h a n n e l - l i k e geometry, i t can be assumed t h a t the predominant winds are e i t h e r up or down channel, i . e . c r o s s - c h a n n e l winds are very much weaker than long-channel winds. T h e r e f o r e , the c r o s s - c h a n n e l component of the wind w i l l be considered to be zero and hence a l l winds coming from the south or southwest w i l l be c o n s i d e r e d to be the up-channel component o f the wind. S i m i l a r l y , s i n c e the l a n d area north of sguamish f u n n e l s the wind i n t o the f j o r d , a l l winds coming from the northwest, n o r t h , or nort h e a s t w i l l be co n s i d e r e d t o be the down channel component of the wind. The same s o r t o f d i v i s i o n i n t o components w i l l be a p p l i e d t o the winds a t the radar s i t e s . The same angular c r i t e r i a w i l l be used f o r weeks 1, 3 and 4 except t h a t winds from the southeast w i l l a l s o be c o n s i d e r e d to be u p - i n l e t . In week 2 the problem i s somewhat more d i f f i c u l t due t o the l o c a t i o n o f the radar s i t e on a sharp bend i n the f j o r d a t the base of a v a l l e y t h a t c o n t r i b u t e d soma winds from the west and northwest. For purposes of the present a n a l y s i s , the winds from t h e west w i l l be c o n s i d e r e d to be u p - i n l e t . A comparison o f the wind data broken up i n t o components as j u s t d e s c r i b e d i s shown i n f i g u r e 10 . The o r i g i n o f the time a x i s f o r each week i n t h i s f i g u r e and i n a l l subsequent s Figure 9 - A wind rose of the t o t a l wind run past the Squamish anemometer for the four weeks cf the experiment. Direction i s defined as the d i r e c t i o n the wind came from. 53 F i g u r e 10 - Comparison between long-channel component o f wind v e l o c i t y as measured a t Squamish ( s o l i d l i n e ) and the radar s i t e s (dotted l i n e ) f o r the f o u r weeks of measurement. a. week 1. b. week 2. c. week 3. d. week 4. O r i g i n of the time a x i s i s OOOOh on the f i r s t day of expected o b s e r v a t i o n each week. The same time o r i g i n s w i l l be used i n a l l subsequent f i g u r e s . 54 ones i s at OOOOh on the f i r s t planned day of observation- i n t h a t week. Thus the time axes go from 0 t o 96 hours. The radar s i t e winds from weeks 2 and 4 can be seen t o be much s m a l l e r than the co r r e s p o n d i n g Sguamish winds as p r e v i o u s l y mentioned and so w i l l be disreg a r d e d , Although the amplitudes of the winds i n weeks 1 and 3 are somewhat l e s s than those measured a t Sguamish , t h e r e i s a gene r a l agreement between the radar s i t e and Sguamish i n the phase and shape of the wind component vs time curves. For the sake of c o n s i s t e n c y i n a n a l y s i s o f the f o u r weeks of data, and because the data c o l l e c t e d by AES i n Sguaaish i s , i n s p i t e of i t s l i m i t a t i o n s , the most g e n e r a l l y r e p r e s e n t a t i v e t h a t i s a v a i l a b l e , the Squamish winds curves w i l l be the ones used i n the subsequent a n a l y s i s . I I I . 2 R i v e r Discharge Discharge of the Squamish B i v e r i s measured at a guaging s t a t i o n a t Brackendale, 17 miles n o r t h o f Squamish. T h i s gauge c o n t i n u o u s l y recorded water l e v e l which was subsequently converted to r a t e of dis c h a r g e on an ho u r l y b a s i s from t a b l e s p r o v i d e d by the Water Survey of Canada. The di s c h a r g e of the Squamish River r e p r e s e n t s almost a l l of the f r e s h water i n p u t i n t o Howe Sound and t h e r e f o r e the gauge records were taken as being i n d i c a t i v e of the t o t a l f r e s h water i n p u t . There were l a r g e v a r i a t i o n s i n the dis c h a r g e of the Squamish River from week t o week but the d a i l y v a r i a t i o n s 55 w i t h i n each week were q u i t e s m a l l . F i g u r e 11 shows the di s c h a r g e curve f o r each week. The average discharge each week i s shown i n t a b l e 3. The l a r g e d i f f e r e n c e between the week 1 dis c h a r g e and the week 2 d i s c h a r g e was caused by two i n t e r v e n i n g days of almost 30°C maximum temperature t h a t seemed to s i g n a l the beginning of the major s p r i n g r u n o f f peak. I t can be seen i n f i g u r e 11 t h a t the p e r i o d o f v a r i a b i l i t y i n the r i v e r flow i s approximately 24 hours, i n d i c a t i n g that the v a r i a t i o n s are due to sun melting of snow i n the Sguamish watershed. T h i s hypothesis i s f u r t h e r borne out by the delay i n time of maximum d a i l y d i s c h a r g e from week 1 to the other weeks, i n d i c a t i n g t h a t , as the season progressed, the l e v e l of snow melt i n g went from the lowlands to higher country t h a t was f a r t h e r away from the mouth o f the r i v e r . Based on an assumed s u r f a c e l a y e r depth of 4m and a channel width o f 2.8km, the approximate mean s u r f a c e l a y e r v e l o c i t y due to the r i v e r d i s c h a r g e may be c a l c u l a t e d . The r e s u l t s o f such c a l c u l a t i o n s are shown i n t a b l e I I I , In t h i s t a b l e , the mean v e l o c i t y i s the dis c h a r g e averaged over t h e t o t a l width of the channel. The mean core v e l o c i t y i s the d i s c h a r g e averaged only over the width of the r i v e r c o r e , t h a t p a r t of the flow t h a t moved down-inlet on average over the whole week. T h i s core w i l l be d i s c u s s e d l a t e r i n chapter IV. The core v e l o c i t y i s more r e p r e s e n t a t i v e of the expected magnitude o f the r i v e r flow i n the i n l e t . In no case i s the expected r i v e r v e l o c i t y g r e a t e r than 9cm/s, and t h e r e f o r e v a r i a t i o n s l i k e those i n week 4 of 6 5 i 3 / s c o u l d 56 Figure 11 -experiment. River discharge for the four weeks of the a. week 1. b. week 2. c. week 3. d. week 4. 57 Table I I I •- Hean r i v e r d i s c h a r g e and the r e s u l t a n t s u r f a c e l a y e r v e l o c i t y t a k i n g entrainment i n t o account. The mean di s c h a r g e f o r each week i s shown with i t s standard d e v i a t i o n . Percent entrainment means the amount of the s a l i n e deeper water necessary t o gi v e the r i v e r water the s a l i n i t y observed on hydrographic c r u i s e s made before and a f t e r the experiment, expressed as a percentage of the volume; of r i v e r water. Seek 1 2 3 4 I discharge} I (mVs) | entrainment j 158±27 527±31 485±34 444±65 12 6 17 0 mean v e l o c i t y (Cffl/S) 2 5 5 4 mean coreJ v e l o c i t y J (crn/s) | -4 2 9 5 7 cause c u r r e n t f l u c t u a t i o n s o f no g r e a t e r than about 1 cm/s. In l i g h t of the d i u r n a l p e r i o d i c i t y of the wind and the st r o n g d i u r n a l component i n the t i d e , i t seems u n l i k e l y t h a t these; d a i l y v a r i a t i o n s i n r i v e r d i s c h a r g e w i l l have an obse r v a b l e e f f e c t on the s u r f a c e c i r c u l a t i o n . I I I . 3 The Tide I t was not f e a s i b l e t o make r e c o r d i n g s of t i d a l height d u r i n g t h i s experiment. P r e d i c t i o n s o f t i d a l height are made by the Canadian Hydrographic S e r v i c e and published a n n u a l l y i n t h e i r Tide T a b l e s . Pt. Atkinson i s a major r e f e r e n c e port i n t h e i r p r e d i c t i o n scheme and t h e r e f o r e the p r e d i c t e d t i d a l h e i g h t s t h e r e should be acc u r a t e t o a few c e n t i m e t r e s . Sguamish i s a secondary port i n the p r e d i c t i o n s meaning t h a t i t v a r i e s i n the same ge n e r a l manner as some r e f e r e n c e p o r t . 58 In t h i s case Pt. Atkinson. Examination of the amplitudes of the t i d a l c o n s t i t u e n t s a t Sguamish and Pt. Atkinson as provided by Dr. P. Crean o f I n s t i t u t e o f Ocean Sciences show d i f f e r e n c e s of only a few cen t i m e t r e s and a few degrees i n phase between the s t a t i o n s i n a l l c o n s t i t u e n t s , i n agreement with t h i s f i n d i n g , the t i d e t a b l e s show o n l y a f o u r minute d e l a y o f high water a t Sguamish from Pt. Atkinson and a h e i g h t d i f f e r e n c e of on l y a few centimetres. Such s m a l l d i f f e r e n c e s i n d i c a t e the absence of any b a r o t r o p i c t i d a l resonance i n the main channel of Howe Sound j o i n i n g these two t i d a l s t a t i o n s . T h e r e f o r e the t i d a l h e i g h t as p r e d i c t e d f o r Pt. Atkinson may be taken as being v a l i d f o r the e n t i r e a rea o f i n t e r e s t i n the sound. A r e c o r d of the t i d a l h e ight a t P t . A t k i n s o n was provided by Dr. P. Crean o f I n s t i t u t e of Ocean Sciences c o n t a i n i n g f o u r values per hour f o r the d u r a t i o n of the experiment. T h i s r e c o r d i s shown i n f i g u r e 12 . The maximum range can be seen to be about 4 metres. Height changes of t h i s magnitude occurred i n about 6 hours once or twice each weak. Since the experimental area i s c l o s e to the head of the i n l e t , these l a r g e t i d a l h e ight v a r i a t i o n s should not cre a t e l a r g e t i d a l v e l o c i t i e s . A simple b a r o t r o p i c t i d a l prism model p r e d i c t s f o r a s i n u s o i d a l l y v a r y i n g height change of 1.5m amplitude and 12h p e r i o d a c u r r e n t amplitude a c r o s s the s i l l (depth 70m) of 5.3 cm/s and of 1.5 cm/s j u s t i n s i d e (depth 250m)., A s l i g h t l y more complex model, d i s c u s s e d i n more d e t a i l i n chapter V I I , taken from R a t t r a y * s (1960) work on g e n e r a t i o n of i n t e r n a l t i d e s on the c o n t i n e n t a l s h e l f , can Figure 12 - T i d a l height for Point Atkinson as predicted the Canadian Hydrographic Se r i v i c e . a. week 1. b. week c. week 3. d. week 4. 60 be used to c a l c u l a t e b a r o t r o p i c and b a r o c l i n i c components of s i n u s o i d a l l y v a r y i n g t i d a l v e l o c i t y i n a two l a y e r system. C o n s i d e r i n g Howe Sound to be such a system with t o p l a y e r t h i c k n e s s 5 metres, t o t a l depth 250m, s i l l depth 70m, and d e n s i t y d i f f e r e n c e o f 2% between the l a y e r s . T h i s model p r e d i c t s j u s t i n s i d e the s i l l a b a r o t r o p i c c u r r e n t amplitude of 1.7 cm/s and a b a r o c l i n i c c u r r e n t amplitude i n the su r f a c e l a y e r of .8 cm/s. Halfway up the i n l e t , the same c u r r e n t amplitudes are ,8 cm/s and 2.8 cm/s r e s p e c t i v e l y . Thus the b a r o c l i n i c component of the t i d a l c u r r e n t may be r e s p o n s i b l e f o r more than a n e g l i g i b l e part o f the observed c u r r e n t f l u c t u a t i o n s at some p o i n t s i n the i n l e t . Although both of these models are o v e r s i m p l i f i e d , they i n d i c a t e t h a t the magnitude of the expected b a r o t r o p i c t i d a l l y induced c u r r e n t s i s smal l i n comparison with the speeds observed i n t h i s experiment. But the b a r o c l i n i c t i d a l e f f e c t s may be l a r g e r , so events having some steady phase r e l a t i o n s h i p with the t i d e were looked f o r i n the data a n a l y s i s . 61 I I I . 4 Dens i t y . M easnrements The water i n a f j o r d i s o f t e n t y p i f i e d as being a d i s c r e t e two-layered system with a small t h i c k n e s s of f r e s h e r water o v e r l a y i n g more s a l i n e deep water. There i s o f t e n a very sharp i n t e r f a c e between the two water types. D e n s i t y p r o f i l e s were made, i n the l a t t e r two weeks of the experiment, of the upper 20m of the water column to a s c e r t a i n the v a l i d i t y of t h i s assumption i n Howe Sound and t o measure the depth of t h i s " s u r f a c e l a y e r " . Sets of f i v e p r o f i l e s were made from the S k i f f or the S a n g s t e r c r a f t a t e g u i d i s t a n t p o i n t s along s e v e r a l l i n e s a c r o s s the i n l e t . In week 3, two s e t s were taken along a l i n e from the radar s i t e a c r o s s the i n l e t t o the o p p o s i t e shore. An Autolab 602 p o r t a b l e s a l i n o m e t e r was used to make the temperature and s a l i n i t y measurements. On the t h i r d s e t o f p r o f i l e s i t broke, c u r t a i l i n g measurements f o r t h a t week. In the f o u r t h week, a Beckman RS-4 was used t o make e i g h t s u c c e s s f u l s e t s o f measurements on l i n e s c r o s s i n g t h e i n l e t near the week 4 radar s i t e . In each p r o f i l e , measurements were made at one metre i n t e r v a l s from 0 to 5m, at 2.5m i n t e r v a l s from 5 to 15m and at 20m. At each l o c a t i o n a bathythermograph c a s t was a l s o made but the temperature s t r u c t u r e alone gave l i t t l e e s t i m a t e of t h e d e n s i t y s t r u c t u r e . F i g u r e 13 shows s a l i n i t y p r o f i l e s taken i n these c r o s s i n l e t s e c t i o n s , one set f o r week 3 and one f o r week 4. The upper s e t of p r o f i l e s , taken near the s i l l , shows the s t r a t i f i c a t i o n at i t s weakest: the lower s e t , taken near 62 Salinity 2 7 June 1 0 1 0 - 1 2 3 5 20J Figure 13 - S a l i n i t y p r o f i l e s taken i n two sections across the i n l e t . Progression from l e f t to riqht i s west to east. The section at the top was taken near the s i l l , the one at the bottom, near the head of the i n l e t , 63 the r i v e r mouth, shows i t a t i t s s t r o n g e s t . , In the case of the s t r o n g e r s t r a t i f i c a t i o n , the water column i s f a i r l y homogeneous t o a depth of about 4m. Then the s a l i n i t y i n c r e a s e s r a p i d l y with depth t o about 8m, where the i n c r e a s e becomes more g r a d u a l . In the weaker ca s e , on the west s i d e , the s a l i n i t y i s r e l a t i v e l y uniform down to 3m, then i n c r e a s e s r a p i d l y below t h a t . However, on the e a s t s i d e , the h a l o c l i n e i s r i g h t at the s u r f a c e . In t h i s l o c a t i o n i t i s d i f f i c u l t t o see any d i s t i n c t s u r f a c e l a y e r . In an attempt to q u a n t i f y the s u r f a c e l a y e r of a f j o r d , Farmer(1972) d e f i n e d an e q u i v a l e n t f r e s h water depth, F, f o r a water column as: where D i s the depth of the water column under c o n s i d e r a t i o n 1 and S(D) i s the s a l i n i t y a t t h a t depth. T h i s q u a n t i t y r e p r e s e n t s the t h i c k n e s s t h a t the f r e s h water l a y e r would be i f the water column were decomposed i n t o two f r a c t i o n s , one completely f r e s h and the o t h e r as s a l t y as the most s a l i n e i n the water column. Table IV shows how t h i s parameter v a r i e d f o r s e v e r a l c r o s s i n l e t s e c t i o n s . In t h i s t a b l e , the s t a t i o n s are arranged with s t a t i o n 1 on the west and 5 on the e a s t as i n f i g u r e 13. The most s t r i k i n g f e a t u r e of t h i s t a b l e i s the v a r i a t i o n i n the f r e s h water depth from one s e c t i o n to the next. Farmer examined v a r i a t i o n s i n t h i s q u a n t i t y i n r e l a t i o n (3.1) o 64 Table IV - E g u i v a l e n t f r e s h water depth ( i n metres) f o r s e v e r a l c r o s s i n l e t s e c t i o n s . The 27 June s e c t i o n s were made along the same c r o s s - i n l e t l i n e . The J u l y s e c t i o n s were a l l made along a d i f f e r e n t l i n e much c l o s e r to the i n l e t head. Date j time) s t n 1| s t n 2 + 27 June | 11001 4.0 | 3.9 \ I 1 27 June 1 1800| 3,6 | 4.3 I I I . 4 1~ - 4 ! ! I 4 J u l y ! 1030| 4.6 \ 4.8 | 4.9 I 1 I 5 J u l y | 17001 5.6 | 5.3 | 5.7 I ! ] 6 J u l y } 0930| 4.4 | 4.8 ( 4.8 I 1 I ; _J _1 1 s t n 3 3. 9 4. 5 stn 4| s t n 5| 4-3.6 4.5 5.1 5.6 4.5 3. 5 4. 7 4.9 5.5 4. 8 to the wind* His measurements i n A l b e r n i I n l e t showed t h a t l a r g e v a r i a t i o n s i n t h i s parameter c o u l d be r e l a t e d t o changes i n the wind s t r e s s over the i n l e t and to the b a r o c l i n i c response of the i n l e t to the t i d e . Thus, v a r i a t i o n s of t h i s magnitude are not unexpected. Another n o t a b l e f e a t u r e o f t h i s t a b l e i s the d e f i n i t e g r a d i e n t of f r e s h water t h i c k n e s s a c r o s s the i n l e t t h a t o c c u r s i n the f i r s t two s e c t i o n s . The deeper p a r t of the l a y e r i s probably i n d i c a t i v e o f the presence o f r i v e r water not y et mixed a c r o s s the i n l e t . T h i s r i v e r core appears to be on the west s i d e of the channel i n the f i r s t s e t of measurements and on the e a s t i n the second. Hiver core movements of t h i s type are not unusual and occur o f t e n on s h i f t s i n wind d i r e c t i o n . A wind s h i f t d i d occur between these two s e t s of measurements, The most important c o n c l u s i o n , however, i s t h a t the l a y e r depth i s everywhere deeper than 2m, the drogue depth, 65 so that the drogues were, a t the time of these measurments and, by e x t r a p o l a t i o n , throughout the experiment, i n the s u r f a c e l a y e r as d e f i n e d by the f r e s h water depth. I t i s , of co u r s e , q u i t e p o s s i b l e t h a t the v e l o c i t y p r o f i l e of the upper 20m of the water column would show a d i f f e r e n t s t r u c t u r e from t h a t suggested by the s a l i n i t y p r o f i l e . The depth of maximum v e l o c i t y g r a d i e n t need not be the same as the depth of maximum d e n s i t y g r a d i e n t ; o r as the depth of the e q u i v a l e n t f r e s h water l a y e r . Determination of the r e l a t i o n s h i p between these parameters i s beyond the scope of these experiments. I t i s l i k e l y however that the depth of maximum v e l o c i t y g r a d i e n t i s below the bottom of the drogues. Observations o f drogue t i l t , as di s c u s e d i n appendix I , and a comparison of drogue v e l o c i t i e s with the v e l o c i t y r e c o r d from a 3 metre deep c u r r e n t meter, as d i s c u s s e d i n the next s e c t i o n , v a l i d a t e t h i s assumption. For some l a t e r c a l c u l a t i o n s i t i s necessary t o provide some a c t u a l measure of the l a y e r depth. S i n c e measurements of the d e n s i t y p r o f i l e were not made i n the f i r s t two weeks and were sparse i n the l a s t two weeks, i t i s i m p o s s i b l e t o d e s c r i b e a c c u r a t e l y the v a r i a t i o n s i n the l a y e r depth. The average depth as c a l c u l a t e d from a l l the measurements taken was about 4.5m. Because of the l a r g e v a r i a t i o n s t h a t were found around t h i s mean, the accuracy o f i t must be taken t o be about ±1a.; 66 I I I . 5 Comparison Of -The Drogue • V e l o c i t j e s With The ' 3m C u r r e n t Meter A comparison between the water v e l o c i t y as recorded by the drogues and by the c u r r e n t meter l o c a t e d at 3m depth a t the l o c a t i o n shown i n f i g u r e 6 provides an i n t e r e s t i n g t e s t both of the d i f f e r e n t methods of measuring c u r r e n t and of the c o n c l u s i o n that the e f f e c t i v e s u r f a c e l a y e r depth i s about 4.5m. Only dur i n g week 3 of the experiment were th e r e s u f f i c i e n t drogues i n the v i c i n i t y of the c u r r e n t meter to allow a comparison with the c u r r e n t meter r e s u l t s . T h i s comparison i s shown i n f i g u r e 14 . In t h i s f i g u r e , the c u r r e n t meter curves are drawn through component values c a l c u l a t e d every 15 minutes, the i n s t r u m e n t ' s sampling i n t e r v a l . The drogue curves were drawn through v a l u e s c a l c u l a t e d as the box average components of drogue v e l o c i t i e s taken every 15 minutes from the s p l i n e f i t t e d r e c o r d s i n a box one mile sguare c e n t r e d on the c u r r e n t meter l o c a t i o n . The 15 minute i n t e r v a l was chosen t o correspond to the c u r r e n t meter sample i n t e r v a l , the one mile box to c o n t a i n enough drogues f o r adequate coverage. However, these dimensions are not c o n s i s t e n t as d e f i n e d i n s e c t i o n II.-4. Thus the average i s more l i k e a s p a t i a l average than a temporal average and might s l i g h t l y o v e r e s t i m a t e the E u l e r i a n average v e l o c i t y i n the box. T h i s o v e r e s t i m a t i o n should be s m a l l enough t o be n e g l i g i b l e i n the l i g h t of seme of the u n c e r t a i n t i e s i n the c u r r e n t meter 67 i Figure 14 - A comparison of surface layer v e l o c i t y in week 3 as measured by the current meter at 3m depth and by the average of the drogues in a 1 mi* box around the current meter s i t e . 68 r e s u l t s . The c u r r e n t meter v e l o c i t y i s o f t e n g r e a t e r i n magnitude than the drogue v e l o c i t y . An e x c e p t i o n occurred a t about 32 hours when the prominent v e l o c i t y core o f the r i v e r passed through the drogue averaging square but not i n the immediate v i c i n i t y of the c u r r e n t meter. The v e l o c i t y as recorded by the drogues was much smoother than t h a t recorded by the c u r r e n t meter. The measurement area f o r the drogue v e l o c i t i e s was much l a r g e r than t h a t f o r the c u r r e n t meter. Thus the e f f e c t s of s m a l l s c a l e (<1Km) t u r b u l e n c e i n the flow are averaged out i n the drogue average but not i n the c u r r e n t meter. Secondly, the c u r r e n t meter, being suspended from a s u r f a c e mooring, i s s u s c e p t i b l e t o mooring n o i s e . In t h i s p a r t i c u l a r meter, b u r s t sampling l e s s e n s but does not remove the problem, as w i l l be d i s c u s s e d i n more d e t a i l i n chapter VI. T h i s n o i s e would be expected t o manifest i t s e l f as l a r g e r speeds and s c a t t e r e d d i r e c t i o n s . The d i f f e r e n c e s between the c u r r e n t meter and drogue v e l o c i t i e s c o u l d be accounted f o r by e i t h e r or both of these e f f e c t s . The l a r g e r s c a l e f e a t u r e s of these two v e l o c i t y r e c o r d s a r e g u i t e similar.-When the d i f f e r e n c e s between the two techni q u e s are taken i n t o account, the s u r f a c e l a y e r appears t o move reas o n a b l y u n i f o r m l y with depth down to at l e a s t 3 metres. The r e s u l t s of the previous s e c t i o n showed a s u r f a c e l a y e r between 3.5m and 5.5m deep based on d e n s i t y i n f o r m a t i o n and assumed t h a t the depth of maximum c u r r e n t shear, i . e . the i n t e r f a c e between the s u r f a c e and deeper l a y e r s based on v e l o c i t y , was somewhere i n t h a t range. The r e s u l t s o f t h i s s e c t i o n do not c o n f l i c t with that assumption and i n d i c a t e t h a t the s u r f a c e l a y e r i s reasonably homogeneous i n v e l o c i t y a t l e a s t t o 3 metres., 70 CHAPTER IV RESULTS OF THE SURFACE LAYER EXPERIMENT IV. 1 I n t r o d u c t i o n The s u r f a c e l a y e r c i r c u l a t i o n experiment was q u i t e s u c c e s s f u l . Observations were made f o r a t o t a l of 255 hours. Over 800 photographs were taken, y i e l d i n g 12,553 o b s e r v a t i o n s of drogue p o s i t i o n s and u l t i m a t e l y 241,115 i n t e r p o l a t e d p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n e s t i m a t e s . A summary of these s t a t i s t i c s on a weekly b a s i s i s gi v e n i n t a b l e V . Table V - A summary of the o b s e r v a t i o n s t a t i s t i c s f o r a l l f o u r weeks of the drogue experiment. The numbers given a r e : week number, number of o b s e r v a t i o n hours i n t h a t week, number of p i c t u r e s taken, number of drogue t r a c k s f o l l o w e d , number of drogue p o s i t i o n o b s e r v a t i o n s and number of p o i n t s i n t e r p o l a t e d a t one minute i n t e r v a l s . ; r — 1—— T — r "" ~ T" r T week i obs ] # ) # | # } # | 'hours j p i c s j - t r a c k s - j obs j i n t e r p 1 I 48.4 | 191 i 180 2 | 70.3 | 204 | 295 3 | 69.8 | 198 | 271 4 | 67.0 \ 236 j 325 I i ! 1 1 • • i „ .+ — , | 2398 \ 45740 | 3009 | 59140 | 3076 | 61416 I 4070 | 75089 I ! _L ; 1 J The time base f o r each week of the experiment was set a t OOOOh P a c i f i c D a y l i g h t Time on the f i r s t planned day of o b s e r v a t i o n . For example, the week 1 time l i n e s t a r t e d a t 71 OOOOh May 8. On t h a t day the s k i f f l o s t a p r o p e l l o r and the weather was miserable so a c t u a l o p e r a t i o n s d i d not s t a r t u n t i l 0600 May 9. Thus the r e c o r d s from t h a t week s t a r t a t 30h. The o b s e r v a t i o n s i n week 1 were cut s h o r t by strong down-inlet winds e a r l y i n the l a s t day t h a t drove a l l the drogues south of the o b s e r v a t i o n area. By the time they were re c o v e r e d i t was time t o pack up the eguipment f o r the week. In the other t h r e e weeks we had g r e a t e r success i n a c h i e v i n g the g o a l of 3 days continuous o b s e r v a t i o n . There are only a few gaps i n the data r e c o r d . These u s u a l l y occurred at n i g h t when the s u r f a c e l a y e r c u r r e n t s made a quick change i n d i r e c t i o n . The one o p e r a t i n g v e s s e l was not f a s t enough both to search f o r drogues l e a v i n g the are a and t o deploy new drogues i n the area to allow the o b s e r v a t i o n s t o conti n u e . T h i s chapter c o n t a i n s f i r s t a general p i c t u r e of the s u r f a c e c i r c u l a t i o n p a t t e r n . T h i s g e n e r a l p i c t u r e i s then s u b s t a n t i a t e d with a s e m i - g u a n t i t a t i v e d e s c r i p t i o n of the flow f i e l d , a d e s c r i p t i o n o f the observed drogue movements i n each of the f o u r weeks. The r e s t o f the chapter g i v e s more q u a n t i t a t i v e a n a l y s e s o f some of the averaged p r o p e r t i e s of the drogue o b s e r v a t i o n s . 72 IV • 2 A.„ General Surface C i r c u l a t i o n P a t t e r n A b a s i c aim of these experiments was t o determine the ge n e r a l p a t t e r n of s u r f a c e l a y e r flow i n the north end of Howe Sound. T h i s d e s c r i p t i o n i s based on an examination of drogue motions i n a l l f o u r weeks and an attempt t o e x t r a p o l a t e from them the u n d e r l y i n g flow f i e l d i n the absence of f o r c i n g by e i t h e r wind or t i d e . The p r i n c i p a l technique used t o obtain t h i s d e s c r i p t i o n was repeated o b s e r v a t i o n o f a s e t of movies computer generated from the s p l i n e - f i t t e d data s e t d e s c r i b e d i n chapter IT. I t was necessary t o c o n s t r u c t these movies because the time l a p s e movies taken of the rad a r screen d u r i n g the experiment were i n t e r m i t t e n t due to camera ma l f u n c t i o n s and contained a l l of the extraneous, d i s t r a c t i n g o b j e c t s d e s c r i b e d p r e v i o u s l y . These computer generated movies were s i m i l a r t o those d i s c u s s e d i n chapter I I but contained more i n f o r m a t i o n and were t r a n s c r i b e d onto 16mm movie f i l m u s i n g the Bolex H16 Refle x camera i n t e r f a c e d t o the PDP-12. A d e s c r i p t i o n o f the movie ge n e r a t i o n techniques i s given i n Appendix I I . And a sample of these movies i s i n c l u d e d as Appendix I I I . The average c i r c u l a t i o n p a t t e r n of the s u r f a c e l a y e r i n Howe Sound as q u a l i t a t i v e l y deduced from these experiments i s shown i n f i g u r e 15 . Each i n d i v i d u a l arrow i n t h i s f i g u r e r e p r e s e n t s the d i r e c t i o n and r e l a t i v e speed o f the c u r r e n t a t t h a t l o c a t i o n . T h i s c i r c u l a t i o n p a t t e r n and the standard s i l t p a t t e r n as seen i n the f r o n t i s p i e c e a r e , not 73 Figure 15 - A general, q u a l i t a t i v e surface c i r c u l a t i o n pattern for upper Howe Sound as deduced from the surface drogue study. Length of the arrows indicates the r e l a t i v e speed of the current; the breadth of each arrow, the persistence of the current at that point. 74 s u r p r i s i n g l y , g u i t e s i m i l a r . However, the sharp boundaries between the s i l t y and n o n - s i l t y water t h a t appear i n the f r o n t i s p i e c e do not i n d i c a t e the presence o f sharp v e l o c i t y g r a d i e n t s as might be expected. I t was observed many times i n the experiment t h a t drogues on o p p o s i t e s i d e s of s i l t boundaries moved at about the same speed. The dominant f e a t u r e o f t h i s c i r c u l a t i o n p a t t e r n i s the " j e t " formed by Sguamish E l v e r water. The c o r e of t h i s j e t , as i n d i c a t e d by the h e a v i e s t arrows, proceeds down-inlet i n a path c o n s t r a i n e d by the shape of the i n l e t . . A f t e r the core l e a v e s the mouth of the r i v e r , i t proceeds a c r o s s the i n l e t and then moves west along the southeast shore. There i s o f t e n a c o u n t e r c l o c k w i s e back eddy on the e a s t s i d e of t h i s j e t t h a t b r i n g s s i l t y r i v e r water i n t o Sguamish harbour. Where the e a s t shore of Howe Sound t u r n s s h a r p l y south j u s t n orth of Watts P o i n t ; the r i v e r core t r a v e r s e s the i n l e t t o the v i c i n i t y o f woodfibre, whence i t f o l l o w s the west shore southward f o r s e v e r a l m iles, When i t passes S t i c k P o i n t 1 i t moves away from the shore t o the c e n t r e o f the channel due t o a sharp bend i n the s h o r e l i n e and a s l i g h t change i n the o r i e n t a t i o n o f the channel. There are two l a r g e slow, p e r s i s t e n t e d d i e s probably d r i v e n by entrainment i n t o t h i s r i v e r flow i n the north part of the b a s i n . The f i r s t , a 1 T h i s p o i n t i s nameless on the Hydrographic c h a r t of Howe Sound, but i s known l o c a l l y as S t i c k Point f o r the f o l l o w i n g reason. Tug boat o p e r a t o r s b r i n g i n g booms and barges up Howe Sound u s u a l l y proceed up the western shore t a k i n g advantage of the slower c u r r e n t s and back eddies south of t h i s p o i n t . They found t h a t as soon as they rounded t h i s p o i n t they got "stuck",!, e. had t r o u b l e g e t t i n g f a r t h e r up the i n l e t . E e s u l t s i n t h i s t h e s i s should make the reason obvious. 75 c l o c k w i s e gyre, occurs between Woodfibre and the mouth of the Sguamish R i v e r , and the second, a c o u n t e r c l o c k w i s e gyre, between B r i t a n n i a Beach and Hatts Points T h i s second gyre i s not so prominent and may be l u s t a wind e f f e c t . I t i s p o s s i b l e but l e s s l i k e l y t h a t the f i r s t gyre i s a l s o wind-d r i v e n . During i t s passage down-inlet, the r i v e r j e t d i v e r g e s s l o w l y . T h i s divergence w i l l be d e s c r i b e d q u a n t i t a t i v e l y i n a l a t e r s e c t i o n . South of S t i c k P o i n t , the j e t i s wide enough to cause a l l the s u r f a c e l a y e r t o move downstream. In the v i c i n i t y o f Porteau Gove, at the southern l i m i t of o b s e r v a t i o n i n these experiments, t h e r e i s s t i l l evidence of h o r i z o n t a l shear i n the s u r f a c e l a y e r . Even a t t h i s p o i n t , 18 km from the r i v e r mouth, the c l a s s i c a l e s t u a r i n e assumption of l a t e r a l l y homogeneous flow has not been ach i e v e d . I t was not c l e a r from the: experiments whether the average s u r f a c e flow u s u a l l y goes to the west of A n v i l I s l a n d or t o the e a s t of i t . The experiments showed both r e s u l t s although flow to the western s i d e seems to be s l i g h t l y favoured..There was no obvious c o r r e l a t i o n between the wind speed or d i r e c t i o n and the s i d e of A n v i l I s l a n d t h a t the c u r r e n t flowed past. 76 1 v • 3 A Synopsis Of The Data Sets IV. 3. 1 • Techniques,"-Of'^P^se^tatipn The data s e t s c o l l e c t e d i n the f o u r weeks of the experiment w i l l be presented i n a s e r i e s of diagrams, each one c o n t a i n i n g a number of averages of the drogue v e l o c i t i e s i n 0.5 n a u t i c a l mile sguares c o v e r i n g the experimental a r e a s . The reasons f o r t h i s box averaging technique and the l i m i t a t i o n s of i t when using such a l a r g e box s i z e were d i s c u s s e d i n c h a p t e r I I . The use of longer times and l a r g e r boxes than suggested i n t h a t chapter probably decreases the measured v e l o c i t i e s s l i g h t l y , but f o r the purposes of a s e m i - g u a n t i t a t i v e d e s c r i p t i o n of these data s e t s , the p o s s i b l e d i s c r e p a n c y should be s m a l l enough to n e g l e c t . To be c o n s i s t e n t with the 0.5 mile averaging g r i d , the c o a s t l i n e i n each diagram has been drawn along the boundaries of a l l those squares c o n t a i n i n g a p p r e c i a b l e water area or which have some water area and an a p p r e c i a b l e number of drogue o b s e r v a t i o n s i n them. The correspondence between t h i s "squared" c o a s t l i n e and the a c t u a l one i s shown i n f i g u r e 1 6 . A t y p i c a l diagram from one o f the sequences i s shown i n f i g u r e 17 . T h i s p a r t i c u l a r one i s f o r t h e p e r i o d beginning at 69 hours and ending at 72 hours o f the f i r s t week. Eig h t e e n arrows r e p r e s e n t i n g t h r e e hour averages of drogue 77 F i g u r e 16 - A c t u a l vs. "sguared" c o a s t l i n e s f o r the f o u r weeks. The double c i r c l e i n d i c a t e s the radar s i t e i n each week. 78 69 HR TO 72 HR start end T ime 50n Water speed (cm/s) 0-\ \ Wind speed (m/s) 0 \ Hour 0 1 Figure 17 - A t y p i c a l diagram from the 3 hour averged data sets that are presented i n figures 19-22. Shown on the figure are the current vectors, wind vectors, t i d a l height and the relevant scales as are described in the text. 79 v e l o c i t i e s i n 0.5 mile squares can be seen w i t h i n the c o n f i n e s o f t h e squared c o a s t l i n e . The s c a l e r e l a t i n g the l e n g t h o f these arrows to the average c a l c u l a t e d drogue speed i s shown on the l e f t of the f i g u r e . Absence o f an arrow i n a square i n d i c a t e s t h a t t h e r e were no drogues i n t h a t square at any time i n the averaging p e r i o d . The t a i l of each arrow i s a t the c e n t r e o f i t s averaging square. T h i s f i g u r e a l s o c o n t a i n s t h r e e v e c t o r s r e p r e s e n t i n g the wind v e l o c i t y from the AES anemometer i n Squamish, one f o r each hour of t h e averaging p e r i o d . The speed s c a l e f o r these v e c t o r s i s a l s o shown. A s e c t i o n of the Pt. Atkinson t i d a l curve i s shown, r e p r e s e n t i n g the h e i g h t of the t i d e d u r i n g the averaging p e r i o d . A l l of the diagrams t o f o l l o w i n t h i s chapter c o n t a i n these component p a r t s , except the s c a l e s , which are shown on one frame per page. There i s no i n d i c a t i o n i n these f i g u r e s of the e r r o r i n the averages, or of the spread o f i n d i v i d u a l v a l u e s about the means. In f i g u r e 18 another t y p i c a l diagram i s shown, but with the observed standard d e v i a t i o n of each component p l o t t e d a t the head of each vect o r . Only i n the case of the s m a l l e s t v e c t o r s i s the standard d e v i a t i o n l a r g e r than the v e c t o r i t s e l f . On average, 15 values were used t o form each v e c t o r , so t h a t the standard e r r o r o f each average should be about 1/4 the s i z e of the e r r o r bars shown. Thus f o r the most p a r t , the v e c t o r s shown i n the next s e c t i o n s are s t a t i s t i c a l l y r e l i a b l e . What f o l l o w s now i s a b r i e f d e s c r i p t i o n of each data s e t accompanied by 17 to 24 diagrams of the s o r t j u s t 36 HR TO 39 HR i t l \ \ * \ \ 1 I f f / i i 1 t / / scale of velocities and error bars 5 0 cm/s F i g u r e 18 - T y p i c a l sguare-averaged p l o t showing e r r o r f ±1 standard d e v i a t i o n a t the head of each arrow. 81 d e s c r i b e d . IV. 3.2 - 2^Mi=iiav^5zlix_-l253 The data c o l l e c t e d i n week 1 of these experiments are shown i n f i g u r e 19 a-g. The week s t a r t e d with almost no wind and an ebbing t i d e . The flow was down-inlet and s t r o n g e r on the west than on the east . At 34 h o u r s , ( f i g . 1 9 c ) the wind s t a r t e d t o blow u p - i n l e t and i n frames d through f the flow can be seen to be slowed down and then r e v e r s e d on the e a s t s i d e and stopped on the west. The t i d e was ebbing throughout most of t h i s p e r i o d . Frame g shows t h a t , although the wind was s t i l l blowing u p - i n l e t and the t i d e was f l o o d i n g , the c u r r e n t on the west s i d e s t a r t e d t o flow down-inlet . Flow on the e a s t s i d e was s t i l l u p - i n l e t * , In frames h to k, the wind blew down-inlet weakly and the t i d e ebbed. Flow was s t r o n g l y down-inlet on the west and moved down-inlet more weakly over t h e r e s t of t h e area. At 58 hours, the wind s t a r t e d t o blow u p - i n l e t again and frames 1 and m show a developing u p - i n l e t flow f i e l d . By frame n the flow on the west had stopped and flow i n the n o r t h had stopped moving u p - i n l e t although i t was s t i l l moving a c r o s s the i n l e t . In the f i n a l frames the wind r e v e r s e d d i r e c t i o n and the flow reversed to be s t r o n g l y down-inlet. In frames o and p the t i d e was f l o o d i n g . In summary o f t h i s week of data, t h e r e were two r e v e r s a l s of flow from down-inlet t o u p - i n l e t t h a t were both a p p a r e n t l y c o r r e l a t e d t o s h i f t s i n the wind. The two s h i f t s 82 39 HR TO 42 HR f ' / r ~ F i g u r e 19 - The week 1 data set, F i g u r e 19 continued 84 F i g u r e 19 cont i n u e d . 85 i n c u r r e n t d i r e c t i o n from u p - i n l e t to down-inlet seemed to be c o r r e l a t e d mainly to e i t h e r c e a s i n g o f the wind or a s h i f t i n i t to down-inlet. There seemed to be some tendancy f o r the u p - i n l e t flow t o slow down d e s p i t e the c o n t i n u i n g u p - i n l e t winds. , The phase o f the t i d e d i d not seem to c o r r e l a t e with any change i n the c u r r e n t . IV. 3. 3 : Weeky2y-^aaV*-"T5^-18. 1973 • The data c o l l e c t e d i n week 2 o f the experiment are shown i n f i g u r e 20 a-x. The i n i t i a l c u r r e n t f i e l d was s t r o n g and down-in l e t except i n the v i c i n i t y of Watts Point where i t was almost s t a t i o n a r y . Winds were n e g l i g i b l e . E i g h t hours of moderate u p - i n l e t winds and a r i s i n g t i d e , as shown i n frames c and d, d i d very l i t t l e t o change t h i s p a t t e r n except t o reduce the s t r e n g t h o f the outflow. When the winds ceased a t 22 hours, the down-inlet c u r r e n t s t r e n g t h appeared t o i n c r e a s e . There was l i t t l e change i n the c u r r e n t p a t t e r n as the p e r i o d of calm continued through t o 36 hours. A s t r o n g l y ebbing t i d e seemed to have l i t t l e e f f e c t . For the next 9 hours, as shown i n f i g . 2 0 j — 1 t h e r e was a moderate u p - i n l e t wind and a r i s i n g t i d e . The down-inlet flow seemed to r e v e r s e t o up-i n l e t flow i n the v i c i n i t y of Watts P o i n t f o r a while. Outflow speeds dropped and t h e . r e g i o n of maximum down-inlet c u r r e n t moved westward. The down-inlet c u r r e n t s became s t r o n g e r and more uniform i n the p e r i o d from 51 to 59 hours as the t i d e ebbed and the wind blew weakly down-inlet. At 60 ? i g u r e 20 - The week 2 data s e t . 87 F i g u r e 20 c o n t i n u e d . 88 F i g u r e 20. c o n t i n u e d . 75 HR TO 78 HR 78 HR TO 81 HR 1 / / I I \ 1 \ \ 'igure 20 co n t i n u e d . v sy / / / 1 ^ I 1 1 i _\ 90 hours, the wind s t a r t e d t o blow f a i r l y s t r o n g l y u p - i n l e t and the down-inlet c u r r e n t v e l o c i t i e s decreased. For the next 12 hours (63h to 75h), the wind continued t o blow i n the same d i r e c t i o n , the t i d e f l o o d e d then remained constant and the s u r f a c e water moved g e n e r a l l y i n the u p - i n l e t d i r e c t i o n . On the western shore however, the down-inlet flow continued. When the wind d i e d , the c u r r e n t became once again uniform and down-inlet. In summary, t h i s week's data showed a flow f i e l d l e s s i n f l u e n c e d by the wind than the p r e v i o u s week's. No s i g n i f i c a n t t i d a l i n f l u e n c e was seen. Only the event from 60 to 72 hours bore much resemblance to the wind-water c o r r e l a t i o n of the week 1 data. IV.3.4 Week 3 - June 26-29,1973 The data c o l l e c t e d i n week 3 of these experiments are shown i n f i g u r e 21 a-w. In the f i r s t few hours, the c u r r e n t was unif o r m l y up-i n l e t . The wind was u p - i n l e t and the t i d e was r e l a t i v e l y s l a c k . At 23 hours, the wind d i e d . The p e r i o d from 24 t o 36 hours saw str o n g down-inlet c u r r e n t s with l i t t l e wind and an ebbing t i d e . At 36 hours the wind again became strong and u p - i n l e t . I t stayed t h a t way u n t i l 46 hours. The t i d e was f l o o d i n g i n frame h then remained r e l a t i v e l y s l a c k f o r 12 hours. The c u r r e n t i n h was s m a l l on average i n d i c a t i n g a change i n d i r e c t i o n from down to u p - i n l e t . The c u r r e n t remained strong and u p - i n l e t u n t i l k when the wind slackened 9 1 Figure 21 - The week 3 data set 92 / / / / v / / » \ / / / /I / / / / / / / / W / 33 HR TO 36 HR J 39 HR TO 42 HR / / N \ \ v i / / / 36 HR TO 39 HR 42 HR TO 45 HR f 1 / / J / 45 HR TO ag HR / '///'/ ' / i / / 48 HR TO 51 HR Figure 21 continued. 93 Figure 21 continued. 94 F i g u r e 21 c o n t i n u e d . 95 somewhat and the water s t a r t e d t o move down-inlet. T h i s continued i n frame 1 i n s p i t e of the u p - i n l e t winds. From 51 t o 60 hours, the c u r r e n t f i e l d was somewhat confused, with the water near the western shore moving b a s i c a l l y down-i n l e t , and the water near the southeast moving very slowly a t f i r s t but i n c r e a s i n g i n speed l a t e r u p - i n l e t . The wind i n t h i s p e r i o d was blowing u p - i n l e t with i n c r e a s i n g magnitude and the t i d e was ebbing. Frames p and g show a s t r o n g uniform u p - i n l e t c u r r e n t f i e l d , a moderate u p - i n l e t wind and a r i s i n g t i d e . A f t e r 66 hours, although the wind was s t i l l blowing u p - i n l e t , the c u r r e n t f i e l d became much l e s s homogeneous. Water i n the southwest was f l o w i n g out while water i n the e a s t was s t i l l f l o w i n g i n . In frame s, the wind almost ceased and a uniform down-inlet c u r r e n t f i e l d was formed t h a t p e r s i s t e d through frame v. The f i n a l frame, w, shows t h a t the down-inlet c u r r e n t had almost stopped. The winds had s t a r t e d t o blow u p - i n l e t and the t i d e was f i n i s h i n g a p e r i o d of ebb. In summary, t h e r e were two r e v e r s a l s o f flow from down-i n l e t t o u p - i n l e t . Both o c c u r r e d with u p - i n l e t winds and f l o o d i n g t i d e . I t seemed as i f a t h i r d r e v e r s a l of t h i s type was beginning i n s y n c h r o n i z a t i o n with an u p - i n l e t wind s h i f t a t the end of the experiment. Of the t h r e e r e v e r s a l s of flow from up- to down-inlet, one occurred as the wind d i e d , one as the wind decreased i n u p - i n l e t i n t e n s i t y and one preceded the c e a s i n g of the wind. The t i d e was r e l a t i v e l y s l a c k f o r two of these r e v e r s a l s and was ebbing f o r the t h i r d . 96 I-?. 3. 5 Ifefcv^ ;,.;T:f;Ju3:v:c-3-6v1973 The d a t a c o l l e c t e d i n week 4 o f t h e e x p e r i m e n t s a r e shown i n f i g u r e 22 a - w . , T h i s week o f d a t a was s i g n i f i c a n t l y d i f f e r e n t f r o m t h e o t h e r t h r e e . The w i n d b l e w u p - i n l e t t h e e n t i r e week and t h e a v e r a g e c u r r e n t v e l o c i t i e s we re r e a s o n a b l y u n i f o r m f o r t h e w h o l e week. A l l t h e f r a m e s show a d o w n - i n l e t c u r r e n t on t h e s o u t h s h o r e a n d an u p - i n l e t c u r r e n t on t h e n o r t h s h o r e . T h e r e a p p e a r e d t o be l i t t l e c h a n g e i n t h e c l o c k w i s e g y r e o f t h i s f l o w c a u s e d e i t h e r by t i d e o r by c h a n g e s i n w i n d s p e e d . 97 •50 •0 F i g u r e 22 - The week 4 data det. 98 F i g u r e 22 co n t i n u e d . 99 Figure 22 continued. 100 F i g u r e 22 c o n t i n u e d . 101 IV.3.6 Summary Of The Observations The f o u r weeks of data e x h i b i t e d two b a s i c a l l y d i f f e r e n t types of behaviour.,Wind and t i d e appeared to have l i t t l e e f f e c t on the c u r r e n t i n week 4 and o n l y a s m a l l e f f e c t i n week 2, t h e weeks c l o s e r t o the head of the i n l e t , while the c o r r e l a t i o n between wind and c u r r e n t appeared to be good i n weeks 1 and 3, the areas f a r t h e r from the head of the i n l e t . The e f f e c t o f the t i d e cannot yet be r u l e d out but c o r r e l a t i o n between t i d a l h e ight and c u r r e n t d i d not appear to be as good as the wind - c u r r e n t c o r r e l a t i o n . Sn attempt t o v e r i f y these hypotheses w i l l be made i n the succeeding s e c t i o n s . 102 IV.4 Temporal And Cross-channel V a r i a t i o n s In Surface -fra-yegFlow-Having now had an overview o f the g e n e r a l aspects of the data from the s u r f a c e l a y e r experiment, l e t us analyse these data i n g r e a t e r d e t a i l . A s e r i e s of f i v e • b a r s 1 were chosen a c r o s s the i n l e t a t the l o c a t i o n s shown i n f i g u r e 23. • E a c h bar, one mile wide i n the long-channel d i r e c t i o n , was s p l i t i n t o ten e q u a l l y s i z e d boxes a c r o s s the channel. The box averages done over one hour time i n t e r v a l s u s i n g these boxes are then c o n s i s t e n t with the s i z e suggested by the expected s c a l e of v a r i a b i l i t y of the flow as d i s c u s s e d i n chapter I I . Figure 24 shows the long-channel component of v e l o c i t y contoured as a f u n c t i o n of c r o s s - i n l e t p o s i t i o n and of time. In a channel of such i r r e g u l a r geometry as Howe Sound, the c h o i c e of the long-channel d i r e c t i o n at any g i v e n p o i n t i n the i n l e t i s somewhat a r b i t r a r y , but has been chosen as the d i r e c t i o n of the l i n e t h a t i s c l o s e s t t o p a r a l l e l t o both s i d e s of the i n l e t at t h a t p o i n t . T h i s d i r e c t i o n i s not n e c e s s a r i l y the d i r e c t i o n of the s t r o n g e s t c u r r e n t s as we s h a l l see. Each of the f i v e frames of t h i s f i g u r e r e p r e s e n t s the data from one of the averaging bars. A l s o i n c l u d e d i n each frame are the t i d a l h e i g h t curve from Pt. Atkinson and the wind v e l o c i t y from Squamish. The top of each frame r e p r e s e n t s the r i g h t hand s i d e of the channel (looking upstream). T h i s i s the southeast shore i n frames a and b, and the e a s t shore i n frames c, d, and e. For convenience. 103 104 Figure 24 - Contours of long-channel v e l o c i t y plotted as a function of time (horzontal) and cross-channel position ( v e r t i c a l ) . Contours are in cm/s. Positive currents are up-i n l e t . a, week 4. b. week 2 (north). c. week 2 (south). d. week 1. e. week 3. D i s t o n c e f r o m w e s t a i d e of channel (km) O - i 106 107 t h i s w i l l be r e f e r r e d to from now on as the e a s t shore i n a l l frames. By the same c r i t e r i o n , the bottom of each frame r e p r e s e n t s the west shore. The frames are arranged i n sequence with the band c l o s e s t t o t h e i n l e t head f i r s t and t h a t c l o s e s t t o the s i l l l a s t . In g e n e r a l t h e r e i s a t r e n d t o g r e a t e r l a t e r a l u n i f o r m i t y from frame a to frame e. T h i s t r e n d i s e v i d e n t i n t h a t the v e l o c i t y contours become more c l o s e l y a l i g n e d to the v e r t i c a l (cross stream) d i r e c t i o n proceeding from frame a t o e. The r e g i o n of s t r o n g e s t down-inlet flow i s on the e a s t i n frames a and b, but s h i f t s t o the west i n frames c and d. I t s l o c a t i o n i s not obvious i n frame e. T h i s presents a p i c t u r e c o n s i s t e n t with the q u a l i t a t i v e flow f i e l d p o s t u l a t e d a t the beginning of t h i s chapter. In frame a t h e r e i s l i t t l e v a r i a t i o n i n wind speed or d i r e c t i o n throughout the whole week. Therefore there should be no l a r g e v a r i a t i o n s i n the s u r f a c e c u r r e n t due t o wind. The peaks i n the down-inlet v e l o c i t y seem t o c o i n c i d e with peaks i n the t i d a l height. I t might be expected t h a t the t i d a l h e i g h t and the c u r r e n t would be 90° out of phase, so t h i s apparent in-phase r e l a t i o n s h i p might be i n d i c a t i v e of the a m p l i f i e d b a r o c l i n i c t i d a l response mentioned i n chapter I I I , T h i s hypothesis w i l l be i n v e s t i g a t e d f u r t h e r i n chapter V I I . Frame b has t h r e e peaks i n the wind curve as w e l l as l a r g e t i d a l v a r i a t i o n s . C o i n c i d e n t with each up-channel wind peak i s an u p - i n l e t c u r r e n t maximum. There i s a s l i g h t i n d i c a t i o n of c o r r e l a t i o n between maximum down-inlet 108 v e l o c i t i e s and peaks i n t i d a l h e i g h t at about 28, 46, 53, 70 and perhaps 78 hours. Frame c, made from data taken the same week as frame b, a l s o shows c o i n c i d e n c e between u p - i n l e t c u r r e n t maxima and up-channel wind maxima. T i d a l height maxima appear t o be c o i n c i d e n t with maxima i n down-inlet v e l o c i t y , but r e s u l t s seem l e s s c e r t a i n than i n frame b. In frame d, the v a r i a t i o n s i n c u r r e n t are more r e g u l a r than i n the previous t h r e e frames. Maxima i n upstream c u r r e n t occur a f t e r s e v e r a l hours of up-channel wind. ,• The onset of u p - i n l e t winds seems t o be c o i n c i d e n t with the time o f down-inlet c u r r e n t maxima. The stop p i n g of these winds and the s t a r t of down-inlet c u r r e n t s seem c o i n c i d e n t . T i d a l e f f e c t s are not obvious. The c u r r e n t maximum at 45 hours occurs j u s t before maximum t i d a l h e i g h t ; the one at 66 hours, at a minimum of t i d a l h e i g h t . Although there are too few c y c l e s to r e a l l y say f o r c e r t a i n , t h e r e does not appear t o be a c o n s i s t e n t r e l a t i o n s h i p between t i d a l h e ight and c u r r e n t maxima. In frame e, the c u r r e n t appears to be more l a t e r a l l y uniform. Temporal v a r i a t i o n s of the c u r r e n t are the stongest of a l l those observed. As i n frame d, maximum u p - i n l e t c u r r e n t s occurred a f t e r s e v e r a l hours o f u p - i n l e t winds. The down-inlet c u r r e n t maximum a t 32 hours was c o i n c i d e n t with the i n c r e a s e i n wind speed at t h a t time. Strongest down-i n l e t c u r r e n t s occurred when the wind speed was low. There d i d not appear to be any t i d a l c o r r e l a t i o n . To summarize t h i s f i g u r e we can say t h a t the wind 109 appeared to p l a y a more dominant r o l e i n f o r c i n g the s u r f a c e c i r c u l a t i o n than d i d the t i d e , although near the head of the i n l e t some t i d a l e f f e c t s seem probable. The h o r i z o n t a l shear decreased In s t r e n g t h from the head of the i n l e t to the s i l l but the magnitude of temporal v a r i a t i o n s i n c r e a s e d . T h i s l a s t o b s e r v a t i o n may be due of course t o d i f f e r e n c e s i n the f o r c i n g f u n c t i o n s from week to week, not to any in h e r e n t property of the i n l e t . Se have looked so f a r only at the long-channel component of the c u r r e n t . F i g u r e 25 shows the v e l o c i t y a t each c r o s s - c h a n n e l p o s i t i o n f o r each hour i n the averaging bars of week 3 and week 2 (north) . In each box, the v e l o c i t y i s represented by a v e c t o r , emerging from a s m a l l c r o s s marking the c e n t r e of the box, p o i n t i n g i n the d i r e c t i o n of the average c u r r e n t . The top and bottom of each frame r e p r e s e n t e a s t and west i n the same sense as the pre v i o u s f i g u r e . A v e c t o r p o i n t i n g t o the r i g h t t h e r e f o r e r e p r e s e n t s an average downstream c u r r e n t . In frame a, the c u r r e n t s are b a s i c a l l y up and down-channel with no s i g n i f i c a n t c r o s s -channel components. However i n frame b, there are two p e r i o d s when the c u r r e n t appears to be flo w i n g d i r e c t l y a c r o s s the i n l e t . I t i s not c l e a r i f t h i s c r o s s - i n l e t flow i s c o r r e l a t e d with the wind maxima or with the maxima i n t i d a l amplitude. These occurrences of c r o s s - i n l e t flow are at times when the r i v e r core i s f o r c e d north of i t s usual c r o s s - i n l e t path between Watts Pt. and Woodfibre., In weeks 1, 3,and 4, the long-channel component of v e l o c i t y was dominant and i n week 2, th e r e were not enough a F i g u r e 25 - R e l a t i v e v e l o c i t y vs c r o s s - c h a n n e l p o s i t i o n ana time f o r ^ a . week 3 b. week 2N. The arrows represent c u r r e n t v e c t o r s . t h e t a i l s of the v e c t o r s are l o c a t e d on s m a l l c r o s s e s at the c e n t r e s of the averaging boxes. They poin t i n the d i r e c t i o n t h at the c u r r e n t was f l o w i n g t o . 111 measurements made of the movements of the r i v e r core to make s t u d i e s o f the cros s - s t r e a m component p o s s i b l e . Further a n a l y s e s t h e r e f o r e are of the long-channel component of the g u a n t i t i e s o f i n t e r e s t o n l y . IV,5 Lateral;Homogeneity Of The V e l o c i t y And A c c e l e r a t i o n F i e l d s The contour p l o t s o f v e l o c i t y d i s c u s s e d i n the l a s t s e c t i o n showed, i n g e n e r a l , a gre a t d e a l o f l a t e r a l v a r i a t i o n i n the flow f i e l d . However the v e l o c i t y extrema occur at about the same time i n every c r o s s - c h a n n e l box. T h i s o b s e r v a t i o n i n d i c a t e s that the time r a t e o f change of v e l o c i t y may be more uniform than the v e l o c i t y i t s e l f . A c c e l e r a t i o n data were c a l c u l a t e d as the second d e r i v a t i v e of the s p l i n e f i t t e d drogue p o s i t i o n s . These a c c e l e r a t i o n s may, on average, be taken to be the time r a t e s o f change of v e l o c i t y i n the weeks 1 and 3 data s e t s as i s d e s c r i b e d l a t e r i n t h i s c h a p t e r . Since the curve f i t was c u b i c , these a c c e l e r a t i o n s are l i n e a r from p o i n t t o point of the i n p u t data. Small e r r o r s i n e s t a b l i s h i n g drogue p o s i t i o n s l e d to much l a r g e r e r r o r s i n the second d e r i v a t i v e s o f these p o s i t i o n e s t i m a t e s . Although the s p l i n e f i t t i n g r o u t i n e attempted t o minimize changes i n second d e r i v a t i v e s , the a c c e l e r a t i o n s cannot be expected to be as smooth as the v e l o c i t i e s . Thus more a c c e l e r a t i o n s than v e l o c i t i e s must be averaged together t o produce a smoothly v a r y i n g f u n c t i o n of 112 time or space. The average number of values i n a s i n g l e box of the s i z e used to generate the contour p l o t s produces smooth v e l o c i t i e s but does not produce smooth a c c e l e r a t i o n s . T h e r e f o r e meaningful contour p l o t s of a c c e l e r a t i o n cannot be produced. The a c c e l e r a t i o n s produced from the week 1 data set were the smoothest of a l l those c a l c u l a t e d and are, on average, e q u i v a l e n t to the time r a t e s of change of the v e l o c i t i e s . Using them, a rough check on the hypothesis of l a t e r a l homogeneity of a c c e l e r a t i o n may be performed. F i g u r e 26 shows v e l o c i t y vs. time and a c c e l e r a t i o n vs. time curves f o r t h r e e s e p a r a t e c r o s s - c h a n n e l l o c a t i o n s i n week 1, The data, from the same s o r t of box averaging done to produce the contour p l o t s of the l a s t s e c t i o n , are f o r box 2, near the e a s t s i d e of the channel; box 5, i n mid-channel ; and box 9, near the west s i d e . The three v e l o c i t y curves can be seen to have e s s e n t i a l l y the same shape but s u b s t a n t i a l l y d i f f e r e n t mean values. The maximum values, a t l e a s t i n the u p - i n l e t d i r e c t i o n , occur w i t h i n an hour of the same time f o r a l l t h r e e curves. Although the a c c e l e r a t i o n curves at f i r s t may appear to be g u i t e d i f f e r e n t from each other due to the high noise l e v e l a s s o c i a t e d with the s m a l l number of data averaged i n each box, the g e n e r a l f e a t u r e s of each curve are the same. The u p - i n l e t a c c e l e r a t i o n s between 36 and 48 hours and the down-inlet a c c e l e r a t i o n s between 48 and 57 hours and between 72 and 79 hours are common to a l l three curves. The high n o i s e l e v e l tends t o obscure the resemblance between the 113 F i g u r e 26 - V e l o c i t y and a c c e l e r a t i o n vs time at 3 c r o s s -channel l o c a t i o n s i n week 1. 114 thr e e curves between 48 and 72 hours, but there i s a common p e r i o d o f down-inlet a c c e l e r a t i o n f o l l o w e d by an u p - i n l e t p e r i o d i n a l l t h r e e . The mean values of the t h r e e curves appear t o be about the same. The high n o i s e l e v e l i n the a c c e l e r a t i o n curves may be due p a r t l y t o l o c a l s p a t i a l g r a d i e n t s of the v e l o c i t y f i e l d . These g r a d i e n t s may make an important c o n t r i b u t i o n t o the a c c e l e r a t i o n on a s m a l l s c a l e , but have a n e g l i g i b l e e f f e c t when averaged over the e n t i r e week 1 data s e t as i s shown i n s e c t i o n IV.8. The v e l o c i t y curves can be i n t e r p r e t e d as showing a mean shear flow o v e r l a i d by a l a t e r a l l y homogeneous time v a r y i n g flow. The a c c e l e r a t i o n curves show no strong evidence o f l a t e r a l v a r i a t i o n , suggesting t h a t the f o r c e s c a u s i n g temporal v a r i a t i o n s act homogeneously a c r o s s the i n l e t , and t h a t the search f o r the r e l a t i o n s h i p between the v a r i o u s f o r c e s and the temporal v a r i a t i o n s i n the s u r f a c e flow f i e l d may be j u s t i f i a b l y performed on l a t e r a l averages of v e l o c i t y and a c c e l e r a t i o n . IV.6 Temppra1 V a r i a t i o n s In 1 a t e r a 1 l y Averaged V e l o c i t i e s And A c c e l e r a t i o n s The t i m e - v a r y i n g c h a r a c t e r of the s u r f a c e l a y e r flow w i l l be presented i n t h i s s e c t i o n using data averaged a c r o s s the i n l e t . Data were taken from each of the f o u r weeks and box-averaged a c c o r d i n g to the scheme d e s c r i b e d e a r l i e r i n t h i s chapter. The ten box averages f o r each hour were averaged t o give the data s e t s presented here. Only one of 115 the week 2 data s e t s has been used. Since the v a r i a t i o n s i n wind v e l o c i t y were very s m a l l i n week 4, the data from week 2 (north) have been used i n s t e a d o f those from week 2 (south) because they r e p r e s e n t the behaviour o f the flow north o f Watts Pt, The l a t e r a l l y averaged v e l o c i t y and a c c e l e r a t i o n data are p l o t t e d i n f i g u r e 27 . The f o u r p l o t s on the l e f t hand s i d e of the f i g u r e are v e l o c i t y vs time p l o t s , the f o u r on the r i g h t are a c c e l e r a t i o n vs time p l o t s . The order from top t o bottom i s from the head of the i n l e t t o the mouth. P l o t a shows the average v e l o c i t y i n week 4. As might be expected from the contour p l o t , the average v e l o c i t y i s c l o s e t o zero with a range of only about ±15cm/s. The s m a l l v a r i a t i o n s i n v e l o c i t y appear t o be almost 180° out of phase with the t i d a l height..The a c c e l e r a t i o n , p l o t b, i s negative f o r almost a l l the time p e r i o d . T h i s r e s u l t i s a m a n i f e s t a t i o n of the d i f f e r e n c e between the t o t a l a c c e l e r a t i o n (Du/Dt=du/3t+u.vu), which the drogues measure, and the E u l e r i a n time r a t e of change, which a c u r r e n t meter would measure, and i n d i c a t e s t h a t the long-channel r a t e of change of v e l o c i t y i s a s i g n i f i c a n t p a r t of the t o t a l a c c e l e r a t i o n . R e s u l t s of c a l c u l a t i o n s of the magnitudes of the temporal and s p a t i a l v e l o c i t y g r a d i e n t s are given i n s e c t i o n IV.8. The v a r i a t i o n s i n the a c c e l e r a t i o n are too s m a l l t o c o r r e l a t e with e i t h e r wind or t i d e . , P l o t c shows the v e l o c i t y vs time i n f o r m a t i o n f o r week 2 n o r t h . The v e l o c i t y stayed at about -25 cm/s f o r about h a l f the time and made e x c u r s i o n s of +40 to -25cm/s from t h i s value. The three peaks i n up-channel v e l o c i t y occur 116 y T (m) (em/s^  fx 10') M * § V / - • r r r i •r 1 Li w (m/s) T 1 1 16 3g |AJ 1 1 •-1 1 —y 56 7S d 1 1 : — 1 1 1 1 - -\ / TJO\ J »_ / 1 L. \ r -a\ fen r • \ " v \ / I \» / V 1 A / 1 1 1 i 1 1 r « 37 57 7? F i g u r e 27 - L a t e r a l l y averaged v e l o c i t y and a c c e l e r a t i o n vs time. V e l o c i t y i s on the l e f t , a c c e l e r a t i o n on the r i g h t . The curved l i n e on the l e f t p l o t s i s the t i d a l h e i g h t , the squared l i n e on a l l p l o t s the long-channel wind component. P r o g r e s s i o n from top to bottom i s from head to s i l l . The e r r o r bars on the v e l o c i t y and a c c e l e r a t i o n p o i n t s are ± 1 SE. a and b. week 4. c and d. week 2N, e and f . week 1 . g and h. week 3. 117 d u r i n g the t h r e e p e r i o d s of up-channel winds. These peaks c o u l d a l s o be a s s o c i a t e d with the t i d a l height but then would have the o p p o s i t e phase r e l a t i o n s h i p with the t i d e to the week 4 data i n p l o t a. As w i l l be shown i n chapter VII, the up-channel v e l o c i t y i s approximately out of phase with the t i d e and thus the c o i n c i d e n c e o f the t i d a l peaks with the wind peaks probably reduces the v e l o c i t y peaks t o below what they would have been i f the t i d a l e f f e c t s d i d not occur. In p l o t d, the week 2 a c c e l e r a t i o n p l o t , p e r i o d s of u p - i n l e t a c c e l e r a t i o n c o i n c i d e with two of the u p - i n l e t wind peaks. Although the v e l o c i t y i n c shows no t r e n d , the a c c e l e r a t i o n i n d i s , i n g e n e r a l , n e g a t i v e , i n d i c a t i n g the same s o r t of r e l a t i o n s h i p between time and space g r a d i e n t s of v e l o c i t y as i n p l o t b. P l o t e shows the v e l o c i t y from the week 1 data s e t . The two v e l o c i t y maxima are i n phase with the wind. A constant phase r e l a t i o n s h i p between the c u r r e n t s and t i d a l height i s not e v i d e n t . The same o b s e r v a t i o n s can be made from p l o t g, the week 3 data. From these o b s e r v a t i o n s i t appears t h a t the wind i s causing the v a r i a t i o n s i n the s u r f a c e c u r r e n t . , The a c c e l e r a t i o n p l o t s , ( f and h ) , f o r weeks 1 and 3 help to c o n f i r m t h i s d e d u c t i o n . They both show p e r i o d s of r e l a t i v e l y c o n s t a n t u p - i n l e t a c c e l e r a t i o n s t a r t i n g a t the onset of up-i n l e t winds. These p e r i o d s l a s t 6 to 8 hours. Each p e r i o d i s f o l l o w e d by a p e r i o d o f negative a c c e l e r a t i o n . T h i s s o r t of behaviour w i l l be shown to be c o n s i s t e n t with a model of i n l e t behaviour t h a t p r e d i c t s a s u r f a c e l a y e r a c c e l e r a t i o n p r o p o r t i o n a l t o wind s t r e s s u n t i l the s t r e s s i s balanced by 11.8 the s u r f a c e pressure g r a d i e n t . IV. 7 Cross-channel Structurej^Of %he V ^ l p c i t y n F i e l d I t i s p o s s i b l e to g a i n some i n s i g h t i n t o the l a t e r a l s t r u c t u r e of t h e long-channel c u r r e n t s i n Howe Sound by l o o k i n g at a temporal average of the data. Data were averaged i n each box i n a c r o s s - c h a n n e l averaging bar f o r the e n t i r e l e n g t h of each week's o b s e r v a t i o n s . These averages were then combined on the p l o t s o f f i g u r e 28 t o show the average c r o s s - c h a n n e l s t r u c t u r e of the c u r r e n t s f o r each week. , When time averaging p e r i o d i c d a t a , i t i s necessary t o use an averaging i n t e r v a l t h a t i s an i n t e g r a l number of p e r i o d s long. Otherwise, anomalous v a l u e s r e s u l t . I t i s apparent from f i g u r e 27 t h a t the v e l o c i t y data from t h i s experiment are g u a s i - p e r i o d i c , p a r t i c u l a r l y i n weeks 1 and 3 when the v a r i a t i o n s i n wind v e l o c i t y were l a r g e . The data are not p e r i o d i c enough however to choose averaging i n t e r v a l s t h a t s t a r t e d and ended with the same amplitude and phase. Thus the average values may be i n e r r o r . However, i f the time v a r i a t i o n s are independent of the c r o s s - c h a n n e l p o s i t i o n as hypothesized, then the temporal averages are r e p r e s e n t a t i v e of the c r o s s - c h a n n e l v a r i a t i o n s i n the flow but the mean flow a c r o s s the channel may be i n e r r o r because o f the averaging over a s m a l l and n o n - i n t e g r a l number of c y c l e s . Looking then a t f i g u r e 28, we see that the down-inlet > - 2 0 J W Cross-Channel Position - i b F i g u r e 28 - Time averaged v e l o c i t y vs c r o s s - c h a n n e l p o s i t i o n . Bars are ± two standar d e r r o r s o f the mean, a. week 4 b. week 2N c. week 2 S d, week 1 e. week 3 . , 120 f l o w i n g r i v e r c o r e moves from the e a s t s i d e o f the channel i n week 4 t o the west s i d e i n week 1. T h i s core spreads out ac r o s s the channel as i t moves down-inlet. There appears t o be somewhat of a decrease i n core width from week 2N to 2S. T h i s change i s probably due to the geometry of the channel between those two averaging areas. The sharp bend around Watts Pt. f o r c e s t h e flow t o the western shore where the f o r c e s causing the flow t o change d i r e c t i o n and hence t o converge seem t o be l a r g e r than those causing i t to spread. The f a c t t h a t these temporal averages produce a p i c t u r e of the s u r f a c e l a y e r c u r r e n t s t r u c t u r e c o n s i s t e n t with the one formed from a l l the other forms o f data p r e s e n t a t i o n i s not p a r t i c u l a r t l y s i g n i f i c a n t . What i s s i g n i f i c a n t i s t h a t t h i s c o n s i s t e n c y supports the hy p o t h e s i s t h a t the l a t e r a l s t r u c t u r e of the s u r f a c e l a y e r i s b a s i c a l l y decoupled from the time v a r y i n g s t r u c t u r e . T h i s c o n c l u s i o n i s based on the premise t h a t , i f the l a t e r a l s t r u c t u r e were s i g n i f i c a n t l y time dependent, then temporal averaging over an a r b i t r a r y p e r i o d would tend t o obscure t h i s s t r u c t u r e . 121 IV,8 Ensemble Averaged V e l o c i t y G r a d i e n t s C a l c u l a t i o n s of the v e l o c i t y g r a d i e n t s du/Bx and bu/Sy i n these experiments e x h i b i t l a r g e s t a t i s t i c a l u n c e r t a n t i e s . These u n c e r t a n t i e s , a r i s i n g from c a l c u l a t i o n s i n v o l v i n g up t o f o u r t h d i f f e r e n c e s of the observed v a l u e s , tend t o obscure any s i g n i f i c a n t temporal or s p a t i a l v a r i a t i o n s i n the g u a n t i t i e s . However, t h e r e are enough determinations of these g u a n t i t i e s each week t o allow s t a t i s t i c a l l y s i g n i f i c a n t ensemble averaging of them. These ensemble averages were formed by c a l c u l a t i n g every v a l u e p o s s i b l e of the g u a n t i t y of i n t e r e s t from the box averaged data each week and averaging these together. I f the c r o s s - c h a n n e l v e l o c i t y v i s assumed to be s m a l l with r e s p e c t to the long-channel v e l o c i t y u, then the a c c e l e r a t i o n as measured by the drogues may be represented by a = a, " +a where a. - H / ^ t and a =u 3 u/ c> x. The term a^ may be approximated from the data s e t by a (t L) = (u ( t - < ( ) -u (t t _t) ) / (t U i - t . ) and hence a_^ may be c a l c u l a t e d from a (t.)=a ( t . ) - a ^ (t. ) . In these equations t, r e p r e s e n t s the time of the i ' t h c r o s s - c h a n n e l average, tj__, the time of the p r e v i o u s average and t- the time of the next average. R a t i o s of a to a, are shown i n t a b l e VI . As seemed apparent from f i g u r e 27, the a c c e l e r a t i o n data from weeks 2 and t are i n f l u e n c e d by s p a t i a l g r a d i e n t s much more g r e a t l y on average than are the data from weeks 1 and 3. In f i g u r e 27 the a c c e l e r a t i o n curves f o r weeks 1 and 3 appear t o be the time d e r i v a t i v e s of the v e l o c i t y curves. T h i s r e s u l t i s 122 Table VI - Ensemble average a c c e l e r a t i o n r a t i o and v e l o c i t y g r a d i e n t s . A c c e l e r a t i o n r a t i o i s u d u / d x d i v i d e d by N / b t . The v e l o c i t y g r a d i e n t s bu/ d x and d u / S y are i n u n i t s o f cm s - 1km- 1. Also shown are the standard d e v i a t i o n and the standard e r r o r of the mean value (or r.m.s.) of each g u a n t i t y . The standard e r r o r g i v e s an i n d i c a t i o n of the accuracy of the value, the standard d e v i a t i o n , of the spread i n values. 1 — _ . T r - " T -. i I Data s e t I wk 4 f wk 2N| wk 2Sl wk 1 | wk 3 | i — i _ _ _ _ _ J . i 1 i -t J — + -j r a t i o 1 1 J | mean 1 -0.88J -0.85J -0.41| 0.02J -0.091 I s t . dev. ! 1.14J 1. 32| 1.301 1.05| 0. 99J j s t . e r r . I 0.07| 0. 14| 0. 09 | 0.08J 0. 07J t | "bu/bx I ! j j j 1 j mean I 1.7 | -2.6 | 2.8 | 4.3 | 0.7 1 1 s t . dev. I 15.6 | 25.0 | 7.3 | 10.0 | 8.8 } I s t . e r r . I 0.9 i 2.6 | 0.5 | 0.7 | 0.6 J I d u/ o y ! | J ] | r . m.s» I 18.5 | 17.4 | 18. 0 | 15.5 | 11.1 | 1 s t . dev. ! 7.9 | 18.7 | 18.6 | 13.8 | 25. 9 I j s t . e r r . I 0.4 | 1.3 | 0.7 | 0.8 j 1.5 J i — _ J L — [ _ t s u b s t a n t i a t e d by the |a/a, I r a t i o s f o r those weeks of l e s s than 0.1. In weeks 4 and 2 (north) the a c c e l e r a t i o n appeared t o have a l a r g e component that d i d not vary as the time d e r i v a t i v e of the v e l o c i t y . T h i s f e a t u r e i s a l s o s u b s t a n t i a t e d by the a c c e l e r a t i o n r a t i o s . One guestion a r i s i n g from t a b l e VI i s the d i f f e r e n c e i n r a t i o s between week 2N and week 2S. I t seems unusual t h a t the a c c e l e r a t i o n r a t i o f o r the southern s e c t i o n should be only h a l f that i n n o r t h e r n s e c t i o n , i n s p i t e of s i m i l a r wind and t i d a l c o n d i t i o n s . The s e c t i o n from week 2 ( n o r t h ) , alone of the f i v e examined, o f t e n had c r o s s - c h a n n e l c u r r e n t s as s t r o n g as the long-channel ones. Therefore i t i s not c o r r e c t to assume 123 t h a t ' U d u / d x >> v d u / d y . Hence the s p l i t of the t o t a l a c c e l e r a t i o n i n t o terms c o n t a i n i n g only g r a d i e n t s of t and of x i s probably i n c o r r e c t . The r a t i o o f the s p a t i a l g r a d i e n t a c c e l e r a t i o n to the temporal g r a d i e n t a c c e l e r a t i o n i s l i k e l y i n c o r r e c t f o r the same reason. These same c a l c u l a t i o n s of a l e a d to the only d i r e c t d e t e r m i n a t i o n of the long-channel v e l o c i t y g r a d i e n t du/^x. Table VI shows the ensemble average of "du/^x f o r each s e c t i o n . These were c a l c u l a t e d by ensemble averaging a l l c a l c u l a b l e values of a^ /u. With the e x c e p t i o n of the week 2N value, a l l are p o s i t i v e as i s expected from the t r a d i t i o n a l e s t u a r i n e s a l t balance equations. The value f o r week 2N i s probably wrong f o r the reasons given above. The remaining values may be combined t o y i e l d an average value f o r ^ u/bx of 2.4±0.8 cm s-» km-*. The c a l c u l a t i o n of Vu/dy was a l s o p o s s i b l e from the box averaged data s e t s . I t was c a l c u l a t e d as an ensemble average o f the g u a n t i t y (u (y- )-u (y . )) / $ y where u(y.) and u (y. ) are s p a t i a l l y adjacent v e l o c i t y estimates and 6~y i s the s e p a r a t i o n between the adjacent boxes. Since i t i s expected t h a t the average measured shear a c r o s s the i n l e t at any one time w i l l be n e a r l y zero due t o i t s change i n s i g n a c r o s s the s e c t i o n , the r.m.s. shear was c a l c u l a t e d r a t h e r than the mean as an estimate of the amount of shear present i n each week of the experiment. The r e s u l t s of these c a l c u l a t i o n s are a l s o shown i n t a b l e VI . These r e s u l t s show the expected decrease i n shear from the head of the i n l e t t o the s i l l . The average o f these values i s 16±3 cm s~l km - 1. 124 These average v e l o c i t y g r a d i e n t s may be used t o deduce c o n s i s t e n t dimensions f o r the averaging boxes used i n t h i s a n a l y s i s . The r a t i o o f o u / bx to o u / o y i s 0.15±0.05. As was d i s c u s s e d i n chapter I I , the r a t i o o f width to l e n g t h (cross-channel dimension to long-channel dimension) of any averaging box should be the same as t h i s r a t i o to be c o n s i s t e n t . The dimensions u s u a l l y used were 0.2 to 0.3km by 1.8km y i e l d i n g r a t i o s between 0.11 and 0.16. Thus the box dimensions used were s a t i s f a c t o r y by t h i s c r i t e r i o n . 125 CHAPTER V INTERLUDE - THE THREE LEVEL DROGUE EXPERIMENT The s u r f a c e l a y e r drogue study j u s t d e s c r i b e d showed remarkable h o r i z o n t a l s p a t i a l v a r i a b i l i t y i n the observed c u r r e n t s . , T h e comprehensive s e t of c u r r e n t meter measurments t h a t w i l l be d i s c u s s e d i n the next chapter provide a p i c t u r e o f the temporal arid v e r t i c a l s p a t i a l v a r i a b i l i t y of the subs u r f a c e c u r r e n t s i n Howe Sound, but u n f o r t u n a t e l y p r o v i d e d no c l u e t o t h e deeper h o r i z o n t a l s t r u c t u r e . On September 6,1973, a s h o r t p i l o t experiment was performed a t the week 1 l o c a t i o n t o gain some i n s i g h t i n t o the h o r i z o n t a l and v e r t i c a l s t r u c t u r e of the c u r r e n t s i n the near s u r f a c e r e g i o n . The b a s i c procedure of the experiment was the same as the s u r f a c e drogue study,. The data were c o l l e c t e e d and recorded i n the manner d e s c r i b e d i n chapter I I . The drogues were, however, deployed i n a somewhat d i f f e r e n t manner. The pole and s a i l assemblies were the same as p r e v i o u s l y d e s c r i b e d but the s a i l s were suspended i n v a r i o u s ways to cover the depth ranges 0-2m, 2-4m and 4-6m. To cover the 0-2m depth range, the s a i l s were attached t o the poles i n the standard manner. To cover the 2-4m range, the s a i l s were attac h e d by t h e i r top r i n g s t o the bottom snap hooks of the po l e s . To cover the U-6m range, the s a i l s were suspended by 2m of polypropylene rope from the bottom snap hooks of the 126 po l e s . These three types of drogue w i l l be r e f e r r e d to from here on as the shallow, i n t e r m e d i a t e and deep drogues r e s p e c t i v e l y . Although the shallow drogues c l o s e l y f o l l o w e d the c u r r e n t from 0~2m, i t i s p o s s i b l e t h a t the i n t e r m e d i a t e and deep drogues d i d not measure the deeper c u r r e n t s as f a i t h f u l l y because of drag on the s u r f a c e area they had i n the shallow zone. The half-submerged f l o t a t i o n sphere had an approximate drag area of 500cm 2 i n the upper 20cm of the water column and the submerged h a l f of the pole had an approximate area of 450cm 2 i n the upper 2m. The drag on t h i s area caused by the v e l o c i t y d i f f e r e n c e between the upper and lower l a y e r s changes the v e l o c i t y e s t i mate of the lower l a y e r made with the drogues a c c o r d i n g to the f o l l o w i n g eguation: assuming t h a t the drag c o e f f i c i e n t s are about the same i n the two l a y e r s and t h a t the drag f o r c e s are a n t i - p a r a l l e l . In t h i s eguation 5 > T i s the t r u e v e l o c i t y a t depth, o i s the measured v e l o c i t y at depth and U i s the t r u e shallow ST v e l o c i t y . As and Aa are the areas o f the drogue i n the shallow and deep zones r e s p e c t i v e l y . Here the r a t i o of A,./A^  i s 1/60. The d i f f e r e n c e |U -0 | i n t h i s experiment had a maximum value of 1 cm/s and was u s u a l l y s m a l l e r . I t w i l l be igno r e d f o r subsequent a n a l y s i s . The drogues were t r a c k e d from 1120 when the experiment 1 2 7 s t a r t e d u n t i l 1420 when r a i n o b l i t e r a t e d the radar p i c t u r e . The shallow drogue t r a c k s are shown i n f i g u r e 29 . The flow observed was a t y p i c a l one. There was a strong southward flow i n the western h a l f of the region and a moderately s t r o n g northward flow i n the e a s t e r n h a l f . Drogue S3 moved c r o s s i n l e t from west t o east i n agreement with the standard eddy p a t t e r n observed i n week 1 of the s u r f a c e experiment. The t r a c k s o f the i n t e r m e d i a t e drogues are shown i n f i g u r e 30 . The westernmost drogue, 11, moved s t e a d i l y down-i n l e t , but the r e s t moved u p - i n l e t . 12 appeared t o s t a r t down but was caught by the u p - i n l e t flow and r e v e r s e d i t s d i r e c t i o n . The s t r o n g e s t flow was roughly mid-channel. The t r a c k s from the deep drogues are shown i n f i g u r e 31 . T h e westernmost drogue, D1, went nowhere but the other f o u r moved u p - i n l e t with the s t r o n g e s t flow e a s t of the c e n t r e of the i n l e t . V e l o c i t i e s were c a l c u l a t e d f o r a l l the drogue t r a c k s and box averaged f o r each l a y e r i n boxes 1/5 of the i n l e t width wide by three hours l o n g . The r e s u l t of t h i s procedure i s shown i n the v e l o c i t y contoured s e c t i o n i n f i g u r e 32 . The obvious f e a t u r e s of t h i s f i g u r e are the wedge of o u t f l o w i n g r i v e r water on the western s i d e and the core of r e t u r n flow j u s t e a s t o f c e n t r e channel a t 3m depth. U n f o r t u n a t e l y , p e r s o n n e l and a v e s s e l were not a v a i l a b l e t o make d e n s i t y measurements at the same time as the drogue measurements, so no comparison can be made between the c u r r e n t s and d e n s i t y s t r u c t u r e . The c o n c l u s i o n from t h i s s h o r t experiment i s t h a t the 128 F i g u r e 2 9 - Shallow drogue t r a c k s . Symbols i n d i c a t e the time o f f i r s t o b s e r v a t i o n of each drogue: x 1 1 5 6 , ° 1 2 2 6 , A 1 3 2 0 , D 1 3 5 2 . Heavier dots are l o c a t e d approximately every h a l f -hour along the t r a c k s . 129 F i g u r e 30 - Intermediate drogue t r a c k s , f i r s t observed at 1124. A l l drogues were 130 Figure 31 - Deep drogue t r a c k s . A l l drogues were f i r s t observed at 1124. c u to CD Q.E <_• " F i g u r e 32 - Contours of u p - i n l e t v e l o c i t y as deduced from 3 hour box-averages of the three l e v e l drogues. T o t a l channel width i s 2.8km. F i f t e e n bow averaged values were used to c o n s t r u c t t h i s contour p l o t , one value i n each o f the three depth ranges i n each o f f i v e c r o s s - c h a n n e l boxes. 132 l a t e r a l inhomogeneities, p r e v i o u s l y d e s c r i b e d i n the s u r f a c e l a y e r flow, are a l s o present i n the sub s u r f a c e flow. Within the " s u r f a c e l a y e r " as d e f i n e d i n chapter I I I , the flow i s not v e r t i c a l l y uniform. The s t r o n g e s t u p - i n l e t flow ocurred, not beneath the seaward flowing s u r f a c e l a y e r , as assumed i n t r a d i t i o n a l f j o r d t h e o r y , but j u s t below the s u r f a c e , a t the same depth as the deeper p a r t s of the outflow. Flow f i e l d s such as t h i s one are known to occur i n some shallow e s t u a r i e s , (Dyer,1973), but are not u s u a l l y a s s o c i a t e d with f j o r d s . The data r e c o r d s were not l o n g enough t o measure r e l i a b l y the drogue a c c e l e r a t i o n s and t o attempt to r e l a t e them t o changes i n the s u r f a c e winds. I f the p r e d i c t i o n s i n pr e v i o u s c h a p t e r s about s u r f a c e l a y e r depth and r e a c t i o n of the s u r f a c e l a y e r t o a wind s t r e s s are c o r r e c t , then the a c c e l e r a t i o n should be the same f o r the s u r f a c e and i n t e r m e d i a t e drogues, but s m a l l e r f o r the deep drogues which were nominally i n the i n t e r f a c e between the l a y e r s . T h i s h y p o t h e s i s remains to be confirmed i n f u t u r e s t u d i e s . The l a r g e l a t e r a l v e l o c i t y g r a d i e n t s found i n both the s u r f a c e l a y e r experiment and t h i s three l e v e l experiment f o r c e the qu e s t i o n of how deep do these l a t e r a l v e l o c i t y g r a d i e n t s p e r s i s t ? Since there i s no i n f o r m a t i o n a v a i l a b l e on t h i s g u e s t i o n at the present time the a n a l y s i s of the da t a from the c u r r e n t meter s t r i n g t h a t i s done i n the next chapter w i l l have t o proceed keeping i n mind the p o s s i b l e e x i s t e n c e of these g r a d i e n t s . 133 CHAPTER VI SUBSURFACE CURRENTS VI. 1 • • •'A.-; Descry pt ion, • Of The -.• ;Subsu, j - f a;cen vg;uy-rg;gt ••• Monito r i n g Proqramae A programme of sub s u r f a c e c u r r e n t monitoring was c a r r i e d out which complemented the s u r f a c e c u r r e n t study. S t r i n g s of c u r r e n t meters were i n s t a l l e d and maintained a t th r e e l o c a t i o n s i n the sound by the C o a s t a l Zone Oceanography Group of the I n s t i t u t e of Ocean S c i e n c e s , P a t r i c i a Bay, B.C. The data from these i n s t a l l a t i o n s have been p u b l i s h e d i n the form of p r o g r e s s i v e vector diagrams (PVD's), histograms of speed, d i r e c t i o n , temperature and s a l i n i t y and three - dimensional - histograms o f speed and d i r e c t i o n by B e l l (1975). Although t h e r e were th r e e d i f f e r e n t s i t e s used i n Howe Sound, on l y the one occupied between 24 November, 1972 and 23 February, 1974, whose l o c a t i o n i s shown i n f i g u r e 6 , w i l l be analysed here because i t was the o n l y one l o c a t e d i n s i d e the nor t h e r n b a s i n . A s e r i e s of oceanographic c r u i s e s was c a r r i e d out monthly by IOUBC p e r s o n e l i n Howe Sound d u r i n g the pe r i o d of c u r r e n t meter i n s t a l l a t i o n s t o monitor water p r o p e r t i e s t o lo o k f o r p o s s i b l e deep water movements too slow f o r the c u r r e n t meters t o r e g i s t e r . The r e l e v a n t r e s u l t s w i l l be 134 d i s c u s s e d l a t e r i n t h i s chapter. The c u r r e n t meters were i n s t a l l e d on t a u t l i n e moorings with s u r f a c e f l o a t a t i o n . Two separate moorings were used about 250m apart to minimize p o t e n t i a l equipment damage or l o s s due t o i n a d v e r t e n t snagging of the i n s t a l l a t i o n s by the many tug boats i n the area. During the o p e r a t i o n a l p e r i o d , no instruments were l o s t or o b v i o u s l y damaged i n t h i s manner. Current meters were i n s t a l l e d at depths of 3m, 5m, 10m, 15m, 20m, 30m, and 150m. A Geodyne model A-850 meter was used at 3m. I t sampled i n b u r s t s , r e c o r d i n g 15 samples of speed and d i r e c t i o n 5 seconds apart four times an hour. The d i r e c t i o n vane on t h i s instrument was g u i t e s m a l l , a l l o w i n g i t t o f o l l o w f a i r l y r a p i d changes i n d i r e c t i o n such as those caused by mooring motion and by the lower f r e g u e n c i e s of wave energy. In the subsequent a n a l y s i s , these b u r s t s were v e c t o r averaged t o minimize p o s s i b l e a l i a s i n g induced by such higher frequency motions. as a r e s u l t the meter produced one sample every 15 minutes. The r e s t of the c u r r e n t meters used were Aanderaa model ECM-4, They were set t o sample once every 10 minutes. The data v a l u e s produced were average c u r r e n t speed over t h e 10 minute i n t e r v a l and d i r e c t i o n as i n s t a n t a n e o u s l y measured a t the data r e c o r d i n g time. The claimed accuracy f o r the Geodyne meter i s ±26mm/s i n speed and ±10° i n d i r e c t i o n . I t s t h r e s h o l d speed i s 26mm/s. The accuracy of the Aanderaa meter i s ±4 mm/s i n speed (from the c a l i b r a t i o n formula) and ±5° i n d i r e c t i o n . I t s t h r e s h o l d i s 15 mm/s. 135 The data from these meters were t r a n s c r i b e d from the meters* i n t e r n a l l y recorded magnetic tapes to IBM compatable magnetic tape and then c a l i b r a t e d a c c o r d i n g t o the manufacturers s p e c f i c a t l o n s by W.H. B e l l of C o a s t a l Zone Oceanography. I t was from these f i n a l c a l i b r a t e d records t h a t t h e a n a l y s i s d e s c r i b e d i n t h i s chapter was done. VI. 2 Time-- S e r i e s • Bec^^:§6^g^Qff';;yh§\:€0^E^l!fe Meters -The time s e r i e s records from the c u r r e n t meters were looked a t f i r s t i n order t o spot any dominant f e a t u r e s and t o f o r e s e e any p o s s i b l e problems t h a t might be encountered i n the subsequent s p e c t r a l a n a l y s i s o f the data. F i g u r e 33 shows a s h o r t s e c t i o n (15 days) of the long-channel component of the c u r r e n t a t s i x depths and of the wind at Sguamish. The c u r r e n t data are a l l one hour vector averages and are p l o t t e d on the same s c a l e . D i u r n a l o s c i l l a t i o n s o f the c u r r e n t s are a dominant f e a t u r e of these r e c o r d s . They occur most s t r o n g l y In the 3m and 5m r e c o r d s but can a l s o be seen even i n the 150m r e c o r d ( f o r example, between 21 and 24 d a y s ) . The r e c o r d at 150m a l s o shows evidence of a s e m i - d i u r n a l o s c i l l a t i o n (from 24 to 28 days). The magnitude of the c u r r e n t s at 150m are l a r g e r than might be expected deep i n a f j o r d behind a s i l l . A study of the phase r e l a t i o n s h i p between the records proves q u i t e i n t e r e s t i n g . For the most p a r t , the 3m and 5m c u r r e n t s are very n e a r l y i n phase, although the 3m seems t o be l e a d i n g by a s m a l l v a r i a b l e amount. These c u r r e n t s a l s o Figure 3 3 - L o n g - c h a n n e l c o m p o n e n t s o f w i n d a t Squamish and currents from c u r r e n t m e t e r s at t h e d e p t h s i n d i c a t e d . Day 0 i s 8 J u l y 1 9 7 3 . A l l r e c o r d s a r e h o u r l y a v e r a g e s of t h e raw data. The s c a l e of a l l c u r r e n t s i s t h e same. Positive currents flow u p - i n l e t . 137 appear to be roughly i n phase with the wind. Throughout most of the r e c o r d the 5 and 10m c u r r e n t s appear t o be out of phase, but there are times, at 23.5 days, a t 25 days and a t 26.5 days f o r example, when the two appear to be i n phase. The 10m, 20m and 30m r e c o r d s appear t o be approximately i n phase. Ex c e p t i o n s occur at 17 days, 26 days and 31.5 days when 10m i s out of phase with 20m and 30m, and at 27.5 days when 20m i s out of phase with 10m and 30m. The phase r e l a t i o n s h i p between the 150m r e c o r d and the others i s not g u i t e as c l e a r but i t does appear t o be roughly out of phase wi t h the 30m meter and i n phase, at l e a s t between 21 and 24 days, with the 3m re c o r d . , T h i s s e c t i o n of data appears t o i n d i c a t e a th r e e l a y e r s t r u c t u r e i n the water column: a s u r f a c e l a y e r extending t o a depth of between 5 and 10m, a middle l a y e r extending t o below 30m t h a t o s c i l l a t e s out of phase with the s u r f a c e l a y e r , and a deep l a y e r encompassing the 150m meter t h a t o s c i l l a t e s i n phase with the s u r f a c e l a y e r . The o c c a s i o n a l d e p a r t u r e s from the standard phase r e l a t i o n s h i p show however that, the l e v e l s of no h o r i z o n t a l motion s e p a r a t i n g the l a y e r s are not constant i n depth i n the water column. L e v e l s o f no motion are d e f i n e d here as the depths a t which the amplitude of the h o r i z o n t a l c u r r e n t goes t o zero as i t changes phase from the waters above t o the waters below. T h i s d e f i n i t i o n i s used throughout the t h e s i s . Looking at the r e l a t i o n s h i p between the c u r r e n t s a t d i f f e r e n t depths i n t h i s f a s h i o n over such a s h o r t record cannot c o n c l u s i v e l y prove anything about the coherence and 138 r e l a t i v e phases o f the c u r r e n t s . Phase a n a l y s i s done i n freguency space v i a s p e c t r a l a n a l y s i s i s i n g e n e r a l much e a s i e r and more c o n v i n c i n g . But t h i s look a t the temporal r e c o r d shows a major problem t h a t w i l l a r i s e i n coherence and phase c a l c u l a t i o n s . T h i s problem i s caused by the s h i f t s i n the l e v e l s o f no motion. Since these s h i f t s cause r a d i c a l changes i n the r e l a t i v e phase of c u r r e n t s recorded by ad j a c e n t c u r r e n t meters, they w i l l cause anomalous r e s u l t s i n any coherence or phase measurements. P e r i o d s of a l t e r n a t e i n phase and out of phase c u r r e n t s w i l l tend to c a n c e l and y i e l d low coherence l e v e l s when the c u r r e n t s are a c t u a l l y q u i t e coherent but with an unsteady phase r e l a t i o n s h i p . The c u r r e n t r e c o r d s shown i n f i g u r e 3 3 c o n t a i n a l a r g e number of ' s p i k e s ' , i . e. a r t i f i c i a l l y l a r g e changes i n magnitude or s i g n such as the one at 20m, 21 days or 10m, 31.2 days. Most of these s p i k e s are due t o mooring motion as w i l l be d i s c u s s e d i n the next s e c t i o n , but th e r e are some very r a p i d changes t h a t are caused by something d i f f e r e n t . As was shown by the r e s u l t s of chapters IV and V, the r i v e r v e l o c i t y core i n the g e n e r a l v i c i n i t y of the c u r r e n t meters i s not uni f o r m l y d i s t r i b u t e d a c r o s s the I n l e t and extends down only 4 or 5 metres. The Bsovement o f s i l t p a t t e r n s and of the drogues i n weeks 1 and 3 shows t h a t t h i s r i v e r core can change i t s p o s i t i o n i n the channel. I f the r i v e r core were not f l o w i n g a c r o s s the c u r r e n t meters, the 3m meter would probably r e g i s t e r an u p - i n l e t flow or a weak down-i n l e t flow. I f the core then moved over the c u r r e n t meters, the 3m meter would be expected t o show a r a p i d i n c r e a s e i n 139 down i n l e t c u r r e n t s t r e n g t h and then a r a p i d decrease as the r i v e r core passed by the meters. T h i s type of event i s seen a t 27 t o 27,5 days. Current v a r i a t i o n s Of t h i s s o r t are uncor r e l a t e d ' with t h e other c u r r e n t measurements i n the f j o r d and are only i n d i r e c t l y r e l a t e d t o the f o r c e s causing the c u r r e n t s . T h i s quick look a t the c u r r e n t r e c o r d s p r o v i d e s some i n s i g h t i n t o what t o expect from t h e i r s p e c t r a l a n a l y s i s . There appears t o be a l a r g e amount of coherent d i u r n a l energy. The c a l c u l a t e d coherence w i l l be l e s s than the r e a l coherence due t o phase r e v e r s a l s of the c u r r e n t s caused by s h i f t s i n the l e v e l s o f no motion. Some s e m i - d i u r n a l energy i s a l s o present but coherence between the c u r r e n t s a t d i f f e r e n t depths at t h i s frequency i s not obvious. Other s t r o n g components a t d i f f e r e n t f r e q u e n c i e s are not o b v i o u s l y p r e s e n t but they may be hidden by the s p i k e s i n the data. The e f f e c t s of these s p i k e s must be i n v e s t i g a t e d before proceeding much f u r t h e r i n t o the a n a l y s i s . VI.3 S p e c t r a l A n a l y s i s Of The Cu r r e n t s The technigue of s p e c t r a l a n a l y s i s was used on the data r e c o r d s of c u r r e n t and wind. The data records analysed covered the high r u n o f f p e r i o d i n the s p r i n g and summer of 1973, spanning a p e r i o d of 177 days from 20 Harch t o 13 September. The anemometer a t Squamish s u f f e r e d many breakdowns d u r i n g the p e r i o d of the c u r r e n t meter i n s t a l l a t i o n s but was o p e r a t i o n a l c o n t i n u o u s l y f o r the 177 140 day p e r i o d . The c u r r e n t meters at 5m, 20m, 30m and 150m operated f o r t h i s e n t i r e p e r i o d . The meter at 3m operated f o r 150 days, from 20 March t o 17 August; the one at 10m f o r 140 days from 26 A p r i l to 13 September. The meter at 15m o n l y operated u n t i l 6 June, producing only two data r e c o r d s and so w i l l not be considered f o r f u r t h e r a n a l y s i s . The data a t each depth c o n s i s t e d of four ' : s e c t i o n s of data between 35 and 68 days long with a gap of u s u a l l y about one day between each s e c t i o n . VI.4 Techniques And Problems Of A n a l y s i s The techniques of s p e c t r a l a n a l y s i s are w e l l known and documented (e.g. Bendat and P i e r s o l , 1971,or Jenkins and Watts,1968) and w i l l not be d e s c r i b e d i n d e t a i l here. Power s p e c t r a and coherences were c a l c u l a t e d using programmes w r i t t e n by Ian T. Webster and d e s c r i b e d i n Webster and Farmer (1976). The programmes transformed the data using the f a s t F o u r i e r t r a n s f o r m (FFT) a l g o r i t h m of S i n g l e t o n (1969). FFTs were c a l c u l a t e d on the f i r s t 76 8 hours (32 days) of each c u r r e n t meter r e c o r d and the same p e r i o d of wind r e c o r d s i m u l t a n e o u s l y . There were no p e r i o d s of missing data t h a t had to be f i l l e d i n any of the r e c o r d s . S p e c t r a l , c o s p e c t r a l and g u a d s p e c t r a l values were c a l c u l a t e d from the F o u r i e r transforms of each data r e c o r d . At each depth these v a l u e s were averaged over the f o u r or f i v e r e c o r d s t o y i e l d •ensemble* averages of the q u a n t i t i e s . Band (frequency) averaging was a l s o done on the s p e c t r a . The bandwidth used 141 was A ( l o g 1 0 f ) = 0.1. Coherence and phase of the s i g n a l s were c a l c u l a t e d from the band and block averaged s p e c t r a l data. A major problem with s u r f a c e moored c u r r e n t meters i s wave induced d i s t o r t i o n o f the s i g n a l which can come e i t h e r from d i r e c t wave a c t i o n on a shallow c u r r e n t meter or i n d i r e c t l y from wave a c t i o n moving the s u r f a c e buoy and hence moving the c u r r e n t meter through the water around i t . E i t h e r way the e f f e c t s on the meter are s i m i l a r . One m a n i f e s t a t i o n of t h i s problem i s e x c e s s i v e l y l a r g e recorded speeds ("rotor pumping") caused by sh o r t p e r i o d wave induced c u r r e n t s . These f i c t i t i o u s speeds are a r e s u l t of the sampling scheme of a Savonius r o t o r s t y l e o f c u r r e n t meter t h a t r e c o r d s an i n t e g r a t e d c u r r e n t speed over the sample p e r i o d o f the meter but onl y r e c o r d s an instantaneous d i r e c t i o n at the end of the sample p e r i o d . The problem i s reduced i n c u r r e n t meters such as the AMF Vector Averaging Cu r r e n t Meter (VACM) whose sample p e r i o d i s dependent on the c u r r e n t speed and i s g e n e r a l l y l e s s than t h a t of the wave induced c u r r e n t s . There have been s e v e r a l e s t i m a t e s of the magnitude of the di s c r e p a n c y between a c t u a l and recorded c u r r e n t s . Saunders (1976) compared drogue measured v e l o c i t i e s with those o f a VACM i n a manner s i m i l a r t o the comparison done i n chapter I I I and found s i m i l a r l y t h a t the two g i v e comparable r e s u l t s . He then compared the VACM r e s u l t s t o an Aanderaa RCM-4 and found a r a t i o of 2.3:1 between the mean v e l o c i t i e s as recorded by the Aanderaa and the VACM over a 12.5 day p e r i o d . However he found t h a t the 142 a c t u a l r o t o r speeds of the two meters were almost i d e n t i c a l , i n d i c a t i n g t h a t the d i f f e r e n c e l a y i n the a l i a s i n g of the r a p i d l y changing c u r r e n t d i r e c t i o n onto the slow sample r a t e o f the Aanderaa's d i r e c t i o n sensor. H i s measurements were made at 12m on a mooring i n 2500m of water. Halpern and P i l l s b u r y (1976) have compared r e s u l t s from s u r f a c e moored and subsurface moored Aanderaa c u r r e n t meters i n shallow (50m) water and found a r a t i o of mean speeds of 2.1:1 between s u r f a c e and subsurface moored meters. However the shapes of the s p e c t r a were the same at f r e q u e n c i e s l e s s than 0.7cph. At g r e a t e r than 0.7 c y c l e s per hour (cph) t h e r e was more energy i n the spectrum o f the s u r f a c e moored meter. S i m i l a r r e s u l t s were obtained by Halpern et a l (1974) i n a shallow water instrument i n t e r c o m p a r i s o n between a s u r f a c e moored VAGH, a s u r f a c e moored Geodyne A-850 and a subsurface moored Aanderaa RCM-4. Below a frequency of 0.45cph they found the c u r r e n t s p e c t r a t o be the same. I t i s d i f f i c u l t t o understand why the shapes of the wave i n f l u e n c e d and the non-wave i n f l u e n c e d s p e c t r a should be the same. P e r i o d i c f l u c t u a t i o n s i n the s t r e n g t h of the wave f i e l d , caused by v a r i a t i o n s i n wind s t r e n g t h , e i t h e r d i u r n a l as expected i n c o a s t a l r e g i o n s l i k e Howe Sound or with the p e r i o d of weather systems as seen i n the oceans, should add energy to the wave i n f l u e n c e d spectrum at these p e r i o d s and hence c r e a t e a l a r g e d i s p a r i t y between the r e c o r d s s p e c i f i c a l l y a t these p e r i o d s . I t i s p o s s i b l e t h a t the r e c o r d s analysed were too s h o r t to examine the behaviour of the s p e c t r a a t f r e q u e n c i e s low enough t o get away from 143 atmospheric p e r i o d i c i t y . These r e s u l t s l e a d t o the c o n c l u s i o n that c u r r e n t meters l i k e the Aanderaa with simple sampling schemes w i l l not reasonably measure the water v e l o c i t y when e i t h e r the meter or the top of the mooring i s exposed to wave a c t i o n . A l l the meters used i n t h i s experiment below a depth of 3m were Aanderaas. I t i s p o s s i b l e t h e r e f o r e t h a t the measured c u r r e n t s w i l l be too l a r g e . However the mooring was i n r e l a t i v e l y shallow, p r o t e c t e d waters so the waves were not l a r g e and the mooring was r e l a t i v e l y s t a b l e . Comparison between the drogues and 3m c u r r e n t s and the 3m and 5m c u r r e n t s showed them to be s i m i l a r i n magnitude so t h a t the wave-induced a m p l i f i c a t i o n of c u r r e n t s does not appear to be l a r g e i n t h i s case. Another symptom of wave a c t i o n on a subsurface c u r r e n t meter i s "vane f l o p " . In s u r f a c e waters the magnitude of the wave induced c u r r e n t s may be much l a r g e r than the mean c u r r e n t s . The magnitude of the wave induced c u r r e n t i s : u=ao exp (- u) 2z/g) (6.1) so f o r example i n a t y p i c a l wave f i e l d of 0.5m, 4 second waves, the c u r r e n t amplitude at 3m depth i s 37cm/s and a t 5m i s 22cm/s. The buoy f o l l o w s the waves to some extent and t h e r e f o r e the meters move i n the same d i r e c t i o n as the water, so the a c t u a l wave-induced c u r r e n t seen by the meters i s s m a l l e r than the above val u e s . An o s c i l l a t i n g c u r r e n t , 144 induced by waves of t h i s f o u r second p e r i o d , superimposed on an average c u r r e n t may cause a complete r e v e r s a l of the c u r r e n t d i r e c t i o n every two seconds. The d i r e c t i o n vane on an Aanderaa meter i s t o o l a r g e t o respond to t h i s r a p i d l y changing d i r e c t i o n , but i t w i l l be d e f l e c t e d from i t s mean p o s i t i o n . Because the d i r e c t i o n i s measured only once per r e c o r d i n g c y c l e , the recorded d i r e c t i o n w i l l be a random s c a t t e r of values about the mean. When speed and d i r e c t i o n a r e l a t e r combined i n t o v e l o c i t y components, t h i s f l o p w i l l m anifest i t s e l f as a s e r i e s o f s p i k e s i n the r e c o r d t h a t decrease the flow along i t s p r i n c i p a l a x i s and i n c r e a s e i t p e r p e n d i c u l a r t o that a x i s . Behaviour of t h i s s o r t i s seen i n f i g u r e 34 . T h i s f i g u r e shows a s h o r t s e c t i o n of data from the 5m c u r r e n t meter. Over the e n t i r e r e c o r d the speed t r a c e i s q u i t e smooth but the d i r e c t i o n t r a c e c o n t a i n s many s p i k e s . The long-channel component of v e l o c i t y i s u s u a l l y decreased by these s p i k e s and the c r o s s - c h a n n e l component i s u s u a l l y i n c r e a s e d . T h i s behaviour i s p a r t i c u l a r l y e v i d e n t i n the v i c i n i t y o f day 3 i n the p l o t . The smoothed long-channel component of v e l o c i t y d i s c u s s e d i n the next paragraphs i s a l s o shown i n t h i s f i g u r e . A simple t e s t o f the e f f e c t of these s p i k e s on the subseguent data a n a l y s i s was performed. The fou r 5m records were p l o t t e d on an i n c r e m e n t a l p l o t t e r a t a s c a l e of 16.67hr/inch. A s u b j e c t i v e l y smooth curve was then drawn through each t r a c e and d i g i t i z e d on a Gradicon d i g i t i z i n g t a b l e at 10 p o i n t s / i n c h . Thus the i n t e r p o l a t e d r e c o r d had about one p o i n t per 1.67 hours. The d i g i t i z e d data were then 145 Figure 34 - A section of record from the 5m current meter showing spikes in the component and di r e c t i o n records due to "vane fl o p " . The smoothed and unsmoothed long-channel v e l o c i t y components were used to calculate the spectra and coherences in f i g 35. The time o r i g i n i s 20 March 1973. 146 s p l i n e - f i t t e d with no e x t r a smoothing allowed and i n t e r p o l a t e d t o r e g a i n the s i x values per hour t h a t the o r i g i n a l r e c o r d s had. These two s e t s of c u r v e s , smoothed and unsmoothed, were then F o u r i e r transformed and s p e c t r a l analysed ~in the manner d e s c r i b e d p r e v i o u s l y . The r e s u l t i n g s p e c t r a are shown i n f i g u r e 35 . A t f r e q u e n c i e s l e s s than 6cpd the s p e c t r a l l e v e l s f o r the smoothed record were about 1db higher on average than those i n the unsmoothed one. .This d i f f e r e n c e i s w i t h i n one standard e r r o r on a l l p o i n t s . Above t h i s frequency, the spectrum of the noisy r e c o r d d i s p l a y s a broad peak c e n t r e d at 20cpd. The spectrum of the smoothed r e c o r d drops o f f r a p i d l y above 6cpd as i t must. T h i s c r i t i c a l frequency of 6cpd i s q u i t e c l o s e to the Nyguist frequency, 7.2cpd, of the smoothed data s e t . The coherence between the two s i g n a l s i s almost u n i t y below f r e q u e n c i e s of 2.4cpd. I t drops r a p i d l y at h i g h e r f r e q u e n c i e s and approaches the expected n o i s e coherence l e v e l a t 9cpd, The phase between the two s i g n a l s i s very c l o s e to zero a t a l l f r e g u e n c i e s l e s s than 9cpd. T h i s "brute f o r c e " removal o f the vane f l o p s p i k e s from the data r e c o r d appears not to have a f f e c t e d the phase of the s i g n a l i n the frequency range of i n t e r e s t and only t o have i n c r e a s e d the low frequency s p e c t r a l l e v e l s s l i g h t l y , i n d i c a t i n g t h a t t h e r e i s l i t t l e leakage of energy from the h i g h f r e q u e n c i e s caused by vane f l o p t o the lower f r e g u e n c i e s t h a t are o f i n t e r e s t i n t h i s a n a l y s i s . These two p o t e n t i a l problems with data from "simple" c u r r e n t meters may l e a d to problems i n the i n t e r p r e t a t i o n o f 147 Figure 35 - Spectra, coherence and phase of the "noisy" 5m c u r r e n t meter records and "smoothed" 5m records. The l i n e on the coherence p l o t i s the expected coherence of two random s i g n a l s with the same number of degrees of freedom as the data, as explained i n the t e x t i n s e c t i o n 6 . 5 . The e r r o r bars on the s p e c t r a l points are +1 SE. 148 the r e s u l t i n g s p e c t r a . However, the shape of the s p e c t r a i n the frequency range of i n t e r e s t i n t h i s experiment appears t o be u n a f f e c t e d by vane f l o p . The s p e c t r a l l e v e l s are probably boosted somewhat by r o t o r pumping. However, s p e c t r a l g u a n t i t i e s l i k e coherence and phase, i n which t h i s i n c r e a s e i n s p e c t r a l l e v e l should be n u l l i f i e d by n o r m a l i z a t i o n , should be r e l a t i v e l y u n a f f e c t e d by problems of s u r f a c e moorings. VI. 5 R e l i a b i l i t y And S t a b i l i t y O f C o h e r e nee Estimates Before we can t r u s t coherence and phase values however, we must have some c r i t e r i o n upon which to judge the s t a b i l i t y and r e l i a b i l i t y o f these measurements. A c r i t e r i o n g i v e n f o r r e l i a b i l i t y i n Bendat and P i e r s o l (1971) i s the ( 1 - ^ ) c o n f i d e n c e i n t e r v a l . They say that a coherence $ has o n l y an c ( t o 1 chance of being o u t s i d e the l i m i t s : tanh ( t a n h - 1 i> - ( V - 2 ) ~ l - z ^ ( V - 2 ) - 1 / 2 ) < t < t a n h ( t a n h - 4 ^ - ( V - 2 ) - * + z , (v-2)-*£) (6.2) where V i s the number o f degrees of freedom of the estimate and z i s a b c i s s a of a standard normal d i s t r i b u t i o n such t h a t the area under the curve between z , and oo i s <x/2. These l i m i t s are v a l i d only f o r 0.35< 95 and f o r S) >20, 149 but are probably not too wrong o u t s i d e these l i m i t s . J e n k i n s and Watts (1968) proposed another approach to the g u e s t i o n of coherence r e l i a b i l i y . They c a l c u l a t e d the expected coherence o f two random s i g n a l s with the same number of degrees of freedom as the coherence estimate under t e s t . T h i s i s ^ r = 1/2/y where V i s the number of degrees of freedom. Since t h i s number r e p r e s e n t s the l e v e l of no r e a l coherence (but with a f i n i t e r e c o r d l e n g t h so t h a t the c a l c u l a t e d coherence i s non-zero), presumably any c a l c u l a t e d coherence above t h i s v alue would be g r e a t e r than z e r o i f an i n f i n i t e r e c o r d l e n g t h were a v a i l a b l e . A t e s t was performed on the r e l a t i o n s h i p between the s t a b i l i t y o f coherence and phase and the number of degrees of freedom by c a l c u l a t i n g FFT•s using the wind s i g n a l and the ho u r l y averaged 5m c u r r e n t as i n p u t s . The f i v e r e s u l t i n g b l o c k s of s p e c t r a l e s t i m a t e s were averaged. D i f f e r e n t numbers of these bands were then averaged together and the coherence and phase between wind and c u r r e n t c a l c u l a t e d . In t a b l e VII the r e s u l t s of t h i s t e s t i n the bands c o n t a i n i n g the 24.00 hour p e r i o d (high coherence expected) and the 12.42 hour p e r i o d (no coherence expected) are shown. Also shown are the 95% c o n f i d e n c e i n t e r v a l s about the coherences and the expected random coherence. Let us look f i r s t at coherence i n the 24 hour band. I t i s high f o r 10 degrees of freedom but l e v e l s o f f to a value near 0.5 between 4 0 and 100 degrees cf freedom. Beyond t h i s p o i n t the coherence drops s l o w l y . In every case, the lower l i m i t of the 95% c o n f i d e n c e l i m i t i s w e l l above zero, 150 T a b l e VII - Coherence and phase estimates between wind and 5m c u r r e n t s f o r d i f f e r e n t numbers of degrees of freedom between 10 and 100 i n two d i f f e r e n t bands. Confidence l i m i t s a r e 95% and are shown j u s t above and below each coherence. V i s the number o f degrees of freedom. The phase angle i s given i n degrees. , ., , f T 1 , I I 24.00 hours | 12.42 hours J n o i s e | 1 V j coh J p h a s e | coh J phasej coh | 1 -I +- 4 4 f 1 I I . 9 1 1 1 . 7 8 ! I 1 j 10 | .75* J -13 j .44* | -101 | .45 | I | . 1 5 | | - . 3 3 | 1 | I I .84 | | . 67 | | | | 20 | .67 | -11 J .38 | -149 | .32 | I ! .29 | j - . 1 2 J | | ! I .78 | | .52 | J | I 30 | .61 | -7 | .24 | -131 | .26 | I I .29 | | - . 1 6 | | | I | .68 | \ .47 ) | | | 40 j .49 | - 5 | .22 f -37 | .22 I I ! . 1 9 | | - . 1 2 | | | ! 1 .71 | | .43 | | | I 50 | .55 | -4 j .22 | -39 | .20 j I | .30 | I - . 1 0 | | | \ I .70 1 | .40 | } | I 60 J .55 1 -3 | .18 | - 40 | . 18 | I I .33 } | - . 0 9 | | | ! I .60 j | .36 | | | | 70 | .44 | 0 | .15 } -114 | .17 | I I .22 J | - . 1 0 J | | I I .58 | | .38 | I | I 80 j .42 | -5 | .19 | -37 | .16 | 1 1 .21 | } - . 0 4 J | | I I .58 i | . 3 1 1 1 I I 90 | .44 | 2 | . 1 2 | -2 J .15 | I ! .25 | J - . 1 0 I J | i | .62 | | .23 | | | I 100 | .49 | - 3 J .05 | -53 | .14 | I ! .32 | | - . 1 6 I | | I L : 1 1 1 | J 151 Table VII continued f o r ^  between 120 and 640. | 24.00 j coh T ~ T" hours J j phase| 12. 42 coh -T— —r-hours | I phase| ~ - •• — i noise | coh | I 120 I .53 I .39 I .22 i 1 1 .23 .06 -.13 T -55 | . 13 j | 160 I .47 I .34 1 .19 J -8 | . 27 .13 -.03 | -45 | • 11 I I 200 I .45 I .34 I . 21 ] -2 | . 22 .09 -.05 ! -45 | .10 | | 320 J .35 I .25 I . 14 ! -5 1 .24 .14 .03 ! 24 | • 08 I I 480 | .32 I .24 I .15 1 0 1 . 13 .04 -.05 -70 | .06 | | 640 J .29 I .22 I . 14 __ _ -2 | — __ . 15 .08 .00 -177 i j .06 { i n d i c a t i n g t h a t t h e r e i s l e s s than a 2.5% chance t h a t any of the c a l c u l a t e d coherences are a c t u a l l y z e r o . A comparison of the coherences with the a s s o c i a t e d random noise coherences shows that the c a l c u l a t e d v a l u e s are a l l w e l l above the n o i s e l e v e l . By both c r i t e r i a o f r e l i a b i l i t y then t h i s band has some coherence. The a c t u a l v alue of the coherence appears t o be about 0.5. T h i s value i s w i t h i n the 95% co n f i d e n c e i n t e r v a l of a l l estimates up to 120 degrees of freedom. Above t h i s number, the freguency band i s wide enough to i n c l u d e enough n o i s e to mask the one narrow band of coherent s i g n a l . The phase of the s i g n a l s however s t a y s remarkably constant at -5°±7° over the e n t i r e range of the t e s t . 152 Looking now a t the 12.42 hour band, we can see t h a t the coherence drops s t e a d i l y as the number of degrees of freedom i s i n c r e a s e d . I t s value i s always c l o s e to the n o i s e coherence f o r the a p p r o p r i a t e number o f degrees of freedom. In a l l cases but one, the lower bound o f the 95% c o n f i d e n c e i n t e r v a l i s egual t o or l e s s than zero. Thus both c r i t e r i a have shown the s i g n a l s i n t h i s band to be i n c o h e r e n t . The phase of the s i g n a l s i s e r r a t i c , showing v a r i a t i o n s of almost ±90°. Both c r i t e r i a f o r r e l i a b i l i t y of coherence estimates appear t o be workable.,From now on only one of the two w i l l be used, the l e v e l of random n o i s e coherence. Below about 40 degrees of freedom, coherence estimates do not appear to have reached a s t a b l e l e v e l . In t h e band averaged s p e c t r a shown i n t h i s chapter, the 24.00 hour band has 70 degrees of freedom, the 12.42 hour band has 130. Both of these bands of i n t e r e s t s hould then produce a c c u r a t e coherence and phase e s t i m a t e s . 153 VI.6 Mean Currents The Fourier transform programme c a l c u l a t e d the mean value o f each i n p u t data b l o c k . The mean value f o r the c u r r e n t at each depth over the 177 days of a n a l y s i s may t h e r e f o r e be c a l c u l a t e d as the average of the mean value s from each of the f o u r o r f i v e data b l o c k s which comprise the e n t i r e r e c o r d at t h a t depth, ft p l o t of mean c u r r e n t as a f u n c t i o n of depth i s shown i n f i g u r e 36 . The bars around the p o i n t s i n t h i s f i g u r e are two standard e r r o r s of the b l o c k means about t h e i r average and so i n d i c a t e the range of the mean value of the c u r r e n t c a l c u l a t e d approximately monthly over h a l f a year. The 3m mean c u r r e n t was always down-inlet i n t h i s time p e r i o d . The mean c u r r e n t at 5m was always u p - i n l e t . Those two r e s u l t s v e r i f y the e x i s t e n c e of the expected g r a v i t a t i o n a l l y - d r i v e n e s t u a r i n e c i r c u l a t i o n p a t t e r n of an o u t f l o w i n g s u r f a c e l a y e r and i n f l o w i n g compensatory flow, although the r e t u r n flow i s somewhat c l o s e r t o the s u r f a c e than was shown i n Pickard and Rodgers, 1959, p o s s i b l y because the Howe Sound measurements were made c l o s e r to the head of the i n l e t than were those i n Knight I n l e t . The mean c u r r e n t s at 10m, 20m and 30m are a l l weak and show marked v a r i a b i l i t y i n d i r e c t i o n over s i x months. Thus they play no c o n s i s t e n t r o l e i n the e s t u a r i n e c i r c u l a t i o n over t h a t e n t i r e p e r i o d . Of course f o r any given s e t of l e v e l s of no motion, the c u r r e n t s a t these depths probably do form p a r t of the l a y e r e d e s t u a r i n e system o f Inflows and outflows. But 154 <£>J I F i g u r e 36 - Mean c u r r e n t s c a l c u l a t e d from z e r o t h harmonics of the F o u r i e r transforms of the c u r r e n t meter r e c o r d s . The bars i n d i c a t i n g s c a t t e r of the values are ± 2 standard e r r o r s of the mean of the z e r o t h harmonics. P o s i t i v e c u r r e n t i s u p - i n l e t as before. 155 as we have seen, these l e v e l s can change, so t h a t a meter, o r i g i n a l l y i n an i n f l o w i n g l a y e r , may f i n d i t s e l f i n an o u t f l o w i n g l a y e r f o r some p e r i o d of time o r v i c e versa. For example, the c u r r e n t at 20m flowed u p - i n l e t on average from 20 March to 21 A p r i l , down-inlet on average from 26 A p r i l t o 31 J u l y and u p - i n l e t again from 14 August t o 15 September. A n a l y s i s of l o n g e r term v a r i a t i o n s of t h i s s o r t was s a c r i f i c e d t o ga i n g r e a t e r s t a t i s t i c a l s i g n i f i c a n c e i n the o v e r a l l mean va l u e s . The c u r r e n t at 150m flowed down-inlet on average f o r the e n t i r e p e r i o d . I t i s d i f f i c u l t to e x p l a i n t h i s r e s u l t i f the c u r r e n t were uniform a c r o s s the channel. Water moving a t 1 cm/s t r a v e l s almost 1km/day. In a b a s i n only about 20km l o n g a c u r r e n t of t h i s s t r e n g t h cannot p e r s i s t f o r lon g e r than 20 days without l e a v i n g the basin. The water mass below s i l l depth i n Howe Sound i s contained by the s i l l , the walls o f the f j o r d and by the d e n s i t y g r a d i e n t above i t so t h a t a flow out of the bas i n i s improbable. Hence there must be some other e x p l a n a t i o n f o r the mean c u r r e n t a t 150m. The d e n s i t y g r a d i e n t i n the lower 175m of Howe Sound was not measurable by the hydrographic a n a l y s i s technigues used on the c r u i s e s t h a t were made i n the Sound. The upper l i m i t on the d e n s i t y change i s t h e r e f o r e 0.02 sigma-t u n i t s , based on the accuracy of temperature and s a l i n i t y measurements'. The maximum l o c a l i n t e r n a l Rossby r a d i u s of deformation as d e f i n e d by: r R = /gh ap/p ' / f (6.3) 156 where h i s the depth of the l a y e r of water, Ap/j° the f r a c t i o n a l d e n s i t y d i f f e r e n c e across i t and f i s the C o r i o l i s parameter, i s equal t o 1.2 km f o r a l a y e r depth of 175m and a d e n s i t y d i f f e r e n c e o f 2 x10- s. Therefore the p o s s i b i l i t y o f C o r i o l i s e f f e c t s cannot be excluded when attempting t o e x p l a i n the mean c u r r e n t at 150 m. Waves i n the deepest p a r t s of the i n l e t may t r a v e l u p - i n l e t on the e a s t s i d e and down-inlet on the west s i d e i n an i n t e r n a l K e l v i n wave-like f a s h i o n . I f t h i s were the case then a c u r r e n t meter suspended c l o s e r to one s i d e of the i n l e t than the other would r e g i s t e r a net c u r r e n t due to the d i f f e r e n c e i n amplitude at t h a t p o i n t between the wave t r a v e l l i n g up-i n l e t and the wave t r a v e l l i n g down-inlet. I t i s u n l i k e l y t h a t the c u r r e n t meter measurement e r r o r s p r e v i o u s l y d i s c u s s e d c o n t r i b u t e d t o t h i s mean c u r r e n t a t 150m s i n c e t h i s depth i s w e l l below the depth of d i r e c t s u r f a c e wave a c t i o n and wave-induced motion of the s u r f a c e buoy and mooring l i n e should be e f f e c t i v e l y damped t h i s f a r below the s u r f a c e . In agreement with t h i s statement, the c u r r e n t meter r e c o r d s a t 150m showed no evidence of the s p i k e s symptomatic of vane f l o p caused by wave a c t i o n . 157 VI.7 Spectra Of The Wind And Currents Although the s p e c t r a l r e g i o n s of g r e a t e s t i n t e r e s t i n t h i s study are i n the v i c i n i t y of the d i u r n a l and semi-d i u r n a l p e r i o d s , a look at the t o t a l frequency range of the s p e c t r a i s a l s o i n t e r e s t i n g . The s p e c t r a of long-channel components : of the wind and the c u r r e n t s at s i x depths are shown i n f i g u r e 37 . On a l l s p e c t r a the d i u r n a l and semi-d i u r n a l f r e q u e n c i e s are marked. The s p e c t r a a l l have the same q e n e r a l shape, r i s i n g from low freguency to a maximum value near 1 to 2cpd and then d e c r e a s i n g at higher f r e g u e n c i e s . They a l l have a b a s i c form c o n s i s t i n g of a l i n e with s l o p e 1 up to a freguency of about 2cpd and a l i n e with -1 slope f o r a l l f r e q u e n c i e s above 2cpd. The i n d i v i d u a l f e a t u r e s of each spectrum are then c h a r a c t e r i z e d by a s e r i e s of peaks above t h i s b a s i c shape. The s p e c t r a l p l o t s are a l l of l o g f cp vs l o g f . A p l o t of f cp vs l o g f i s variance p r e s e r v i n g , i . e . 2,3 j \ f cp d l o g f = § cp df = v a r i a n c e . The l o g - l o g p l o t s used are not v a r i a n c e p r e s e r v i n g but i t i s s t i l l c l e a r where the dominant c o n t r i b u t i o n s to the v a r i a n c e occur. In c o n t r a s t , a l o g cp vs l o g f p l o t emphasizes the low f r e q u e n c i e s . Log-log p l o t s are used because they allow the f u l l dynamic range of of the v a r i a b l e to be d i s p l a y e d and they show any power law r e l a t i o n s h i p s t h a t e x i s t . The spectrum of a sguare wave with p e r i o d 1 day i s zero f o r f < 1cpd and then a s e r i e s of d i s c r e t e values whose a to *- a-o o 05 CM »- Q-o to </)-Q -E co V) • •- Q-O t(s/ujo) 0, 6o| Q TS C F i g u r e 37 - Spectra o f the wind and c u r r e n t s at the depths i n d i c a t e d . D and S i n d i c a t e the d i u r n a l and s e m i - d i u r n a l f r e g u e n c i e s r e s p e c t i v e l y . L i n e s o f s l o p e 1 and -1 are shown on the 150m spectrum. The e r r o r bars on the s p e c t r a l p o i n t s are ±1 SE. 159 magnitudes decrease as f - 2 f o r f > 1cpd. Making the p e r i o d of the sguare wave random about 1 day and g i v i n g each c y c l e of the wave a random asymmetry i n j e c t s e s s e n t i a l l y random n o i s e at f < 1cpd ca u s i n g a constant s p e c t r a l l e v e l at those f r e g u e n c i e s and makes the spectrum f o r f > 1cpd more continuous but preserves the s l o p e of f - 2 . When p l o t t e d on a l o g fey vs l o g f p l o t , t h i s spectrum i s a l i n e with s l o p e 1 f o r f < 1cpd and o f sl o p e -1 f o r f > 1cpd, e x a c t l y as p o s t u l a t e d f o r the u n d e r l y i n g spectrum of the observed c u r r e n t s . another look a t f i g u r e 33 w i l l show that the wind and c u r r e n t s appear to r i s e q u i c k l y t o some p a r t i c u l a r value and then hold i t f o r some l e n q t h of time before r a p i d l y changing to another value. Thus there i s a reasonable b a s i s f o r the i n t e r p r e t a t i o n of the b a s i c shape of the s p e c t r a as being due t o a random sguare wave behaviour of d i u r n a l p e r i o d with some departures from t h i s base shape. Looking f i r s t at the high freguency end of the s p e c t r a , the wind and the 150m s p e c t r a show slopes o f -1. The other s p e c t r a show a high freguency t a i l whose slope decreases with i n c r e a s i n g freguency, i n d i c a t i n g more energy at high f r e q u e n c i e s than expected from the simple sguare wave model. T h i s high frequency t a i l i s probably due to the presence of the vane f l o p s p i k e s and other noise i n the data r e c o r d s . Now l e t us look at the low frequency end of the s p e c t r a . The wind spectrum has a low frequency s l o p e of about 1/2 i n d i c a t i n g t h a t there i s more energy at these f r e q u e n c i e s than expected from j u s t random l e n g t h s of 160 d i u r n a l wind pu l s e s . There should be energy i n the wind a t l o n g e r p e r i o d s due to v a r i a t i o n s on the s c a l e of weather systems. There i s a peak i n the spectrum a t 0.2cpd, a reasonable value f o r the p e r i o d of weather systems a t t h i s time of year i n B r i t i s h Columbia. The s p e c t r a of the c u r r e n t s at low f r e q u e n c i e s show, f o r depths other than 150m, s l o p e s l e s s than 1 suggesting some i n f l u e n c e of the low frequency wind energy on the c u r r e n t s . At 150m the low freguency s l o p e i s almost e x a c t l y 1 suggesting t h a t most of the energy i s a s s o c i a t e d with random e f f e c t s i n the d i u r n a l and s e m i - d i u r n a l c o n s t i t u e n t s . T h i s s o r t of change i n s p e c t r a l shape with depth can be i n t e r p r e t e d as f o l l o w s . The shallow low frequency c u r r e n t s move i n response t o the wind. The e f f e c t of the wind i s a l s o f e l t deeper i n the water column but the e f f e c t s of the'higher f r e g u e n c i e s are reduced more at depth than those of the lower f r e g u e n c i e s . Thus the wind energy which appears at a l l f r e q u e n c i e s below 1cpd at 3m only seems to appear below 0.2cpd at 30m and may only be present at the lowest f r e q u e n c i e s of o b s e r v a t i o n at 150m. Peaks i n the d i u r n a l and s e m i - d i u r n a l bands are a major f e a t u r e of the s p e c t r a . The band l a b e l l e d " d i u r n a l " covers the ranqe of periods from 23.63 to 30.12 hours. Thus i t c o n t a i n s enerqy from a l l of the d i u r n a l t i d a l c o n s t i t u e n t s and from the d i u r n a l wind. The band l a b e l l e d " s e m i - d i u r n a l " c o v e r s the range from 15.21 t o 12.09 hours. Thus t h i s band c o n t a i n s energy from the major s e m i - d i u r n a l t i d a l c o n s t i t u e n t , M 2, but not from the S z t i d e o r from any wind f l u c t u a t i o n s with a 12.00 hour p e r i o d . In t h i s manner any 161 wind e f f e c t s are separated from the s e m i - d i u r n a l s p e c t r a l peak. The wind spectrum shows a d i u r n a l peak 9db above the r e s t of the spectrum but no s e m i - d i u r n a l peak. The band above the s e m i - d i u r n a l shows a sm a l l peak i n d i c a t i n g t h a t t h e r e i s some energy i n the wind at 12.OOh. Thus the s e p a r a t i o n of wind energy from the s e m i - d i u r n a l band d i d occur, The c u r r e n t s p e c t r a a l l show both d i u r n a l and semi-d i u r n a l peaks. They do not show any peaks i n the band above the s e m i - d i u r n a l band, with the e x c e p t i o n of 30ra, the r a t i o of the d i u r n a l peak t o the s e m i - d i u r n a l peak decreases with i n c r e a s i n g depth. T h i s f e a t u r e i s t o be expected s i n c e the d i u r n a l peak c o n t a i n s both wind and t i d a l energy but the s e m i - d i u r n a l peak c o n t a i n s o n l y t i d a l energy. , An i n t e r e s t i n g comparison can be made using the amplitudes of these peaks. A measure of the mean sguare c u r r e n t i n any freguency range may be made by m u l t i p l y i n g the s p e c t r a l estimate by i t s band width; The r a t i o s of such e s t i m a t e s i n the d i u r n a l band to e s t i m a t e s i n the semi-d i u r n a l band f o r a l l the s p e c t r a are shown i n t a b l e VIII . A l s o shown i s a r a t i o of mean sguare t i d a l c u r r e n t s c a l c u l a t e d from the amplitudes of t i d a l c o n s t i t u e n t s a t Sguamish. The t i d a l c u r r e n t s are assumed t o be p r o p o r t i o n a l t o the time d e r i v a t i v e s of the t i d a l h e i g h t s and hence have amplitudes p r o p o r t i o n a l to the product of the height and the frequency. Both the d i u r n a l and s e m i - d i u r n a l bands c o n t a i n e d s e v e r a l t i d a l c o n s t i t u e n t s o f s l i g h t l y d i f f e r e n t freguency. Although the r e l a t i v e phases of these c o n s t i t u e n t s were not taken e x p l i c i t l y i n t o account i n the averaging p r o c e s s , the 162 Table VIII - R a t i o s of the mean square c u r r e n t s i n the d i u r n a l band to those i n the s e m i - d i u r n a l band f o r a l l depths c a l c u l a t e d from s p e c t r a l v a l u e s . A l s o shown i s the t i d a l c u r r e n t r a t i o c a l c u l a t e d from the amplitudes of the t i d a l components as d e s c r i b e d i n the t e x t . averaging p e r i o d of the s p e c t r a was l o n g enough t o allow a l l p o s s i b l e phases between the c o n s t i t u e n t s . Hence the t o t a l t i d a l c u r r e n t i n each band was computed as the sum of the sguares of the c o n s t i t u e n t s . The d i u r n a l band contained the 0t rv\ and K( c o n s t i t u e n t s , the s e m i - d i u r n a l the N., and M^. The r e s u l t i n g r a t i o should be r e p r e s e n t a t i v e i f the t i d a l c u r r e n t s i n both bands are p r i m a r i l y b a r o t r o p i c . The r a t i o s o f mean sguare c u r r e n t shown i n t a b l e VIII i n d i c a t e the r e l a t i v e amounts of k i n e t i c energy i n the d i u r n a l to the s e m i - d i u r n a l freguency bands. Only at 150m does the r a t i o appear to be near to the expected b a r o t r o p i c t i d a l r a t i o as c a l c u l a t e d from the amplitudes of the t i d a l c o n s t i t u e n t s . At a l l other depths t h e r e i s more d i u r n a l energy than may be e x p l a i n e d by the b a r o t r o p i c t i d e . The r a t i o g e n e r a l l y decreases with i n c r e a s i n g depth. T h i s o b s e r v a t i o n i s c o n s i s t e n t with the hypothesis t h a t the wind d r i v e n c o n t r i b u t i o n to the c u r r e n t s decreases with 163 i n c r e a s i n g depth. There i s an anomaly i n t h i s o b s e r v a t i o n a t 30m where the r a t i o i n c r e a s e s t o a value between the 5 and 10m values. One p o s s i b l e e x p l a n a t i o n cf t h i s r e s u l t i s t h a t the t i d a l c u r r e n t s are b a r o c l i n i c and 30m i s near a node i n the v e r t i c a l s t r u c t u r e of the s e m i - d i u r n a l t i d e . T h i s look at t h e s p e c t r a of wind and c u r r e n t s has shown s e v e r a l important t h i n g s about the r e l a t i o n s h i p of the wind, t i d e and c u r r e n t s . One i s that wind e f f e c t s are prominent i n the near s u r f a c e c u r r e n t s but decrease i n importance with i n c r e a s i n g depth. The depth of wind i n f l u e n c e may be freguency dependent. T i d a l c u r r e n t s are present i n a l l c u r r e n t r e c o r d s and there i s evidence of b a r o c l i n i c i t y i n them. I t i s these a s p e c t s of the o b s e r v a t i o n s t h a t w i l l be i n v e s t i g a t e d i n g r e a t e r d e t a i l i n the r e s t of the chapter. VI. 8 Coherence Of The «ind An,d Currents Estimates of coherence and phase between wind and c u r r e n t records were made i n a e f f o r t t o determine the extent of the c o u p l i n g between them. The r e s u l t s of t h i s study show s m a l l e r coherences than might be expected. F i g u r e 38 shows the coherence and phase between the wind and c u r r e n t s at a l l s i x depths. Let us look f i r s t at the r e s u l t s from 3m i n f i g u r e 38, where we might expect the coherence to be high. At periods g r e a t e r than 10h the coherence i s u s u a l l y w e l l above the n o i s e l e v e l and the c u r r e n t l e a d s the wind by about 20°. At p e r i o d s of 10h and l e s s , the coherence i s near the noise 164 Coherence Phase 10 F i g u r e 38 - Coherence ana phase between the wind and the c u r r e n t ^ at the metered depths. P o s i t i v e phase means c u r r e n t l e a d s wind. The s o l i d l i n e on the coherence p l o t s r e p r e s e n t s the expected random coherence as before. 165 Coherence Phase 0.01 0.1 1 1 0 Frequency (cpdj 180-, 90] -90-^ 1 0 0 166 l e v e l . These r e s u l t s are very d i f f e r e n t f r o o those obtained by Farmer (1972) i n A l b e r n i I n l e t . He found t h a t the values of coherence-squared between the wind and c u r r e n t s a t 2m depth were c o n s i s t e n t l y above 0.8 f o r f r e q u e n c i e s l e s s than 1.2cpd. At higher f r e q u e n c i e s i t decreased to l e s s than 0.2. The phase v a r i e d l i n e a r l y with the l o g a r i t h m of freguency from -90° (wind l a g g i n g c u r r e n t ) at a p e r i o d of about 500h to 180° at 2h. Farmer a t t r i b u t e d t h i s behaviour to the le n g t h of time necessary f o r the wind energy to d i f f u s e through the d e n s i t y g r a d i e n t from the s u r f a c e t o the depth o f the c u r r e n t meter. He p o s t u l a t e d a simple d i f f u s i o n model f o r t h i s behaviour t h a t r e l a t e d the phase angle between wind and c u r r e n t t o the sguare root o f the freguency and the i n v e r s e square root o f the eddy v i s c o s i t y . Thus, i n e f f e c t , he s t a t e d t h a t as the frequency of the wind o s c i l l a t i o n i n c r e a s e d , the p e r i o d of time f o r the wind energy t o d i f f u s e downwards, as a f r a c t i o n of the p e r i o d o f o s c i l l a t i o n , i n c r e a s e d . The d i f f e r e n c e i n behaviour between Howe Sound and A l b e r n i I n l e t probably l i e s i n the d i f f e r e n c e i n the d e n s i t y s t r u c t u r e of t h e i r s u r f a c e l a y e r s . In A l b e r n i a t the time o f Farmer's measurements, i n the winter of 1971, there was a reasonably constant g r a d i e n t through the s u r f a c e few meters whereas i n Howe Sound the g r a d i e n t was very weak t o below the depth of the'3m c u r r e n t meter and very s t r o n g a t some depth below t h a t , Hind energy, which took some time to propagate through the g r a d i e n t i n A l b e r n i , could propagate to the p y c n o c l i n e i n Howe Sound q u i t e r a p i d l y through the 1 6 7 weak g r a d i e n t , i . , e . i n Howe Sound, the le n g t h of time needed f o r wind energy to propagate downwards past the 3ra c u r r e n t meter was only an i n s i g n i f i c a n t p a r t of the p e r i o d of o s c i l l a t i o n of t h e d r i v i n g f o r c e . The phase angle between wind and c u r r e n t at 3m i n Howe Sound was t h e r e f o r e r e l a t i v e l y c o n s t a n t . The coherence i n Howe Sound i s probably lower than i n A l b e r n i f o r reasons t h a t a l s o r e l a t e t o the d i f f e r i n g d e n s i t y s t r u c t u r e of the s u r f a c e l a y e r . I t was shown i n f i g u r e 33 th a t the l e v e l s o f no motion i n Howe Sound could s h i f t , c a u s i n g r e l a t i v e phase r e v e r s a l s between adjacent c u r r e n t meters consequently l o w e r i n g the coherence between them. The 3m c u r r e n t meter i n Howe Sound i s r a t h e r c l o s e to the l e v e l of no motion a s s o c i a t e d with the py c n o c l i n e and t h e r e f o r e might be s u b j e c t t o the o c c a s i o n a l phase r e v e r s a l with r e s p e c t t o the wind. Such behaviour would c e r t a i n l y lower the coherence between the two. The d e n s i t y s t r u c t u r e i n A l b e r n i was such t h a t an e q u i v a l e n t e f f e c t should not be found. Thus the coherence between wind and shallow c u r r e n t should be g r e a t e r i n A l b e r n i than i n Howe Sound. The coherence and phase between the wind and the 5m c u r r e n t meter as shown i n f i g u r e 38 are q u i t e d i f f e r e n t from between the wind and the 3m meter. The coherences are i n ge n e r a l q u i t e a b i t lower and the phase appears to be random. The d i f f e r e n c e between the response at 3m and t h a t at 5m i s due no doubt t o the presence of the sharp p y c n o c l i n e between the two that i n h i b i t s d i r e c t energy t r a n s f e r . 168 The coherence and phase p l o t s at other depths resemble the 5m p l o t s . Phase appears to be b a s i c a l l y random i n a l l c a s e s . Coherence v a l u e s , except f o r a few i n s t a n c e s , l i e on or hear the random coherence l e v e l . No frequency band i s c o n s i s t e n t l y above the noi s e l e v e l at a l l depths. The number of s t a t i s t i c a l l y s i g n i f i c a n t coherences decreases from 10m to 30m but t h e n , somewhat s u r p r i s i n g l y , r i s e s again a t 150m. Since the dominant peak of the wind spectrum i s a t 24h l e t us look at the coherence of the wind and c u r r e n t s i n t h i s band. Table IX shows t h a t the coherence drops r a p i d l y as a f u n c t i o n of depth. The o n l y s i g n i f i c a n t coherences i n Table IX - Coherence and phase between the wind and c u r r e n t s i n the d i u r n a l band. P o s i t i v e phase i s d e f i n e d as c u r r e n t l e a d i n g wind. The random coherence l e v e l i s 0.19. r——— ———r—: ~—-— • — - 1 depth I coh X ' _ I phase — T T 3 m \ 0.74 I -2 5m I 0.43 \ -5 10m 1 0.22 \ -156 20m 1 0.25 I 55 30m 1 0. 13 I 26 150m ! 0.36 I -66 •: I i ;——I J 1 t h i s t a b l e are at 3m, 5m and 150m. At the shallow depths the wind and c u r r e n t s are e s s e n t i a l l y i n phase, T h i s r e s u l t s u b s t a n t i a t e s what was seen i n f i g u r e 33. I t i s c u r i o u s that 150m should show a s i g n i f i c a n t c o r r e l a t i o n with the wind when none i s shown at i n t e r m e d i a t e depths and when t a b l e 9 showed that the r a t i o of energy i n the d i u r n a l band to t h a t i n the s e m i - d i u r n a l band was almost e x a c t l y what could be a t t r i b u t e d t o the b a r o t r o p i c t i d e . The r e s u l t i s probably due t o one weakness of coherence a n a l y s i s . Two d i f f e r e n t 169 s i g n a l s o c c u r r i n g a t the same freguency i n the F o u r i e r a n a l y s i s w i l l show a coherence with a t h i r d s i g n a l i f e i t h e r one of the two i s coherent with the t h i r d . In t h i s case the d i u r n a l wind and t h e d i u r n a l t i d e both a c t i n the same' frequency band, The wind i s t h e r e f o r e coherent with the t i d e (although p h y s i c a l l y r e l a t e d o n l y i n d i r e c t l y of course) and w i l l be coherent with any s i g n a l d r i v e n by the t i d e , i n t h i s case the 150m c u r r e n t . Higher coherences were not recorded i n the mid-depth meters because of the r e l a t i v e phase r e v e r s a l problems d i s c u s s e d e a r l i e r . The 150m meter was presumably i n a r e g i o n of smooth enough d e n s i t y g r a d i e n t so t h a t r e l a t i v e phase r e v e r s a l s d i d not occur o f t e n . VI .9 • T i d a l I n f l u e n c e On The C u r r e n t s Since no records of a c t u a l t i d a l height were made d u r i n g the c u r r e n t meter experiment, the extent of t i d a l i n f l u e n c e on the c u r r e n t s i n Howe Sound has to be i n f e r r e d from the p r e d i c t e d amplitudes of the t i d a l c o n s t i t u e n t s at Sguamish, the s p e c t r a of the c u r r e n t s and the coherence and phase measurements between the c u r r e n t s at d i f f e r e n t depths at t i d a l f r e q u e n c i e s . The amplitudes and p e r i o d s of the s i x l a r g e s t t i d a l c o n s t i t u e n t s at Sguamish are shown i n t a b l e X4 . Although the sum of the squares o f the amplitudes of the s e m i - d i u r n a l components i s 9*\% of the sum o f the squares of the d i u r n a l components, the k i n e t i c energy a s s o c i a t e d with p u r e l y b a r o t r o p i c t i d a l c u r r e n t s c a l c u l a t e d as the d e r i v a t i v e s o f s i n u s o i d s with the amplitudes and p e r i o d s 170 Table X - Amplitude and p e r i o d of the s i x major t i d a l c o n s t i t u e n t s a t Sguamish. Amplitudes are i n cm, p e r i o d s i n hours. The sum of t h e s e c o n s t i t u e n t s r e p r e s e n t s about 80S of the sum of the amplitudes o f a l l the c o n s t i t u e n t s a t Sguamish. » 1 T "J I name | amp | peri o d j f— r + 1 I 0, | 49.26 | 25.82 j I P, I 27.16 | 24.07 J I K, j 87.45 } 23. 93 | I N t | 19.42 J 12.66 | I H t I 94.21 | 12.42 | I S^ | 23.23 J 12.00 | t ; 1 1 1 g i v e n i n t a b l e X i s 3.5 times g r e a t e r i n the s e m i - d i u r n a l than i n the d i u r n a l band. As was shown i n t a b l e IX, the r a t i o of mean sguare c u r r e n t s i n the s e m i - d i u r n a l to d i u r n a l bands as determined from the s p e c t r a was found to be c l o s e to t h i s value at 150 m. At s h a l l o w e r depths, there was more energy i n the d i u r n a l band than c o u l d be accounted f o r by a p u r e l y b a r o t r o p i c t i d e . I t seems l i k e l y from the r e s u l t s of the p r e v i o u s s e c t i o n s that much of t h i s e x t r a energy comes from the d i u r n a l wind. Coherence and phase were c a l c u l a t e d between the c u r r e n t s at a l l depths i n order t o determine the extent t h a t the c u r r e n t s at one depth were r e l a t e d to those a t another. Values of coherence between c u r r e n t s presented j u s t as ambiguous a p i c t u r e i n g e n e r a l as d i d those c a l c u l a t e d between the wind and the c u r r e n t s . Problems of r e l a t i v e phase r e v e r s a l probably are a t l e a s t p a r t l y r e s p o n s i b l e f o r the low coherence values as d i s c u s s e d e a r l i e r . Measurements of coherence and phase i n the two bands of probable t i d a l e x c i t a t i o n however do present an i n t e r e s t i n g p i c t u r e . Table XI shows these measurements. The coherence of the 3m 171 T a b l e X I - C o h e r e n c e and p h a s e b e t w e e n t h e c u r r e n t s a t d i f f e r e n t d e p t h s a t two d i f f e r e n t p e r i o d s . I n e a c h c a s e , t h e c o h e r e n c e i s l i s t e d f i r s t f o l l o w e d by t h e p h a s e i n d e g r e e s . P o s i t i t v e p h a s e i n d i c a t e s t h e c u r r e n t a t row d e p t h l e a d s t h e c u r r e n t a t c o l u m n d e p t h . *** i n d i c a t e s t h a t t h e c o h e r e n c e was a t o r b e l o w t h e random l e v e l . Random c o h e r e n c e l e v e l i n t h e d i u r n a l band i s 0.19; i n t h e s e m i - d i u r n a l band i t i s 0.11. d i u r n a l band (23.63 t o 30.12 h o u r s ) , , ; _: — 1 , , , r 1 5 10 20 30 150 ] I 3 I .69 - 24 .35 -88 .35 27 *** 31 -49 ! I ! 5 ! . 53 -11 .40 68 .41 73 . 31 -112 I 10 1 .40 31 .34 65 . 39 179 I | 20 1 .50 -1 *** I | 30 I « 66 144 i -X -r -I— s e m i - d i u r n a l band (1-2.09 t o 15.21 h o u r s ) "1 J I 5 10 20 30 150 j j. _ + , . — _ _ ~ — . - 4 | 3 j .33 -60 . 32 105 .21 21 *** . 28 112 | J 5 | . 53 -24 . 46 60 .46 -94 . 24 56 J I 10 | 1 20 | j 30 j i 1 — ; . — . .21 21 *** . 28 112 . 46 60 .46 -94 .24 56 .79 - 3 9 .72 -55 .61 68 .46 -2 . 36 89 .68 127 c u r r e n t s w i t h t h o s e a t g r e a t e r d e p t h i s g r e a t e r i n t h e d i u r n a l b a n d t h a n i n t h e s e m i - d i u r n a l band. T h i s o b s e r v a t i o n i n d i c a t e s t h a t t h e s u r f a c e l a y e r i s c o u p l e d t o a g r e a t e r e x t e n t w i t h t h e d e e p e r w a t e r s a t t h e l o n g e r p e r i o d . I n t h e c o n c l u d i n g c h a p t e r t h i s d i f f e r e n c e w i l l be d i s c u s s e d f r o m t h e p o i n t o f v i e w o f t h e d i f f e r e n c e s i n t h e b a s i c n a t u r e o f t h e f o r c i n g f u n c t i o n s o f w i n d and t i d e . I n a l m o s t a l l c a s e s c a l c u l a t e d f o r c u r r e n t s b e l o w 3m, t h e c o h e r e n c e i n t h e s e m i - d i u r n a l b a nd was g r e a t e r t h a n t h e c o h e r e n c e i n t h e d i u r n a l b a n d , s u g g e s t i n g t h a t t i d a l l y d r i v e n deep c u r r e n t s a r e more c o h e r e n t t h a n a r e t h o s e f o r c e d p a r t i a l l y by t h e w i n d , o r more l i k e l y , t h a t t h e e f f e c t s o f t i d a l f o r c i n g e x t e n d d e e p e r i n t h e w a t e r c o l u m n t h a n do t h e 172 e f f e c t s of wind f o r c i n g hence the coherence of t i d a l l y f o r c e d c u r r e n t s should be higher. The phase d i f f e r e n c e between adjacent c u r r e n t s v a r i e s more r e g u l a r l y i n the s e m i - d i u r n a l band than i n the d i u r n a l band, i . e . the deeper c u r r e n t always l a g s the sh a l l o w e r i n the s e m i - d i u r n a l band ( i f the 127° l e a d o f the 150m c u r r e n t over the 30m may be i n t e r p r e t e d as a 233° lag) but i n the d i u r n a l band the 3m c u r r e n t l e a d s t h a t at 5m, which l e a d s t h a t at 10m, which l a g s those a t 20m and 30m. The d i f f e r e n c e i s best seen i n f i g u r e 39 which shows phasor diagrams f o r the c u r r e n t s i n each band. The l e n g t h o f each v e c t o r r e p r e s e n t s the r.m.s. c u r r e n t at t h a t depth at th a t p e r i o d and the angle r e p r e s e n t s the phase of the c u r r e n t r e l a t i v e t o t h a t at 150m. This phase was a c t u a l l y c a l c u l a t e d from the phase d i f f e r e n c e between adjacent meters. S e v e r a l b a s i c d i f f e r e n c e s can be seen on these diagrams between the c u r r e n t s i n the s e m i - d i u r n a l band and i n the d i u r n a l band. The c u r r e n t s i n the d i u r n a l band are s t r o n g e s t near the s u r f a c e and decrease c o n t i n u o u s l y as a f u n c t i o n of depth while those i n the s e m i - d i u r n a l band have a maximum a t 10m and decrease towards the s u r f a c e . The c u r r e n t s t r e n g t h i n the s e m i - d i u r n a l band a l s o decreases from 10m to 30m but then i n c r e a s e s at 150m. The v a r i a t i o n i n the s t r e n g t h of the c u r r e n t s as a f u n c t i o n o f depth i s g r e a t e r i n the d i u r n a l band, where the minimum i s only 18% as strong as the maximum, than i n the s e m i - d i u r n a l band where the minimum i s U1% of the"maximum., There are a l s o d i s t i n c t d i f f e r e n c e s i n the r e l a t i v e 150m 4 S e m i - D i u r n a l Figure 39 - Current phasors for the diurnal and semi-diurnal freguency bands. 174 phases of the c u r r e n t s i n these two bands. As was mentioned e a r l i e r , the deeper c u r r e n t s always l a g the shallower ones i n the s e m i - d i u r n a l band but i n the d i u r n a l band the 20m and 30m c u r r e n t s appear to l e a d the 5m and 10m c u r r e n t s . ,The phasor diagrams show t h a t the 3m and 150m c u r r e n t s are i n phase i n the s e m i - d i u r n a l band but i n the d i u r n a l band the 150m c u r r e n t i s out of phase with the other c u r r e n t s . , Thus the d i u r n a l band appears to have a two l a y e r e d s t r u c t u r e with the i n t e r f a c e between the two l a y e r s between 30 and 150 m. The s e m i - d i u r n a l band appears to have a more con t i n o u s phase d i s t r i b u t i o n , but one t h a t might be t y p i f i e d by a t h r e e l a y e r s t r u c t u r e with the s u r f a c e and deep waters i n phase. However, the accuracy of the phase de t e r m i n a t i o n s has not been c a l c u l a t e d so t h a t attempting t o draw any c o n c l u s i o n s based on the d e t a i l s of the phase r e l a t i o n s h i p s i s hazardous. VI.10 Changes In Hydrogr a p h i c P r o p e r t j e s As '' 1 B d i c a t o r s Of Currents -The s p e c t r a l a n a l y s i s of the c u r r e n t s t h a t was done i n t h i s chapter c o u l d only examine f l u c t u a t i n g c u r r e n t s a t f r e g u e n c i e s higher than 0.03cpd (periods l e s s than 768h). Lower freguency c u r r e n t s c o u l d only appear as trends i n the mean value s of s u c c e s s i v e b l o c k s of the data. Low freguency c u r r e n t s can o f t e n be i n f e r r e d however from changes i n the d e n s i t y f i e l d and i n other p r o p e r t i e s of the i n l e t . The hydrographic c r u i s e s mentioned i n the i n t r o d u c t i o n t o t h i s 175 t h e s i s were c a r r i e d out to measure such changes. C r u i s e s were made c o v e r i n g two summers and two w i n t e r s , from J u l y 1972 t o March 1974. During the p e r i o d from March t o September, 1973, f o r which c u r r e n t meter data were analysed, no s i g n i f i c a n t changes were seen i n the d e n s i t y below 125m depth. A more s e n s i t i v e q u a n t i t y t o water changes i n Howe Sound i s temperature.....A contoured time s e r i e s of temperature vs depth and time a t s t a t i o n How 4 i s shown i n f i g u r e 40 . Only temperatures at depths of 50m and below have been p l o t t e d . In the waters above 100m, the e f f e c t s o f seasonal i n s o l a t i o n can be seen, but below t h i s depth t h e r e i s l i t t l e change. From March to September t h e r e was a change of onl y -0.08°C at 200m. These measurements i n d i c a t e t h a t there were no s i g n i f i c a n t events c a u s i n g slow deep c u r r e n t s . , The dramatic drop of the isotherms between September and November i n d i c a t e s t h a t a deep-basin f l u s h i n g event took p l a c e . Temperature s e c t i o n s o f the sound on the 20 September c r u i s e and on the 13 November c r u i s e are shown i n f i g u r e 41 . These two s e c t i o n s show t h a t the deep water i n September was d i s p l a c e d to mid-depth near the head of the i n l e t by water from 75 t o 80m o u t s i d e the s i l l . Although the isotherms i n the November s e c t i o n are t i l t e d the i s o p y c n a l s are l e v e l and roughly the same as i n f i g u r e 2. There was no d e t e c t a b l e d e n s i t y d i f f e r e n c e between the water a t depth i n s i d e the s i l l i n September and i n November. The p r o g r e s s i v e v e c t o r diagrams (PVD's) c a l c u l a t e d by Bell(1975) from the c u r r e n t meter data a t 150m over the p e r i o d 7 November t o 27 November 1973 show a continuous 176 F i g u r e 41 - Isotherm s e c t i o n s of Howe Sound a. L o n g i t u d i n a l s e c t i o n taken 20 September 1973 b. L o n g i t u d i n a l s e c t i o n taken 1.3 November 1973. c. Cross i n l e t s e c t i o n taken with STD i n s t e a d of b o t t l e s 21 Novembe 1973. Data above 30m have not been used. 178 i n f l o w run of about 12.5km from November 9 to 13. T h i s t o t a l d i s t a n c e i s c o n s i s t e n t with the d i s t a n c e t h a t the 8.5° iso t h e r m had t o move from s i l l depth i n the 20 September s e c t i o n to 220m depth a t How 4.7 i n the 13 November s e c t i o n . The PVD shows t h a t the flow i s not steady but o s c i l l a t e d with approximately d i u r n a l p e r i o d . The s t r o n g e s t i n f l o w was on November 10th. On November 9th, s t r o n g n o r t h e r l y winds p e r s i s t e d f o r most; of the day. These winds co u l d have caused enough movement of d e n s i t y s u r f a c e s i n the sound t o cause denser water t o s p i l l over the s i l l i n t o the i n n e r b a s i n . There was only one other p e r i o d of i n f l o w o f more than one day d u r a t i o n i n the e n t i r e s e r i e s o f PVD*s shown by B e l l . I t occu r r e d under s i m i l a r circumstances i n mid-December 1972 and caused s i m i l a r changes i n the hydrographic s t r u c t u r e of the waters i n the f j o r d . The r e s t of the PVD's showed v a r y i n g amounts of outflow. The PVD's a l s o showed l a r g e net c r o s s - i n l e t c u r r e n t s u s u a l l y to the e a s t . These can l i k e l y be e x p l a i n e d by the same s o r t of r o t a t i o n a l l y i n f l u e n c e d waves t h a t cause the net down-inlet c u r r e n t a t 150m. Although these data seem t o present a c o n s i s t e n t p i c t u r e of t h i s a d v e c t i o n of water i n t o the b a s i n , a c a u t i o n a r y note must be made. A s e r i e s of three STD c a s t s was made i n Howe Sound on November 21, 1973 with a B i s s e t -Berman model 9060 instrument at e g u a l l y spaced l o c a t i o n s a c r o s s the channel at a long-channel p o s i t i o n between How 4 and How 4.5. T h i s temperature s e c t i o n shown i n f i g u r e 41c i n d i c a t e s t h a t there was a l a r g e c r o s s - c h a n n e l g r a d i e n t i n 179 temperature i n the deeper waters of the same order as the long-channel g r a d i e n t s shown i n f i g u r e 41b. The new warmer i n f l o w i n g water i s on the r i g h t of the channel as i t should be i n a channel flow a f f e c t e d by the ear t h ' s r o t a t i o n . The volume of water t h a t entered the i n l e t cannot be c a l c u l a t e d on the b a s i s of the d i f f e r e n c e between the long-channel isotherm s e c t i o n s i n f i g u r e 41 a and b because of these s t r o n g c r o s s channel v a r i a t i o n s . T h i s event i n Howe Sound has been s t u d i e d i n more d e t a i l by Bi l o d e a u and 0sborn(1976) who looked at the temperature m i c r o s t r u c t u r e i n the i n n e r b a s i n of Howe Sound as w e l l as the hydrographic f e a t u r e s . 180 CHAPTER VII SUMMARY OF RESULTS AND COMPARISON HUH THEORY T h i s chapter begins with a summary o f the r e s u l t s of the s u r f a c e l a y e r experiment described" i n chapter IV and of the subsurface c u r r e n t experiment d e s c r i b e d i n chapter VI. Some of these r e s u l t s are then compared with models of e s t u a r i n e c i r c u l a t i o n . The adequacy of each model t o d e s c r i b e the a p p r o p r i a t e f e a t u r e s w i l l be assessed. VII.1 Summary Of The Experimental R e s u l t s V I I . 1.1 The Surf ace .Layer-Experiment -The s u r f a c e l a y e r experiment provided a great d e a l o f i n f o r m a t i o n on the s p a t i a l and temporal s t r u c t u r e of the s u r f a c e waters near the head of a f j o r d . The s u r f a c e l a y e r flow was found to be h i g h l y v a r i a b l e , both i n space and i n time. The dominant time s c a l e of the v a r i a t i o n s was d i u r n a l ; the amplitude was about f i v e times the averaged (both t e m p o r a l l y and cross-channel) s u r f a c e f l o w , i n c l u d i n g entrainment, expected from the r i v e r as was seen i n s e c t i o n IV.6. S e c t i o n IV.7 showed t h a t the s p a t i a l s c a l e of v a r i a t i o n i n the t r a n s v e r s e d i r e c t i o n o f the l o n g -181 channel component of v e l o c i t y was on the order of the i n l e t width. Near the head of the i n l e t , the waters u s u a l l y flowed i n o p p o s i t e d i r e c t i o n s on o p p o s i t e s i d e s o f the i n l e t ; near t h e s i l l , the flow was more s p a t i a l l y uniform. I t was shown i n s e c t i o n IV,8 th a t the long-channel v e l o c i t y g r a d i e n t s were l a r g e r near the head than near the s i l l , . T h e r e was some i n d i r e c t evidence, from s e c t i o n s IV,5 and IV.7, t h a t the s p a t i a l s t r u c t u r e of the v e l o c i t y f i e l d was independent of the time f l u c t u a t i o n s of the f i e l d . The measured a c c e l e r a t i o n f i e l d c o n tained s i m i l a r temporal v a r i a t i o n s . , I t appeared i n s e c t i o n IV,5 however t h a t the a c c e l e r a t i o n was much l e s s s p a t i a l l y v a r i a b l e than was the v e l o c i t y . The c o n t r i b u t i o n t o the long-channel component of a c c e l e r a t i o n from the s p a t i a l v e l o c i t y g r a d i e n t s was much l e s s than that from the temporal g r a d i e n t s except near the head of the i n l e t . There the c o n t r i b u t i o n s were of s i m i l a r magnitude. The temporal v a r i a t i o n s i n v e l o c i t y , d i s c u s s e d i n s e c t i o n s IV.4 and IV.6, oc c u r r e d i n s y n c h r o n i z a t i o n with v a r i a t i o n s i n the wind. A f t e r the onset of the wind, the a c c e l e r a t i o n of the s u r f a c e l a y e r was constant f o r s e v e r a l hours. Then i t decreased, changed s i g n , and f i n a l l y r e t u r n e d t o a value near zero even though the wind co n t i n u e d t o blow. These e f f e c t s were more obvious away from the head of the i n l e t . Near the head of the i n l e t a c o i n c i d e n c e between maximum t i d a l height and maximum down-inlet v e l o c i t y was seen. This c o r r e l a t i o n may have o c c u r r e d f a r t h e r down the i n l e t too but might have been masked by the much s t r o n g e r 182 wind e f f e c t . The s i l t p a t t e r n s i n the s u r f a c e l a y e r , resembling a r i v e r meandering through the waters of the i n l e t , do correspond i n ge n e r a l to the p a t t e r n of s u r f a c e c i r c u l a t i o n i n Howe Sound, However, the n o n - s i l t y water o f t e n moves as f a s t as the s i l t y water, so c a u t i o n i s necessary when attempting t o r e l a t e s i l t p a t t e r n s to the s u r f a c e l a y e r c u r r e n t s t r u c t u r e . V I I . 1. 2 ..The^Spbsurface Gurrent^lxperiment The r e s u l t s of the c u r r e n t meter experiment v e r i f i e d the e x i s t e n c e i n Howe Sound of the t r a d i t i o n a l e s t u a r i n e c i r c u l a t i o n p a t t e r n . The mean v e l o c i t i e s , shown i n s e c t i o n VI.6 i n d i c a t e d the p o s s i b l e presence o f s e v e r a l l a y e r s i n t h i s p a t t e r n . The depths o f these l e v e l s appear t o s h i f t o c c a s i o n a l l y . Superimposed on the mean flow f i e l d were v a r i a t i o n s s e v e r a l times l a r g e r than the mean v e l o c i t e s . S p e c t r a o f these v a r i a t i o n s from s e c t i o n VI.7 showed t h a t they e x i s t e d predominantly at two f r e g u e n c i e s : d i u r n a l and s e m i - d i u r n a l . The shallow meters a l s o i n d i c a t e d the presence of some energy at lower f r e g u e n c i e s . I t was shown i n s e c t i o n VI.8 that the c u r r e n t s at 3m had r e l a t i v e l y high coherence with the wind. The c u r r e n t l e d the wind by an e s s e n t i a l l y constant 20° f o r periods l o n g e r than t e n hours. The c u r r e n t s at 5m and deeper were not as coherent with the wind and showed no p a r t i c u l a r phase r e l a t i o n s h i p with i t . Evidence t h a t wind e f f e c t s penetrated 183 below 3m came from two sources: the shape of the low-frequency end of the c u r r e n t s p e c t r a and the k i n e t i c energy r a t i o s of the d i u r n a l t o the s e m i - d i u r n a l s p e c t r a l peaks. Both sources i n d i c a t e d t h a t wind f o r c i n g of the c u r r e n t s decreased with depth and was not s i g n i f i c a n t a t 150m. T i d a l energy, d i s c u s s e d i n s e c t i o n VI.9, was present a t a l l depths, as evidenced by the s p e c t r a l peak at 2 cpd. The r o o t mean square (r.m.s.) c u r r e n t s a t t h i s frequency v a r i e d i n s t r e n g t h only by a f a c t o r of two over the e n t i r e depth range, with the s t r o n g e s t c u r r e n t o c c u r r i n g c l o s e t o , but below the s u r f a c e . In c o n t r a s t , i n the 1 cpd band the r.m.s. c u r r e n t s t r e n g t h v a r i e d by a f a c t o r o f 6 and was g r e a t e s t a t the s u r f a c e . Examination o f the phase r e l a t i o n s h i p between the c u r r e n t s i n these two freguency bands a l s o i n d i c a t e d t h a t the c u r r e n t s were b a r o c l i n i c . The phase s t r u c t u r e was markedly d i f f e r e n t i n the two bands. A s u r p r i s i n g f e a t u r e was the net c u r r e n t f l o w i n g down-i n l e t a t 150m. This o b s e r v a t i o n might i n d i c a t e the e x i s t e n c e of C o r i c l i s e f f e c t s on the motions i n the deep waters of the f j o r d . The o n l y e x c e p t i o n s to t h i s outflow at 150m, d i s c u s s e d i n s e c t i o n VI.10, occurred f o r two per i o d s of i n -f l o w i n g c u r r e n t f o r a few days i n the winters of 1972 and 1973. Hydrographic data taken at the same time showed changes i n water p r o p e r t i e s i n the deeper p a r t s o f the f j o r d i n d i c a t i v e of a deep-basin water replacement event. The 1973 hydrographic data c l e a r l y showed a c r o s s - i n l e t asymmetry i n the i n - f l o w s u g g e s t i v e o f the i n f l u e n c e o f the e a r t h ' s r o t a t i o n on the flow. 184 Cross-channel asymmetry i n the flow below the s u r f a c e was a l s o made ev i d e n t i n a t h r e e - l e v e l drogue experiment, d e s c r i b e d i n chapter V, i n which v e l o c i t i e s i n the upper 6m of the water column were observed f o r a few hours. V11.2 Drag . C o e f f i c i e n t - C a l c u l a t i o n s The p y c n o c l i n e i n Howe Sound i s shallow and abrupt at about 4m depth. The c u r r e n t s at 3m and 5m show d i f f e r e n t behaviour. These f a c t s lend credence to the assumption o f a d i s c r e t e s u r f a c e l a y e r . As a f i r s t approximation, l e t us assume t h a t the f r i c t i o n between t h i s s u r f a c e l a y e r and the u n d e r l y i n g waters i s n e g l i g i b l e . T h i s assumption i s warranted on the f o l l o w i n g grounds. The grad i e n t Richardson number Ri=-g ( a p / 3 z) (7.1) p ( d u/ S z) 2 i s about 20 f o r t y p i c a l values of d e n s i t y g r a d i e n t taken from the s a l i n i t y g r a d i e n t s i n f i g u r e 13 and v e l o c i t y g r a d i e n t s taken from f i g u r e 32. Because of the crude s c a l e of measurement o f the v e l o c i t y p r o f i l e and the non-s i m u l t a n e i t y of the measurements, t h i s v alue i s only a rough approximation, probably w i t h i n an order of magnitude. Since R i » 1/4, the i n t e r f a c e between the l a y e r s i s q u i t e s t a b l e to p e r t u r b a t i o n s and hence t h e r e should be no l a r g e t u r b u l e n t drag due t o mixing on the i n t e r f a c e . Further evidence o f s t a b i l i t y i s given by the measured s a l i n i t y 185 change i n the s u r f a c e l a y e r of o n l y 4°/ 0 0 from the r i v e r mouth to the s i l l a t Porteau Cove. Since the v e r t i c a l d e n s i t y g r a d i e n t i n the s u r f a c e l a y e r i s s m a l l i t may a l s o be reasonable t o assume t h a t momentum in p u t by the wind through the water s u r f a c e d i f f u s e s r a p i d l y down t o the p y c n o c l i n e . T h i s assumption i s c o n s i s t e n t with the r e l a t i v e l y constant phase between wind and 3m c u r r e n t at p e r i o d s g r e a t e r than 10h. Hence a wind s t r e s s a p p l i e d to the water s u r f a c e should act as a body f o r c e on the s u r f a c e l a y e r to a c c e l e r a t e the water u n t i l the s t r e s s i s balanced by the pressure g r a d i e n t . We may r e l a t e the a c c e l e r a t i o n of the s u r f a c e l a y e r to the wind speed using the standard sguare law wind drag formula: D f / a = P ^ o i D l (7.2) where 0 i s the wind v e l o c i t y , a i s the drogue a c c e l e r a t i o n D the depth of the s u r f a c e l a y e r , p.. and p w the d e n s i t i e s of a i r and water and C^ the drag c o e f f i c i e n t . , In the experiments we had no measure of the cross-stream components o f the wind v e l o c i t y D , but from the geometry of the channel i t had to be s m a l l with r e s p e c t to the long - channel component; hence i t w i l l be l e f t out of the succeeding c a l c u l a t i o n s . There i s some u n c e r t a i n t y i n the value of D to be used, as w i l l be d i s c u s s e d s h o r t l y . The only unknown i n t h i s eguation i s the drag c o e f f i c i e n t Cv. I t s value as computed d i r e c t l y from the downward f l u x o f wind momentum 186 above the sea s u r f a c e i s about 1 to 1.5x10 _ 3 (Pond et a l (1974), Stewart (1974)). was c a l c u l a t e d using eguation 7.2 f o r each h o u r l y average of wind speed and drogue a c c e l e r a t i o n . The r e s u l t s are p l o t t e d ( f i g u r e 42). Only those v a l u e s i n the range - 4 x 1 0 - 3 < C i< 4 x 1 0 - 3 are p l o t t e d . Values o u t s i d e t h i s range and n e g a t i v e values i n t h i s range o b v i o u s l y c o n t r a d i c t the b a s i c assumption t h a t the wind i s the dominant cause o f the water a c c e l e r a t i o n . P o s i t i v e values i n t h i s range i n d i c a t e t h a t , by t h i s c r i t e r i o n , the wind s t r e s s i s l i k e l y the dominant f o r c e d r i v i n g the s u r f a c e c i r c u l a t i o n . Such p e r i o d s should occur a t the onset of s t r o n g winds. They do i n week 1 a t 35 hours and 60 hours ( f i g 42c), and i n week 3 at 36 hours and 58 hours ( f i g 42d). In a l l these cases the drag c o e f f i c i e n t s had values of 1-2x10- 3. What i s a l s o i n t e r e s t i n g i s t h a t the values of remained approximately constant f o r s e v e r a l hours a f t e r the onset of the winds. A f t e r t h i s p e r i o d they decreased, became neg a t i v e and i n one case returned t o zero. T h i s behaviour i s i n d i c a t i v e of the takeover of some other f o r c e as the dominant term i n the f o r c e balance eguation f o r the s u r f a c e l a y e r . The c a l c u l a t e d drag c o e f i c i e n t s from week 4 ( f i g 42a) show t h a t t h e r e were no s i g n i f i c a n t p e r i o d s of wind-dominated c i r c u l a t i o n . Since there were only small v a r i a t i o n s i n a f a i r l y steady u p - i n l e t wind throughout the week, the u p - i n l e t wind s t r e s s presumably would have been balanced by a down-inlet pressure g r a d i e n t throughout the week. There were l a r g e v a r i a t i o n s i n wind v e l o c i t y i n the Figure 42 - Drag c o e f f i c i e n t s calculated from hourly averaged wind v e l o c i t i e s and water accelerations. a. week 4. b. week 2N. c. week 1. d. week 3. The s o l i d l i n e i s the Sguamish wind as has been previously described. The error bars are ± one standard error of the mean cf a l l values of calculated that hour. 188 week 2 (north) data s e t ( f i g 42b) but, as was shown i n chapter IV, the c u r r e n t s d i d not appear to respond to changes i n the wind i n - t h e same simple way of weeks 1 and 3. The drag c o e f f i c i e n t c a l c u l a t i o n s c o n firm t h i s c o n c l u s i o n . Only i n the p e r i o d of u p - i n l e t winds from 61 to 71 hours are t h e r e c o e f f i c i e n t s of the proper s i g n and magnitude. There i s no p e r i o d of constant p o s i t i v e drag c o e f f i c i e n t i n t h i s i n t e r v a l but from 65 to 71 hours there appears t o be the same s o r t of swing from wind s t r e s s domination t o pressure g r a d i e n t domination to e q u i l i b r i u m t h a t was seen i n the week 1 and week 3 c a l c u l a t i o n s . Measurements of the s u r f a c e l a y e r d e n s i t y s t r u c t u r e were made only d u r i n g weeks 3 and 4, From the week 3 s a l i n i t y p r o f i l e s shown i n f i g u r e 13, the middle of the h a l o c l i n e was seen t o be about 3.5m. This depth corresponds g u i t e w e l l t o the depth of the p y c n o c l i n e and so was used as the constant l a y e r depth f o r the drag c o e f f i c i e n t c a l c u l a t i o n s . Farmer (1972) showed that wind e f f e c t s caused a v a r i a t i o n i n depth of the s u r f a c e l a y e r . . A p p l i c a t i o n of a form of h i s model to Howe Sound shows t h a t , away from the ends of the f j o r d , the s u r f a c e l a y e r depth remains constant f o r a p e r i o d of hours a f t e r the onset of the wind, so a co n s t a n t l a y e r depth approximation i s adeguate. T h i s model w i l l be d i s c u s s e d i n more d e t a i l i n the next s e c t i o n . S ince d e n s i t y p r o f i l e s were not measured i n weeks 1 or 2, the l a y e r depth can o n l y be approximated by the week 3 v a l u e s . T h i s assumption may be p a r t l y r e s p o n s i b l e f o r the s c a t t e r o f the drag c o e f f i c i e n t values i n the week 1 c a l c u l a t i o n s . 189 Another q u e s t i o n t h a t a r i s e s i s the r e l a t i o n s h i p of the p y c n o c l i n e depth to the depth of zero c u r r e n t as was d i s c u s s e d i n chapter I I I , I f the zero c u r r e n t depth were somewhat s m a l l e r than the p y c n o c l i n e depth or i f the p y c n o c l i n e depth were s m a l l e r , then the v a l u e s of drag c o e f f i c i e n t c a l c u l a t e d would be s m a l l e r and c l o s e r t o the accepted values of 1 to 1.5x1Q-3. These c a l c u l a t i o n s have shown t h a t a two-layer model, with l i t t l e f r i c t i o n between the l a y e r s , may be used to e x p l a i n some of the wind d r i v e n c i r c u l a t i o n f e a t u r e s of the s u r f a c e l a y e r , V I I . 3 Farmer's .Model Of,.ft Hind-Driven, Surf ace ..Layer As p a r t of h i s study i n A l b e r n i I n l e t , Farmer (1972) developed a l i n e a r two-layer model to d e s c r i b e the behaviour of the s u r f a c e waters of a f j o r d under the i n f l u e n c e of a wind s t r e s s . The model w i l l not be developed i n d e t a i l here: o n l y enough of the f e a t u r e s w i l l be d i s c u s s e d to present adequately the r e s u l t s and compare them with o b s e r v a t i o n s i n Howe Sound. Farmer approximated the i n l e t by a s e m i - i n f i n i t e c a n a l o f uniform width and depth c o n t a i n i n q two homogeneous l a y e r s of d i f f e r e n t d e n s i t y . He d e s c r i b e d the system with l i n e a r i z e d equations of motion and c o n t i n u i t y f o r a two-l a y e r f l u i d . They were v e r t i c a l l y i n t e g r a t e d over each l a y e r and converted to a "normal mode" r e p r e s e n t a t i o n . Farmer then proceeded to s o l v e the f o l l o w i n g equations f o r U, the upper 190 l a y e r i n t e r n a l mode ( b a r o c l i n i c ) t r a n s p o r t and ••-YJ , the displacement of the i n t e r f a c e from the mean l a y e r depth, h. cjzrj/at* = c 2 ^ 20/dx 2+ d(T-KU) / ^ t (7.3) * U/^t = c 2 ^ / ^ x + T (7.4) In these eguations T i s the kinematic wind s t r e s s , c i s the i n t e r n a l wave speed and K i s an i n t e r f a c i a l f r i c t i o n c o e f f i c i e n t f o r the i n t e r n a l mode. Farmer c o n s i d e r e d s o l u t i o n s f o r c e d by a wind s t r e s s a p p l i e d from x=0, the head of the i n l e t t o x=d, some point f a r t h e r down the i n l e t . Performing a Laplace transform with r e s p e c t t o time of egua t i o n 7.3 and a p p l y i n g the a p p r o p r i a t e boundary c o n d i t i o n s he a r r i v e d a t the s o l u t i o n s IT =__T_(-exp(-*x) +exp_(-^(d+x)) -exp(- *(d-x)) +1) (7.5) (s+K) 2 2 f o r x < d. Here the overbar i n d i c a t e s the transformed g u a n t i t y and s i s the transform v a r i a b l e . The i n t e r f a c e displacement eguation then became *n = _T_(exp (-* x) -exp (- *(d+x)) -exp (-* (d-x))) (7.6) 1 c 2 2 2 where ^ =js (s+K) / c . From t h i s p o i n t , Farmer i n v e r t e d the l a y e r depth eguation and examined i t s behaviour f o r s h o r t 191 p e r i o d s of wind s t r e s s i n the re g i o n near the i n l e t head where x/c<(d-x)/c. Let us now d i v e r g e from h i s work and examine the t r a n s p o r t and i n t e r f a c e displacement f o r an u p - i n l e t wind s t r e s s a p p l i e d f o r a long time ( t>(d+x)/c ) i n a f r i c t i o n -f r e e s i t u a t i o n (K=0) . The i n v e r s e transforms of equations 7,5 and 7.6 a r e : U=T < t - (t-x/c) H (t-x/c) + (1/2) ( t - (d+x) /c) H(t- (d + x) /c) -(1/2) ( t - (d-x)/c) H(t- (d-x)/c) I (7.7) and T | = (T/c) | (t-x/c) H (t-x/c) - (1/2) ( t - (d-x) /c) H ( t - (d-x) /c) -(1/2) ( t - ( d + x ) / c ) H ( t - ( d + x ) / c ) | (7.8) where fl(t) i s the Heaviside u n i t step f u n c t i o n . These s o l u t i o n s break n a t u r a l l y i n t o two d i f f e r e n t s e t s : those where x/c < (d-x)/c and those where x/c > (d-x)/c. In Howe Sound the l o g i c a l c h o i c e f o r x=d i s a t the s i l l , where the u p - i n l e t wind speed i n c r e a s e s markedly due to topographic f u n n e l l i n g . Using the " s l a b " model we can c a l c u l a t e from the t r a n s p o r t and l a y e r depth, the mean v e l o c i t y of the l a y e r as u=U/(h + T T | ) . For l a t e r comparison with measured drogue a c c e l e r a t i o n s , the a c c e l e r a t i o n of the water i n the s u r f a c e l a y e r may be c a l c u l a t e d as ^ u /H. Since the model i s l i n e a r . 192 the s p a t i a l gradient terms i n the acceleration may be neglected. The solutions to t h i s system (eguations 7.7 and 7.8) for O,1^ , u, and a are as follows: x/c < (d-x)/c (d-x)/c < x/c t ; , , | 0 < t < x/c | 0 < t < (d-x)/c 1 . H V=Tt j u=Tt/h | r-a=T/h J i , 1 x/c < t < (d-x)/c i - | | (d-x) /c < t < x/c | ! D=Tx/c | D=(T/2) (t+(d-x)/c) | i <r| = (T/C) (t-X/C) | (T/2c) (t- (d-x) /c) | ! u=x/(t-x/c+ch/T) | u= ct+d-x | I 2ch/T-t+ (d-x) /c | I a=-x/ (t-x/c+ch/T) 2 1 a= 2 (c2h/T+d-x) I I (2ch/T+(d-x)/c-t) z l P--L ,., i ,. i (d-x)/c < t < (d+x)/c i ,, ,. | x/c < t < (d+x) /c | .. ,„ ,,. „ A 1 r 0= (T/2) (-t+ (d+x)/c) | ^= (T/2c) (t+(d-3x)/c) } u= (-ct + d+x) J 2ch/T+t+(d-3x)/c | a= 2 (-c*h/T-d+x) I (2ch/T+(d-3x)/c+t)2 j L. — 1 193 T h i s model o f a s u r f a c e l a y e r may be f i t t e d approximately to the n o r t h end of Howe Sound by choosing d=20km, h=5m and c=1m/s. For a steady wind of 10m/s, T^C^UJDI ( p , / f j = 1 . 56x10-* (cm/s) 2 f o r (^ = 1. 25x10 - 3 , P l o t s of average l a y e r v e l o c i t y and a c c e l e r a t i o n vs time c a l c u l a t e d from the above model are shown i n f i g u r e 43 f o r x=6km and x=15km. These val u e s of x correspond roughly to p o s i t i o n s o f the week 2 (north) and week 3 averaging bands, A d i r e c t comparison may be made between the v e l o c i t y and a c c e l e r a t i o n curves i n f i g u r e 43 (case 1) and f i g u r e 27 c and d and between f i g u r e 43 (case 2) and f i g u r e 27 g and h. The a c c e l e r a t i o n and v e l o c i t y curves i n f i g u r e 43 can be seen to be composed of three separate s e c t i o n s c o rresponding t o the d i f f e r e n t f o r c e s on the s u r f a c e l a y e r . The i n i t i a l f o r c i n g a r i s e s only from the wind s t r e s s which c o n s t a n t l y a c c e l e r a t e s the s u r f a c e l a y e r . The other f o r c e a r i s e s from s u r f a c e pressure g r a d i e n t s which propagate along the i n l e t as waves, one of which t r a v e l s from the head of the i n l e t and the other of which t r a v e l s toward the head of the i n l e t from the p o i n t d. Both waves t r a v e l at the i n t e r n a l wave speed. The wave t h a t propagates from the head 194 Figure 43 - Velocity and acceleration of the surface l a y e r vs time calculated from Farmer's model for an up-inlet wind of 10m/s applied at t=0. Curves lab e l l e d 1 are f o r x=6km, 2 are for x=15km. Model parameters are discussed in the t e x t . 195 o f the i n l e t , c a l l e d h e r e a f t e r the head wave, r e s u l t s from the c o l l e c t i n g of water pushed towards the head of the i n l e t by the u p - i n l e t wind d r i v e n t r a n s p o r t . T h i s water e l e v a t e s the s u r f a c e of the f j o r d c r e a t i n g a pressure g r a d i e n t t h a t balances the wind s t r e s s . The e l e v a t i o n o f the s u r f a c e causes a simultaneous d e p r e s s i o n of the i n t e r f a c e . The r a t i o of s u r f a c e e l e v a t i o n t o i n t e r f a c e depression i s approximately ap / p . The wave propagating from the point d^ c a l l e d the end wave by Farmer, i s caused by the n e c e s s i t y of having c o n t i n u i t y of t r a n s p o r t i n the s u r f a c e l a y e r a t t h a t p o i n t and hence c a u s i n g a s h a l l o w i n g o f the i n t e r f a c e . Before e i t h e r wave a r r i v e s at some po i n t x, the wind causes the constant a c c e l e r a t i o n of the s u r f a c e l a y e r t h a t was d i s c u s s e d i n the l a s t s e c t i o n . The l a y e r depth does not change. In f i g u r e 4 3, case 1, which i s c l o s e r to the head of the i n l e t , the head wave a r r i v e s before the end wave. The u p - i n l e t t r a n s p o r t then becomes constant and the l a y e r depth i n c r e a s e s , hence the v e l o c i t y decreases and the a c c e l e r a t i o n becomes negative. When the end waves a r r i v e s l a t e r the n e g a t i v e a c c e l e r a t i o n i n c r e a s e s i n magnitude u n t i l the time (d+x)/c when t r a n s p o r t , v e l o c i t y and a c c e l e r a t i o n become zero. In f i g u r e 43, case 2, nearer the po i n t d, the end wave a r r i v e s f i r s t . Since the l a y e r depth i s de c r e a s i n g and the t r a n s p o r t i s i n c r e a s i n g the a c c e l e r a i o n remains p o s i t i v e . However when the head wave a r r i v e s , the a c c e l e r a t i o n drops d r a m a t i c a l l y and becomes negative. Again, at time (d+x)/c the v e l o c i t y becomes zero as does the a c c e l e r a t i o n . These a c c e l e r a t i o n curves bear a resemblance t o those 196 shown in figure 27 measured i n Howe Sound. The curves i n figure 13 of course were f r i c t i o n l e s s . I f f r i c t i o n were added to t h e s o l u t i o n the sharp corners i n the velocity curves would disappear, the sharp changes i n acceleration would disappear and the acceleration values would, i n general, decrease i n magnitude. A l l these factors should help to bring the theory more i n l i n e with the observations. The t h e o r e t i c a l acceleration curve remains r e l a t i v e l y constant and positive u n t i l the time that the head wave a r r i v e s , at which time i t becomes negative. The observations agree: the period of constant acceleration increases from week 2 to week 1 to week 3. The range of both the t h e o r e t i c a l and observed acceleration i s 8x10- 3cm/s 2. The range of both the observed and t h e o r e t i c a l v e l o c i t i e s i s about 60cm/s. There are however some major differences between theory and observations. Theory says that the length of time of negative acceleration should be much longer than the time of positive acceleration. The observations show that, although the negative phase i s longer than the posit i v e phase, i t i s only s l i g h t l y longer. Theory shows a rapid change from positive to negative acceleration and a slow return to zero, while observation shows rates of change from positive to negative and negative to positive that are almost the same. The ve l o c i t y curves too show some difference between observation and theory. The t h e o r e t i c a l v e l o c i t i e s are only up-inlet. They must be superimposed on the mean r i v e r flow to be comparable to the observed v e l o c i t i e s . Even with the -5cm/s of the mean r i v e r flow 197 added they do not approach the down-inlet s t r e n g t h of the observed c u r r e n t s . A r r i v a l o f the waves a t a point a f t e r a few hours causes the v e l o c i t y t o drop even though the wind c o n t i n u e s . Thus the c u r r e n t peak nay occur before the wind peak and hence the c u r r e n t may appear t o l e a d the wind as i t d i d i n chapter VI. Farmer's model seems t o d e s c r i b e reasonably w e l l many of the observed f e a t u r e s o f the time v a r i a t i o n s of the s u r f a c e l a y e r c i r c u l a t i o n . . I t does not agree with the o b s e r v a t i o n s when the pressure g r a d i e n t s a re i n t e r a c t i n g with t h e wind-stress d r i v e n f l o w , i . e . when the i n t e r f a c i a l waves reach the point o f measurement. The model i s l i n e a r while the o b s e r v a t i o n s have shown that f o r the important r e g i o n near the head the flow regime i s n o n - l i n e a r . Thus once the pre s s u r e g r a d i e n t s that have propagated through t h i s r e g i o n i n t e r a c t with the purely wind-driven flow, we can expect d i s c r e p a n c i e s . Heaps and Hamsbottom (1966) have suggested t h a t a c i r c u l a t i o n e x i s t s w i t h i n a homogeneous s u r f a c e l a y e r t h a t i s i n dynamic balance between a wind s t r e s s and a s u r f a c e pressure g r a d i e n t . Under these circumstances the " s l a b " r e p r e s e n t a t i o n o f the s u r f a c e l a y e r used i n t h i s t h e s i s would not be v a l i d and the t h e o r e t i c a l v e l o c i t y e s t i m a t e s would be wrong as they do appear t o be. However Farmer's model and the " s l a b " r e p r e s e n t a t i o n of the s u r f a c e l a y e r seem t o be i n remarkable agreement with the f i r s t few hours of the observed i n t e r a c t i o n between the wind and the s u r f a c e l a y e r i n Howe Sound. 198 VII.4 T i d e s And A Normal-Mode F i o r d Hodel S e v e r a l s e t s of o b s e r v a t i o n s of the c u r r e n t s i n Hcwe Sound can be e x p l a i n e d by the presence of a b a r o c l i n i c t i d e . Observed c u r r e n t s a t a l l depths were st r o n g e r than 2 cm/s i n the s e r a i - d i u r n a l band but a b a r o t r o p i c t i d a l prism model f o r Howe Sound mentioned i n chapter I I I p r e d i c t s only 0.7 cm/s a t the c u r r e n t meter l o c a t i o n . The phasor diagram i n f i g u r e 39 f o r the s e m i - d i u r n a l c u r r e n t s showed l a r g e phase d i f f e r e n c e s between the c u r r e n t s at d i f f e r e n t depths. The u p - i n l e t s u r f a c e l a y e r c u r r e n t s near the head of the i n l e t appeared to be 180° out of phase with the t i d a l h e i g h t , not 90° out of phase as would be expected i f the c u r r e n t were uniform with depth. I t has been shown (Proudman,1953) t h a t depth d i s c o n t i n u i t i e s i n a s t r a t i f i e d f l u i d can cause a b a r o c l i n i c response t o b a r o t r o p i c f o r c i n g . Rattray (1960) computed the b a r o c l i n i c response of the deep ocean to the i n t e r a c t i o n between a b a r o t r o p i c t i d a l wave and the c o n t i n e n t a l s h e l f . A s i m i l a r study was c a r r i e d out by Buckley (1974) f o r b a r o t r o p i c f o r c i n g at the mouth of a f j o r d - l i k e b a s i n . Both s t u d i e s were of the si m p l e s t p o s s i b l e two-layer f r i c t i o n -f r e e type. The f o r m u l a t i o n and r e s u l t s of both models were very s i m i l a r but the technigues of s o l u t i o n o f the equations d i f f e r e d . The r e s u l t s w i l l be presented i n the form given i n R a t t r a y . The model i s based on the equations of momentum and c o n t i n u i t y i n each of two homogeneous l a y e r s i n a narrow 199 s e m i - i n f i n i t e c a n a l . The s o l u t i o n s t o these equations are d i f f e r e n t i n r e g i o n s o f d i f f e r e n t depth and so are s u b j e c t t o a matching c o n d i t i o n f o r i n t e r f a c e h e i g h t and t r a n s p o r t i n each l a y e r a t the depth d i s c o n t i n u i t y . Time dependence of the system i s assumed to be p r o p o r t i o n a l to e x p ( - i e - t ) so a l l time d e r i v a t i v e s are r e p l a c e d by - i r and the system o f equations i s s o l v e d f o r s p a t i a l dependance a l o n e . R a t t r a y ' s model c o n t a i n s no t r a n s v e r s e g r a d i e n t s of the v a r i a b l e s but does allow f o r a constant t r a n s v e r s e c u r r e n t d r i v e n by C o r i o l i s f o r c e . Since Howe Sound i s too narrow f o r r o t a t i o n a l e f f e c t s t o be s i g n i f i c a n t at the i n t e r f a c e , the model has been modified by removing the e f f e c t s of the e a r t h ' s r o t a t i o n . > T h i s m o d i f i c a t i o n i s c o n s i s t e n t with the a d d i t i o n of l a t e r a l boundaries t o R a t t r a y ' s v e r s i o n of the model. F i g u r e 44 shows the bas i n geometry used and i n d i c a t e s the v a r i a b l e s and parameters i n the problem. The eguations a r e s o l v e d f o r the f o u r v a r i a b l e s u», u", and \" where u' i s the s u r f a c e l a y e r t r a n s p o r t / u" the bottom l a y e r t r a n s p o r t , J,' the s u r f a c e height d e v i a t i o n from the mean and the i n t e r f a c e height d e v i a t i o n from the mean., The equations can however be separated i n t o a "normal-mode" r e p r e s e n t a t i o n such t h a t each v a r i a b l e i s broken i n t o a b a r o t r o p i c part and a b a r o c l i n i c part i . e . u*=u* +uj where u5' i s the surface: l a y e r t r a n s p o r t due to a b a r o t r o p i c wave and u'. i s the s u r f a c e l a y e r t r a n s p o r t due to a b a r o c l i n i c wave. S o l u t i o n s are c a l c u l a t e d f o r the r e g i o n s 0<x<L and x>L r e p r e s e n t i n g the r e g i o n s i n s i d e the s i l l and i n the r e g i o n o f the s i l l . The s o l u t i o n s given by Ra t t r a y f o r 0<x<L 200 Figure 44 - Basin geometry and parameters used for the two-layer b a r o c l i n i c t i d a l model. 201 n e g l e c t i n g r o t a t i o n a l terms are il (7.9) t"=h» j> (7.10) S s —©7 ^»=A cos (k, x) (7.12) h'u.i = (D-h») u»= ( i «- /k. ) A s i n ( k ( x) (7,13) where • K , 2 = - " ' P . (7. 14) h« (D-h«) g ^ kf= ^zp^ (7. 15) h» (D rh«) g A* A= ^*h« (1/D, -1/D X) -Jl+kfL*'• K'exp ( i ( ^ - p ) ) (7.16) K= s/cos 2k, L+ ( k f / k f ) si&'k,-cx =tan-i (k r_) P =tan~» ((k^/k,) tan (k ,L)) i n these e q u a t i o n s , L i s the b a s i n l e n g t h , D, i s the basin depth, Dj_ i s the s i l l depth, h* i s the s u r f a c e l a y e r depth and cr i s the freguency. A s i m i l a r s e t of s o l u t i o n s e x i s t s f o r x>_, The system i s f o r c e d by a b a r o t r o p i c t i d e imposed as from the r e g i o n x>_. Since the system l e n g t h L i s very s m a l l with r e s p e c t t o the wavelength of the b a r o t r o p i c t i d e * ^ can be assumed t o have no s p a t i a l v a r i a t i o n . 202 What i s of most i n t e r e s t t o us now i s the phase r e l a t i o n s h i p of the c u r r e n t s t o the d r i v i n g f o r c e . The t o t a l s u r f a c e l a y e r c u r r e n t i s : u'=u«+u* (7.J7) =i<5- \'x+i e~A s i n (k x) (-7,.18) I f A i s s p l i t i n t o i t s r e a l and imaginary p a r t s such t h a t A=A» (cos (*-p) +i sin(<7\-p)) (7.19) then the s u r f a c e - l a y e r c u r r e n t may be w r i t t e n as u=f+i g (7.20) where f=A' <o s i n (cst-p) s i n (k, x) (7. 21) U»Is, and g=A« <s-cos(rt-p) s i n (k, x) -g^»x (7.22) The phase of the s u r f a c e c u r r e n t with r e s p e c t t o the f o r c i n g t i d a l amplitude i s t h e r e f o r e : 6 =tan-»(g/f) (7.23) 203 and the amplitude o f the c u r r e n t i s |u| = /f2+g2' (7.24) In Howe Sound an a p p r o p r i a t e c h o i c e f o r the parameters i n these eguations might be: L=2x10* cm D =2x10* cm D =7x10 3 cm h'=500 cm ^ P=2x10-z f Using the observed M z amplitude g i v e s (t)*-94cm and o--1.41x10-* rad/s. Table XII shows the amplitude and phase of the s u r f a c e l a y e r c u r r e n t f o r v a r i o u s values o f x. Since Table XII - Amplitude of the s u r f a c e l a y e r c u r r e n t and phase r e l a t i v e to the s u r f a c e e l e v a t i o n as c a l c u l a t e d from R a t t r a y ' s two-layer model parameterized t o f i t Howe Sound as d e s c r i b e d i n the t e x t . Speed amplitudes are i n cm/s, phase i n degrees. The d i s t a n c e x i s measured i n km from the head of the i n l e t . I • — T — ~ ' t—"—'~ 1 I x I amp | phase | | 5 | 1.79 I -14 J } 10 1 2.74 | -17 | | 15 J 2.47 | -27 | | 20 | 1.53 j -63 | L_ J , I t h i s model has the l o n g - i n l e t a x i s d i r e c t e d down-inlet i n s t e a d of u p - i n l e t as d i d the o b s e r v a t i o n s , the phase 204 a n g l e s c l o s e to zero i n d i c a t e t h a t down-inlet c u r r e n t and s u r f a c e e l e v a t i o n are n e a r l y i n phase. T h i s i s e x a c t l y what was observed i n the upper r e g i o n s of Howe Sound as shown i n f i g u r e s 24 and 27..Figure 45 shows the v a r i a t i o n along the i n l e t of the amplitude and phase of the s u r f a c e - l a y e r c u r r e n t s as p r e d i c t e d by t h i s model f o r an incoming wave r e p r e s e n t i n g the » z t i d e at Sguamish. The phase remains e s s e n t i a l l y constant i n the upper h a l f of the i n l e t but s t a r t s changing r a p i d l y near the s i l l . The amplitude has a maximum value almost halfway between the head and the s i l l . The amplitude of the c u r r e n t v a r i a t i o n s shown i n f i g u r e 27 f o r weeks 4 and 2N appears to be about 10cm/s, much l a r g e r than t h i s model p r e d i c t s . However, the model was c a l c u l a t e d o n l y f o r a pure H 1 t i d e of amplitude 92cm, but the a c t u a l t i d a l height change i n s i x hours duri n g those weeks was as much as 4m. The response of the s u r f a c e l a y e r to t h i s l a r g e r t i d a l change should be p r o p o r t i o n a t e l y l a r g e r , A comparison between the amplitude of the 3m c u r r e n t i n the s e m i - d i u r n a l band and the model-generated amplitude of the s u r f a c e l a y e r c u r r e n t of the H z t i d e a t x=15km shows t h a t the former i s about t r i p l e the l a t t e r amplitude. C o n s i d e r i n g the severe d i s t o r t i o n of the f j o r d topography necessary to s i m p l i f y i t enough f o r the two-layer model, e s p e c i a l l y i n the important r e g i o n of the s i l l , the d i f f e r e n c e between the two i s s m a l l enough to i n d i c a t e t h a t the model works w e l l enough t o v e r i f y t h a t these s u r f a c e c u r r e n t s c o u l d be caused by the suggested t i d a l mechanism. Thus t h i s two-layer normal mode model appears to Figure 45 - Amplitude of the surface l a y e r current and phase with respect t o the surface t i d a l amplitude as a f u n c t i o n of l o n g i t u d i n a l p o s i t i o n i n the i n l e t , x=0 i s the head of the i n l e t , x=20km i s the s i l l . Values were c a l c u l a t e d from the b a r o c l i n i c t i d a l model. 206 s u c c e s s f u l l y p r e d i c t the phase response of the s u r f a c e l a y e r t o a b a r o t r o p i c t i d a l f o r c i n g ana somewhat l e s s s u c c e s s f u l l y the amplitude response. The model does not however p r e d i c t s u c c e s s f u l l y the behaviour of the deeper water. The phasor diagram i i i f i g u r e 39 shows t h a t the amplitude of the ftz c u r r e n t i n c r e a s e s below the s u r f a c e l a y e r , r a t h e r than d e c r e a s i n g as t h i s model p r e d i c t s . The r e l a t i v e phase of the deeper c u r r e n t s i s not observed t o be con s t a n t as a f u n c t i o n of depth as i s p r e d i c t e d i n t h i s model. Therefore a more complex f o r m u l a t i o n i s needed t o model the behaviour of the deeper waters. E a t t r a y et al.(1969) have proposed a c o n t i n u o u s l y s t r a t i f i e d model of i n t e r n a l wave g e n e r a t i o n i n the ocean, s i m i l a r i n p r i n c i p l e t o the two-layer model j u s t d i s c u s s e d . The continuous s t r a t i f i c a t i o n i s modelled, i n the same manner as by L i g h t h i l l (1969), by an i n f i n i t e sum of normal modes based on the v e r t i c a l d e n s i t y s t r u c t u r e of the water column. The equations are s o l v e d f o r each mode i n d i v i d u a l l y . S i nce the model i s l i n e a r , the f i n a l s o l u t i o n i s the l i n e a r s u p e r p o s i t i o n o f the i n d i v i d u a l s o l u t i o n s . The modes form a complete s e t of orthogonal f u n c t i o n s , and so f o r c i n g f u n c t i o n s l i k e an incoming t i d a l wave or a v e r t i c a l wind-s t r e s s g r a d i e n t may be r e p r e s e n t e d by sums of these modes. The amplitude of each mode i n the sum r e p r e s e n t s the c o n t r i b u t i o n of the f o r c i n g f u n c t i o n t o t h a t mode. Such a model i n a b a s i n of f j o r d - l i k e geometry has been developed and d e s c r i b e d by Buckley (1974). Since the two-layered model worked w e l l t o d e s c r i b e the 207 s u r f a c e l a y e r behaviour, i t i s probable t h a t t h i s multi-mode model w i l l d e s c r i b e the behaviour of the deeper waters i n a much more r e a l i s t i c f a s h i o n . VII.5 ' Summary Of -Whe<::-Model^:Re;su-lts -The behaviour of the s u r f a c e l a y e r o f a f j o r d under the i n f l u e n c e of wind and t i d a l f o r c i n g was s t u d i e d with s e v e r a l simple models. The s u r f a c e l a y e r was f i r s t approximated by a s l a b under the i n f l u e n c e o f a wind s t r e s s g r a d i e n t as a body f o r c e . C a l c u l a t i o n s o f a drag c o e f f i c i e n t c o n s i s t e n t with those c a l c u l a t e d by other t e c h n i q u e s showed t h i s to be a v a l i d approximation f o r the f i r s t few hours a f t e r the onset of a wind. A v e r s i o n of Farmer's model f o r a wind-driven s u r f a c e l a y e r produced s a t i s f a c t o r y agreement with the o b s e r v a t i o n s i n the maqnitude of change;in v e l o c i t y and a c c e l e r a t i o n and i n the approximate shape of the v e l o c i t y and a c c e l e r a t i o n vs time curves. I t d i d not reproduce adequately the a c t u a l observed s u r f a c e l a y e r v e l o c i t i e s or the a c c e l e r a t i o n many hours a f t e r the onset of the wind. A mod i f i e d form of B a t t r a y ' s i n t e r n a l t i d e •'••generation model s u c c e s s f u l l y reproduced the observed phases o f the s u r f a c e l a y e r c u r r e n t s near the head of the f j o r d . Approximately the r i g h t amplitudes were a l s o produced by t h i s model which showed the production of a b a r o c l i n i c response t o a b a r o t r o p i c t i d a l f o r c i n g over the s i l l . Based on these two reasonably s u c c e s s f u l two-layer normal mode models, a s t r a t i f i e d normal-mode model was 2 0 8 suggested t h a t might reproduce many of the observed f e a t u r e s o f the c i r c u l a t i o n of a f j o r d l i k e Howe Sound. 209 BIBLIOGRAPHY B e l l , 9 , H . 1975..The Howe Sound c u r r e n t metering program. Pac. Mar. S c i . Rept. 75-7, I n s t i t u t e o f Ocean S c i e n c e s , P a t r i c i a Bay, B.C. 3 v o l s . , Bendat,J.S. and A . G . P i e r s o l . 1971. 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Water Survey of Canada, 1974. H i s t o r i c a l streamflow summary, B r i t i s h Columbia to 1973, Inland Waters Directorate, Dept. Of the Environment, Ottawa. 694p. Webster,I.T. and D.M.Farmer. 1976. Analysis of s a l i n i t y and temperature records taken at three lighthouse stations on the B.C. coast. Pac, Mar. Sci, Rep, 76-11, I n s t i t u t e of Ocean Sciences , P a t r i c i a Bay, B.C. Webster,P.J. and D.G.Curtin. 1974. Interpretations of the EOLE experiment I: temporal variations in Eulerian quantities. J. Atmos. Sci, ,31:1 860-1875, Wylie,F,J. 1968. The use of radar at sea. American Elsevier Pub. Co. New York , 280p, Zeilon,N. 1913. On the seiches of the Gullmar Fjord. Svensk, Hyd-biol. Skr. V, 22p. 213 APPENDIX I BEHAVIOUR OF A DROGUE IN A VERTICAL SHEAR The movement o f a drogue i s governed by drag and torque f o r c e s generated on i t by the surrounding a i r and water. These f o r c e s may be estimated by using the standard drag approximation f o r a f l a t p l a t e p e r p e n d i c u l a r to the flow: F - ( p C i/2)U|U|A (A. 1.1) where p i s the d e n s i t y of the f l u i d , C j i s the drag c o e f f i c i e n t f o r f l u i d flow p e r p e n d i c u l a r t o a f i n i t e r e c t a n g u l a r p l a t e , U i s the v e l o c i t y of the f l u i d past the p l a t e and A i s the area of the p l a t e . The e f f e c t s of wind and s u r f a c e c u r r e n t s on a deep drogue have been c a l c u l a t e d by Kirwan e t a l . (1975). The 214 drogues used i n t h i s experiment behave d i f f e r e n t l y s i n c e t h e i r drag elements are r i g i d l y a t t a c h e d to the s u r f a c e f l o a t a t i o n u n i t . An a n a l y s i s of t h e i r behaviour f o l l o w s . The major f o r c e s on the drogue are as f o l l o w s : i ) F M . T h i s f o r c e , the drogue weight, i s d i r e c t e d v e r t i c a l l y downward and , s i n c e i t i s c o n c e n t r a t e d mostly i n the r e i n f o r c i n g rod, i s taken to act at the cEntre o f the rod. i i ) F . The buoyancy f o r c e i s e x a c t l y egual i n magnitude and o p p o s i t e i n s i g n t o the drogue weight. I t a c t s from near to but s l i g h t l y below the centr e of the buoyant sphere. i i i ) F_. The wind drag on the drogue may be estimated by assuming t h a t the f o r c e a c t s only on the radar r e f l e c t o r . The wind drag on the pole i s Included i n t h i s f i g u r e by adding a s m a l l amount to the a c t u a l area of the r e f l e c t o r . I t s magnitude i s p r o p o r t i o n a l t o the d i f f e r e n c e between the wind v e l o c i t y and the drogue v e l o c i t y . T h i s f o r c e a c t s i n a h o r i z o n t a l d i r e c t i o n . iv) Fs . The water drag on the drogue may be, i n most cas e s , c o n v e n i e n t l y broken up i n t o two s e c t i o n s ; F f , the f o r c e a c t i n g i n the d i r e c t i o n of the drogue v e l o c i t y caused by the water moving f a s t e r than the drogue, and 215 F R , the f o r c e a c t i n g i n the d i r e c t i o n a g a i n s t the drogue v e l o c i t y caused by water moving more slo w l y than the drogue. The former f o r c e u s u a l l y a c t s on the drogue from the water s u r f a c e down t o the depth at which the drogue v e l o c i t y equals the water v e l o c i t y . The l a t t e r f o r c e a c t s from t h i s point to the bottom of the drogue. These f o r c e s are shown s c h e m a t i c a l l y i n f i g u r e 46 and are t a b u l a t e d i n t a b l e XIII . When the drogue i s i n e q u i l i b r i u m with these f o r c e s , they must balance i n the h o r i z o n t a l and i n the v e r t i c a l d i r e c t i o n . Thus: The f i r s t eguation has the s o l u t i o n Fs=-mg. The other can o n l y be so l v e d i n s p e c i f i c circumstances. These f i v e f o r c e s a l s o e x e r t torgues on the drogue which must sum to zero f o r the drogue t o be i n e q u i l i b r i u m . Thus: (A.I. 2) and: F w + F F + F f c = ° (A.I.3) T +T +T +T +T =0 (A.1.4) 216 F i g u r e 46 - Forces on a drogue i n a v e r t i c a l . , c u r r e n t shear. u G i s the speed of the drogue. 217 Table XIII - The f o r c e s and torques on a drogue. The f o r c e s are those shown i n f i g u r e 46. The torgues are about the p o i n t z . Source f o r c e torgue mass V= mg T =-mg ( D ~ 2 0 / c o s e ) s i n e buoyancy F B=B T B=-B (z 0 /cose) s i n e wind drag F w = P . q / 2 ( t L - u 0 ) T w = f . q / 2 ( 0 ^ - u o ) . (D+zo /coso) cos © water drag F F = » p u C : > / 2 . [ ( u - u o ) zdz [ ( U - U c ) 2 ( Z - Z o ) d Z water drag T) cx>s e j ( u - u 0 ) 2 d z 1. COS © , ( U - U Q ) 2 ( z - 2 ) d z f V = d e n s i t y of a i r u ^ v e l o c i t y o f water p w=density of water u D = v e l o c i t y of drogue A =area of drogue i n a i r U w = v e l o c i t y of wind w, =width of drogue i n water m =mass of drogue & =angle of drogue w.r.t. v e r t i c a l B =buoyancy f o r c e D =depth of drogue i n water, height of r e f l e c t o r above water z D=depth at which drogue velocity=water v e l o c i t y 218 These two equations must be s o l v e d f o r the three unknowns u 0 , z o a n d Q . A t h i r d e q uation must be provided f o r s o l u t i o n . I t i s u s u a l l y an equation r e l a t i n g water v e l o c i t y t o depth, u=u ( z ) . We w i l l now assume s e v e r a l simple forms of the v e l o c i t y p r o f i l e and s o l v e the system to examine i t s behaviour. In the f i r s t case, l e t us take a c o n s t a n t c u r r e n t of v e l o c i t y u(z)=c. I f the wind v e l o c i t y i s i n the same d i r e c t i o n as the c u r r e n t , u 0>c, a l l the water moves more s l o w l y than the drogue and hence z 0=0. I f the wind d i r e c t i o n i s o pposite to that of the c u r r e n t , then u o<c and z 0=DcosQ. C o n s i d e r i n g the case where the wind and c u r r e n t are i n the same d i r e c t i o n and the wind speed i s g r e a t e r than the c u r r e n t speed, the f o r c e balance eguation becomes: ^ M f l ^ - u j z - i i fLDcos0(c-u o) 2=0 (A. 1.5) The torgue balance equation becomes: -mgDsine + ^C^/2 (U^-u 0) 2A+ pJJC^/2 ( C - U Q ) 2 D 2 c o s 2 0 /2=0 (A.1.6) To s o l v e these eguations the f o l l o w i n g v a l u e s are used: 2 1 9 (V=1, 25x10-3 gm/cm3 pw=1 gm/cm3 0^=1.2 (from Binder, 1962) D=200 cm W=300 cm g=980 cm/sec 2 A=930 cm* m=20000 gm For a range of values of 0^ and c, the r e s u l t s are given i n t a b l e XIV . Table XIV - Drogue speed and t i l t angle f o r v a r i o u s c u r r e n t and wind speeds i n a homogeneous c u r r e n t of magnitude c. The wind speed i s 0\ . r - c I 0 cm/s ... i t 10 cm/s ~~t— 2 5 " - - 1 cm/s | i °* m/s i l -cm/s l e 1 deg • 1 1 cm/s —f~ - 4— e deg I cm/s 0 ! deg | i i i 1 i ! T 1 1 0 . 4 \ 0 . 0 3 ! 1 0 . 4 ! 0 . 0 3 ! 2 5 . 3 i 0 . 0 2 | 1 0 1 | 2 . 6 2 I 1 4 . 0 I 2 . 6 0 | 2 9 . 0 ! 2 . 5 8 I 2 0 ! 8 . 2 I 1 0 . 3 8 ! 1 8 . 2 ! 1 0 . 3 5 | 3 3 . 2 ! 1 0 . 3 0 | ±. . i _ X _ . L _. . X . . i From t h i s t a b l e i t can be seen that the d i f f e r e n c e between drogue v e l o c i t y and water v e l o c i t y i s about 0 . 4 % of the wind v e l o c i t y and t h a t the drogue t i l t i s g u i t e s m a l l . The t i l t , as expected, i n c r e a s e s roughly as the sguare of the wind speed. The only d i f f e r e n c e s i n drogue behaviour when the wind 220 and the current oppose each other are that the drogue t i l t w i l l be i n the opposite d i r e c t i o n , i . e. the drogue w i l l s t i l l t i l t downwind, and the sign of (u 0-c) w i l l change so that the drogue v e l o c i t y w i l l be decreased rather than increased as i s the case when the wind and the current are i n the same d i r e c t i o n . Considering now the case of a linear v e r t i c a l shear u(z)=s (1-z/D) with the wind i n the same di r e c t i o n as the current, the horizontal force balance eguation becomes: ffcMD,-u (J«-i fw/3 (s/D) z ( (Dcos 6 -z o) 3 - z o 3)=o (A. 1.7) The torgue balance eguation i s : -mgDsine + (U w-s+sz 0 /D) 2A (Dcos 6 +zo ) + ^ W(C3>/8) (s/D) 2 ( (Dcos e -z o ) *+z „*) =0 (A. 1.8) The solutions to these eguations are tabulated i n table XV for various values of 0 and s. This table shows that the r e l a t i v e l y strong shear of 25 cm/s/m causes by i t s e l f only a t i l t of 8°.,A wind speed of 10 m/s, the maximum allowable f o r performing the experiment, only increased t h i s by 2°. Comparison with the i d e n t i c a l c a lculations done holdinge=0 shows that the ef f e c t of the 221 Table XV -c u r r e n t shear speeds are i i n degrees f r o were not c a l c u f o r wind-indu the maximum cu s p e c i a l case c o n c l u s i o n s . Values o f drogue speed and t i l t i n a l i n e a r f o r v a r i o u s wind and c u r r e n t speeds. Mind n m/s. Current speeds are i n cm/s, t i l t a ngles m the v e r t i c a l . The values i n d i c a t e d by — l a t e d because the eguations used are not v a l i d ced drogue motions g r e a t e r i n magnitude than r r e n t speed and because c a l c u l a t i o n of t h i s would not make any d i f f e r e n c e t o the general f s j. T -! 10 cm/s 20 cm/s l + I I u 0 50 cm/s | 1 e G 0 l 5 . 0 | 0 . 3 j 10 .0 i 1.3 I 2 5 . 2 1 7 .9 10 8 .0 I • 3. 1 I 11 .7 I 3 , 9 I 26. 1 1 10 .2 20 1 1 I ! 16. 3 I 12. 3 1 28, 9 I 17.1 t i l t angle i s to i n c r e a s e the drogue speed by a f a c t o r of (1/cos0), This d i f f e r e n c e i s not s i g n i f i c a n t f o r the drogue t i l t s observed i n t h i s experiment, amounting t o 2% at 10° and 6% at 20°. These two t a b l e s show that the e f f e c t of the wind on the drogue's speed and t i l t decreases with i n c r e a s i n g shear. A 20m/s wind i n c r e a s e s the drogue speed by 8.2 cm/s over the average water speed when there i s no shear but o n l y by 3.9cm/s i n a shear of 25cm/s/m. T h i s r e s u l t i s a conseguence of the v e l o c i t y sguared dependence of the drag f o r c e s . Since the mean square v e l o c i t y d i f f e r e n c e i n c r e a s e s as the s t r e n g t h of the shear i n c r e a s e s f o r a constant d i f f e r e n c e i n v e l o c i t y between the drogue and the water a s m a l l e r v e l o c i t y d i f f e r e n c e i s necessary i n the presence of a shear t o keep the drogue i n e g u i l i b r i u m with the wind drag. When the wind opposes the c u r r e n t d i r e c t i o n , the 222 e f f e c t of the wind on the drogue v e l o c i t y i s i n h i b i t e d even more. The t i l t angle of the drogue e s t a b l i s h e d by the shear i s decreased by the wind and hence the depth of the bottom of the drogue i s i n c r e a s e d , exposing the drogue to more of the shear. Thus a s m a l l e r d i f f e r e n c e i s needed between the drogue v e l o c i t y and the mean water v e l o c i t y t o c r e a t e a drag f o r c e to balance the wind drag. In the most severe case shown i n t a b l e 7 with s=50cm/s and wind and c u r r e n t i n the same d i r e c t i o n , a wind of 20m/s i n c r e a s e s the drogue speed by 3.7cm/s and the drogue t i l t by 9.2° over the zero wind v a l u e s . Hhen the wind and c u r r e n t are opposed, the speed d i f f e r e n c e i s -2.9cm/s and the angle d i f f e r e n c e i s -10.3°. The d i f f e r e n c e s between the two cases are s m a l l even i n t h i s extreme example and decrease i n l e s s extreme dnes. N e g l e c t i n g now the sma l l e f f e c t of t i l t on the drogue speeds, i t i s necessary o n l y t o s o l v e the f o r c e balance equation with 6=0 t o f i n d the e f f e c t s of v a r i o u s shears and wind v e l o c i t i e s on the drogue. Looking at equation A.I.5 with c=0 and approximating n u » u 0 « 0 = x/TpoA/ ' 0^ (A.I. 9) f o r the parameters r e l e v a n t t o t h i s experiment then u o = (4.56 x 10 - 3 ) u (A.I.10) 223 T h i s r e s u l t , s t r i c t l y t r u e o n l y f o r wind over completely s t i l l water, p r o v i d e s a reasonable upper estimate of the d i f f e r e n c e between drogue speed and water speed as a f u n c t i o n of wind speed. I g n o r i n g now the e f f e c t s of wind drag as w e l l as those of t i l t , l e t us look a t the r e l a t i o n s h i p of u 0 , the drogue v e l o c i t y , t o the mean and r.m.s. v e l o c i t i e s of v a r i o u s a n a l y t i c v e r t i c a l c u r r e n t shears. The t h r e e to be c o n s i d e r e d are a l i n e a r p r o f i l e , u(z) = 1-z/D ; a q u a d r a t i c p r o f i l e , u (z) = 1-z 2/D 2, and an e x p o n e n t i a l p r o f i l e u (z)=exp(-z/D). The comparison between these i s shown i n t a b l e XVI . In the q u a d r a t i c case, where the d i f f e r e n c e between mean and drogue v e l o c i t i e s i s the g r e a t e s t , the shear i s much st r o n g e r than one would expect to f i n d i n Howe Sound. A weaker shear (deeper z e r o - c r o s s i n g ) would show l e s s discrepancy between the v e l o c i t y e stimates. From t h i s t a b l e i t seems apparent t h a t there i s no simple u n i v e r s a l r e l a t i o n between drogue v e l o c i t y and mean v e l o c i t y or r.m.s. v e l o c i t y f o r the p r o f i l e s examined. T h e r e f o r e such a r e l a t i o n should not be expected f o r any a r b i t r a r y p r o f i l e . The r e s u l t s o f the t h r e e - l e v e l experiment d e s c r i b e d i n chapter V showed a maximum shear of 10cm/s/m corresponding to the middle column of t a b l e XV i f the shear were l i n e a r . There were not enough data p o i n t s i n the v e r t i c a l t o determine the shape of the shear p r o f i l e . I f the shear p r o f i l e i s s i m i l a r to any o f those i n t a b l e XVI then the r e s u l t s i n t a b l e XIV i n d i c a t e t h a t the v e l o c i t i e s determined 224 Tabl e XVI - Drogue v e l o c i t y , mean v e l o c i t y and r.m.s. v e l o c i t y f o r three a n a l y t i c shears. The mean and r.m.s. v e l o c i t i e s are c a l c u l a t e d over drogue depth. P r o f i l e l i n e a r o a. o Drogue .5 Mean . 5 r.m.s. . 58 g u a d r a t i c . 75 . 67 .73 e x p o n e n t i a l . 64 5 . 632 .658 from the drogues i n the experiment should be very c l o s e to the mean v e l o c i t y o f the upper l a y e r . The average wind speed d u r i n g the experiment was about 5 m/s. This would cause a maximum e r r o r i n drogue speed of 2 cm/s. Since the r.m.s. drogue speed was g r e a t e r than ten times t h i s , c o r r e c t i o n s f o r wind drag on the drogues have 225 been neglect©- and the drogue v e l o c i t i e s taken as the water v e l o c i t y . 226 APPENDIX II COMPUTER MOVIE GENERATION The computer programme MOVIE on the IBM 370/168 , took i n p u t data from many sources and combined them t o produce a magnetic tape t h a t c o u l d be i n t e r p r e t e d as a movie by programme MAP6 on t h e PDP-12 . These input data were: Drogue p o s i t i o n s i n t e r p o l a t e d a t one minute i n t e r v a l s , s o r t e d i n temporal order and s t o r e d on magtape as the output from *S0RT . T h i s i s the tape r e f e r r e d to as DATA2 i n chapter I I . : Hind speeds and d i r e c t i o n s on a minute by minute b a s i s as i n t e r p o l a t e d from the winds at Sguamish. T i d a l h e i g h t s on a h a l f - h o u r l y b a s i s as taken from the r e c o r d a t Pt. Atkinson. A c o a s t o u t l i n e e x a c t l y as prepared f o r input 227 to programme MAPS . The c o a s t l i n e and t i d a l height curve were w r i t t e n out a t the beginning o f the output tape. The remainder of the tape contained a s e r i e s of r e c o r d s , each one corresponding t o the s t a t u s o f the i n l e t at one p a r t i c u l a r minute of the experiment. Each re c o r d c o n t a i n e d the time that the record r e p r e s e n t e d , the p o s i t i o n of a l l the drogues i n the water a t t h a t time and a s e r i e s of numbers t h a t corresponded to the p o s i t i o n s of dots forming an arrow whose len g t h and d i r e c t i o n corresponded to the speed and d i r e c t i o n of the wind at t h a t time. The drogue p o s i t i o n s and wind v e c t o r dot p o s i t i o n s were, of course, s c a l e d to PDP-12 screen co-o r d i n a t e s . Programme HAP6 con t a i n e d b a s i c a l l y the same tape h a n d l i n g and d i s p l a y s u b r o u t i n e s as d i d MAP5 . Both programmes c o u l d produce "worm" movies on the screen of the PDP-12 as d e s c r i b e d i n chapter I I . The d i f f e r e n c e between the two programmes was that MAP6 had a great d e a l of f l e x i b i l i t y i n the d i s p l a y mode and c ontained an i n t e r f a c e r o u t i n e t o c o n t r o l a movie camera. I t was p o s s i b l e i n MAP6 t o s e l e c t the l e n g t h of the worm d i s p l a y e d and t o c o n t r o l the d i s p l a y speed by v a r y i n g the number of p i c t u r e s d i s p l a y e d s i m u l t a n e o u s l y on the screen and the number of minutes between each p i c t u r e d i s p l a y e d , r e s p e c t i v e l y . Wind speed and d i r e c t i o n was i n d i c a t e d on each frame of t h e movie by an arrow. T i d a l height was i n d i c a t e d on the t i d a l curve by a c u r s o r whose p o s i t i o n was c a l c u l a t e d from t h e r e l a t i v e time of t h a t p i c t u r e from the beginning of the 228 experiment. To t r a n s f e r t h e image from the screen of the PDP-12 t o f i l m , the programme c o n t r o l l e d a r e l a y t h a t t r i g g e r e d a s o l e n o i d t h a t t r i g g e r e d a Bolex H16 R e f l e x movie camera. Using Kodak T r i - X R e v e r s a l 16ma f i l m , the CRT screen was dim enough to allow one second exposures a t f11, By va r y i n g the r a t i o o f camera frames to computer movie frames, the time compression of the f i n a l movie could be c o n t r o l l e d . For example, i f the p i c t u r e s advanced at 2 minute i n t e r v a l s and the camera took 3 frames of each p i c t u r e , then t h e r e would be 30 p i c t u r e s d i s p l a y e d of each hour and 90 frames taken of each hour . fit a p r o j e c t i o n r a t e of 18 frames per second, the time compression i s 720:1. T h i s i s 1 hour i n 5 seconds or 1 day i n 2 minutes. fi f a s t e r r a t e i s obtained by advancing the p i c t u r e s a t 5 minute i n t e r v a l s and t a k i n g 2 frames of each. T h i s y i e l d s a compression o f 2700:1 or 1 day i n 32 seconds. appendix I I I i s a s e c t i o n of movie t h a t was made i n t h i s f a s h i o n . I t c o n t a i n s two s e c t i o n s of f i l m . The f i r s t i s the e n t i r e week 1 data set shot at the f a s t e r r a t e p r e v i o u s l y d i s c u s s e d . I t i s fo l l o w e d by a s e c t i o n of week 1 data at the slower r a t e showing i n d e t a i l the e f f e c t o f the wind event between 56 and 76 hours. 

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