UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Internal oscillations of tidal character in certain B.C. inlets Davis, Patrick Austin 1960

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1960_A8 D2 I6.pdf [ 6.07MB ]
Metadata
JSON: 831-1.0085378.json
JSON-LD: 831-1.0085378-ld.json
RDF/XML (Pretty): 831-1.0085378-rdf.xml
RDF/JSON: 831-1.0085378-rdf.json
Turtle: 831-1.0085378-turtle.txt
N-Triples: 831-1.0085378-rdf-ntriples.txt
Original Record: 831-1.0085378-source.json
Full Text
831-1.0085378-fulltext.txt
Citation
831-1.0085378.ris

Full Text

(i)  INTERNAL OSCILLATIONS OP TIDAL CHARACTER IN CERTAIN B.C. INLETS  by PATRICK AUSTIN DAVIS B.A., U n i v e r s i t y o f B r i t i s h Polumbia, 1960  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A. i n the Department of PHYSICS  ¥ 0 accept t h i s t h e s i s as conforming required  t o the  standard  THE UNIVERSITY OF BRITISH COLUMBIA April,  1960  In p r e s e n t i n g the  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  University  o f B r i t i s h Columbia, I agree t h a t  the  Library  s h a l l make  it  and  study.  I further  f r e e l y available f o r reference  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the Head of  Department o r by h i s r e p r e s e n t a t i v e s .  my  I t i s understood  t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not  be allowed without my  The U n i v e r s i t y of B r i t i s h Vancouver Canada.  Columbia,  written  permission.  (ii)  Abstract A study o f s e r i e s of p r o f i l e s o f temperature and c u r r e n t at one s t a t i o n i n Knight I n l e t , and o f temperature at two simultaneous s t a t i o n s i n Bute, have been made i n c o n j u n c t i o n with seasonal p r o f i l e s of temperature, s a l i n i t y , and the a s s o c i a t e d d e n s i t y .  Gn t h i s b a s i s c e r t a i n hypo-  t h e t i c a l models have been f i t t e d to the dynamics w i t h i n the inlets. A c a l c u l a t i o n o f the p o s s i b l e modes of p r o g r e s s i v e i n t e r n a l waves f o r the two i n l e t s has l e d to< agreement i n Bute I n l e t .  only  A q u a l i t a t i v e e x p l a n a t i o n of the c o n d i t i o n  i n K n i g h t i n terms of the dynamic  c i r c u l a t i o n over the  sill  has l e d to suggestions as to the mechanism, of exchange i n the deeper waters o f the i n l e t , and s p e c u l a t i o n as t o the p o s s i b i l i t y of p r e d i c t i o n of s t a t e s w i t h i n an i n l e t i n terms of i t s topography, r u n o f f c y c l e , and communication with the c o a s t a l waters.  *iii) Table o f Contests  Page<t>  Introduction  1  Chapter I 1) D i s t r i b u t i o n o f Oceanographic  Properties  i n 8*C. i n l e t s  3 5  2) T i d e s 3) The ^ R e l a t i o n Oceanographic  o f T i d e s t o the D i s t r i b u t i o n , o f Properties  10  Chapter I I 1) The Oceanogrgphic  S t r u c t u r e o f Bute and Knight I n l e t s  12  2) S e r i a l D i s t r i b u t i o n o f P r o p e r t i e s  19  3) Harmonic A n a l y s i s  23  4) Theorem o f C o n t i n u i t y  28  Chapter I I I  The Equations o f Motion  1) I n t e r n a l Waves (i)  32  The s o l u t i o n f o r a continuous d e n s i t y  d i s t r i b u t i o n 32  ( i i ) Approximate forms  41  2) Other Forms o f O s c i l l a t o r y Motion (i)  44  The s o l u t i o n , f o r f i n i t e l e n g t h and v a r i a b l e depth  ( i i ) A f i n i t e b a r r i e r a t the month o f an i n l e t Conclusions  47 50  Tables 1) Comparison o f amplitude c a l c u l a t e d theorem with d e f l e c t i o n s  from  continuity  o f isotherms.  2) Wave v e l o c i t i e s and dppths o f maximum amplitude. 3) Computed v a l u e s o f sr corresponding to depths f o r observed  44  amplitudes.  4) Regression c o e f f i c i e n t s  (iv) 5) Comparison  o f computed and observed v a l u e s o f amplitude Kn 5a.  6) Comparison  o f computed and observed v a l u e s o f c u r r e n t Kn 5a.  7) Comparison  o f computed and observed v a l u e s o f amplitude Bu 4*  8) Comparison  o f computed and observed v a l u e s o f amplitude Bu 6.  9) Values f o r c o n s t a n t s o f the approximate form f o r the s t a b i l i t y * 10) Depthi o f maximum amplitude and r e l a t i o n o f average phase t o t h a t o f t i d e f o r anchor s t a t i o n s i n Bute I n l e t f o r which thereRare harmonic analyses* Figures 1) L o c a t i o n o f s t a t i o n s Knight and Bute I n l e t s . 2) P r o f i l e s of temperature Knight and Bute  Inlets.  3) S e r i e s o f temperature p r o f i l e s Bute I n l e t 1957 to 1958. 4) P r o f i l e s o f s a l i n i t y Knight and Bute  Inletss  5) P r o f i l e s o f d e n s i t y Knight and Bute I n l e t s . 6) S e r i e s o f s t a b i l i t y p l o t s through Knight I n l e t 1956. 7) T-S diagrams through Knight I n l e t 1956. 8) Time S e r i e s d e n s i t y a t Knight 8-1/2. 9) Time s e r i e s o f p l o t s temperature, temperature  gradient,  d i f f e r e n c e from mean temperature, and c u r r e n t s a t K n i g h t 5 ( J u l y 4 t o 6, 1956). 10) Average  temperature f o r time s e r i e s p l o t s Knight 5,  11) S e r i a l data Knight 5. 12) Brunt f r e q u e n c i e s Knight 5, Bute 4. 13) Harmonic a n a l y s i s of t i d e s a t A l e r t Bay ( J u l y 4 t o 6, 1956). 14) V e r t i c a l o s c i l l a t i o n s and temperature f l u c t u a t i o n s Kn 5a. 15) V e r t i c a l o s c i l l a t i o n s Knight 5b ( i ) and ( i i ) . 16) H o r i z o n t a l c u r r e n t s a t Knight 5.  (T)  Figures  (cootAd)  17)  V e r t i c a l o s c i l l a t i o n s at Bute 4 and 6  18)  O s c i l l a t i o n s e x h i b i t e d with phase according  19)  Density lity  to p e r i o d  d e s t r i b u t i o n s and l o g a r i t h m i c p l o t o f s t a b i -  Knight 5a  20)  Mean d e n s i t i e s a t Bute 4 and 6 used f o r i n t e g r a t i o n  21)  Logarithmic  p l o t S t a b i l i t y d e r i v e d from mean d e n s i t y  Bute 4 and 6 22)  I n t e g r a t i o n Knight 5a  23)  I n t e g r a t i o n Bute 4  24)  Results  25)  Synthesis  o f v e r t i c a l o s c i l l a t i o n s Knight 5  26)  Synthesis  o f h o r i z o n t a l c u r r e n t s Knight 5  27)  Synthesis  o f v e r t i c a l o s c i l l a t i o n s Bute 4 and 6  28)  Diagram i l l u s t r a t i n g f l o w over b a r r i e r i n two-  of r e g r e s s i o n  analysis  l a y e r system 29)  Diagram i l l u s t r a t i n g flow over a b a r r i e r o f a. continuously  stratified  system.  (vi)  Acknowledgements The r e s e a r c h was c a r r i e d out under the superv i s i o n o f Dr. G.L. P i e k a r d , with the f i n a n c i a l a s s i s t a n c e of the Defence Research Board o f Canada.  F a c i l i t i e s of  the ALWAC computer were made a v a i l a b l e through the mathematics department o f the U n i v e r s i t y of B r i t i s h Columbia. The author would a l s o l i k e to acknowledge the a s s i s t a n c e he has gained through c o n s u l t a t i o n with members o f the I n s t i t u t e o f Oceanography and other departments, i n p a r t i c u l a r the k i M l y  i n t e r e s t the members o f the s t a f f o f the  computing c e n t e r have always taken i n h i s work*  Introduction' The oceanography  o f c o a s t a l waters, t e a much  g r e a t e r extent than t h a t o f the open ocean, i s i n f l u e n c e d by the a s t r o n o m i c a l t i d e s , b o t h i n the dynamics o f the water body as a whole and i n the r e l a t i v e d i s t r i b u t i o n and mixing o f the p r o p e r t i e s at depths below the s u r f a c e .  This  i s p a r t i c u l a r l y t r u e o f the B*C* c o a s t , broken as i t i s by many deep i n l e t s o f g r e a t extent i n t o which the t i d e must penetrate d u r i n g every t i d a l  cycle*  The d i s t r i b u t i o n o f p r o p e r t i e s and the dynamics o f the i n l e t s are c a l c u l a t e d from surveys which i n v o l v e t e n or twelve hydrographic c a s t s w i t h readings a t some dozen depths taken o f t e n over a p e r i o d o f a day or mere.  It i s difficult  to make a c l o s e r g r i d without i n c r e a s i n g the p o s s i b i l i t y o f change o f p r o p e r t i e s d u r i n g the time o f run, nor to make a s w i f t e r survey without l o s i n g d e f i n i t i o n through too few stations.  Thus a r i s e s the need f o r some s o r t o f model or  hypothesis based on some elementary hydrodynamic  model t o  r e l a t e the r e a d i n g s both i n time and space* The v a r i o u s models proposed so f a r have been based on an assumption o f steady s t a t e and the t i d a l and other r e l a t i v e l y short term p e r i o d i c motions have e i t h e r been i g n o r e d or averaged out*  The d i s t r i b u t i o n o f p r o p e r t i e s shows a change  of the phase with depth o f the p e r i o d i c movement o f the waters with the t i d e , and a d e f i n i t e s h i f t o f phase between s t a t i o n s which i s incompatible with the very s h o r t phase l a g of the s u r f a c e t i d e s , i n d i c a t i n g some form o f i n t e r n a l motion a s s o -  e l a t e d with-, t h e s t r a t i f i c a t i o n o f t h e deeper water*of  Series  r e a d i n g s o f temperature a t s e v e r a l anchor s t a t i o n s i n d i c a t e  an i n t e r n a l m o t i o n 'with .a dbf i & i t e Hiaxiaim o f a m p l i t u d e a t same depth below the s u r f a c e . '<Tsr t h i s t h e s i s c a l c u l a t i o n s ' a r e made'- fsrosi a m o d e l o f s  an' i n t e r n a l ^aya  i a ' a s t r a t i f i e d fluid'making' use e f a method  devil sad by,, • S j a l d s t a d ' {1938) and adapted f o r use on a d i g i t a l computer *•'' .'She r e s u l t s of'such an'integration, have boon compared at/Several s t a t i o n s with t h e ' d e t a i l e d harmonic a n a l y s i s of  vertical Oscillations*  sill  A t a s t a t i o n some d i s t a n c e from t h e  (a bottom e l e v a t i o n , o c c u r r i n g c l o s e t o t h e s o u t h o f most  inlets)''tK©'"calculations f i t " q u i t e ' w e l l *  I n the v i c i n i t y of  the'••silly oav t h e o t h e r hand* t h e r e i s l i t t l e c o r r e s p o n d e n c e , A f u r t h e r h y p o t h e s i s as to- t h e mcde o f f l o w o f a s t r a t i f i e d f l u i d over a f i n i t e b a r r i e r formed b y Long ( 1 9 S 4  2  s  based o n model experiments per-*  1955} i s suggested as a p o s s i b l e esspla-  n a t i o n , of -the d i f f e r e n t c h a r a c t e r o f t h e m o t i o n between t h e 1  stations"''la"the- two i n l e t s studied*,  I n t h i s system, t h e s i l l  height''and'-froude number' ar© c r i t i c a l i a d e t e r m i n i n g tsaethes? the  motion-'is s t r i c t l y p e r i o d i c o r develops' i n t o a h y d r a u l i c  jump f o r a two f l u i d s y s t e c .  T h i s goes o v e r t o a system o f  eddies' f o r "the- case o f c o n t i n u o u s l y s t r a t i f i e d f l o w in. t h e lee  "of s u c h a b a r r i e r * '•'•'Data from c r u i s e s and anchor s t a t i o n s made i n But©  and K n i g h t I n l e t s a r e f i r s t examined q u a l i t a t i v e l y t o e s t a b l i s h tho  nature o f the t i d a l motion.  S e r i a l d a t a a r e then a n a l y s e d  q u a n t i t a t i v e l y t h r o u g h harmonic a n a l y s i s and p r e s e n t e d as b a r  diagrams.  C a l c u l a t i o n s frosa the mean, d e n s i t y d i s t r i b u t i o n s  a t oao s t a t i o n f r o m each, i n l e t a r e made t o f i n d modes, o f i n t e r n a l waves..  the possible  She unknown p a r a m e t e r s a r e e v a l u a t e d  • from' t h e o b s e r v e d / o s c i l l a t i o n s a n d t h e . s y n t h e s i s ' c h e c k e d  a g a i n s t 'the '<^b&.0yr^-.r^i\iea^ uniform  . The p o s s i b l e e f f e c t o f non~ ..  d e p t h and h o u n d e d end on, t h e s f o r m o f t h e motion, axe.  e x a m i n e d , a n d t h e ,^two  m a j o r obstacles'-"'to t h e a p p l i c a t i o n : ' o f  liong^js. .theory f o r . £ low 'of a s t r a t i f i e d f l u i d are  explained.  over a b a r r i e r  , An a t t e m p t i s made ;i» t h e c o n c l u s i o n s  c a t e what f u r t h e r work 'could c o n t r i b u t e  t o a ©ore  to indi-  realistic  h y p o t h e t i c a l model .for. t h e i n l e t s , . C h a p t e r I.  , .: r i  1). -The • d i s t r i b u t i o n of. Oceaoograph'ie P r o p e r t i e s i n B . C . I n l e t s . • yi:Mk$ d i s t r i b u t i o n o f o c e a n o g r a p h i c p r o p e r t i e s i n t h e • •, -governed b y two $aajor p r o c e s s e s g. t h e t i d e s a n d t h e  inlets  ' runoffv'i';dd#^ sed o f th© d i s c h a r g e " 'from- t h e m a j o r r i v e r s a n d t h e :  marginal.' stre'asas.* ;  by  She c l a s s i f i c a t i o n o f i n l e t s i s p r i m a r i l y  f a c t o r s -which i n f l u e n c e e i t h e r one o f t h o s e  proeessesss  '(Pickard -1955) 9  a)  D i v i s i o n - o f i s l e t s fey r u n o f f * In large runoff  inlets  the s t r a t i f i c a t i o n  pronounced toward t h e head o f t h e i n l e t per  ( a n i n c r e a s e o f 2S p a r t s  t h o u s a n d i n t h e f i r s t . h a i o e l i n e between 5 a n d 12 m e t e r s a n d  airs, i n c r e a s e the  i s most  t o 90$ a t 20 m e t e r s , f r o m t h e a l m o s t f r e s h , w a t e r a t  surface).  I n the low runoff  decreases as"abruptly  i n l e t s the s a l i n i t y  a s th© w a t e r © o f t h e o t h e r  nowhere  group  (ranging  f r o © 7 t o - 2 8 p a r t s p e r t h o u s a n d i n t h e s u r f a c e w a t e r n e a r th© head).'  T h i s marked v a r i a t i o n o f s a l i n i t y  in. t h e s u r f a c e  layers  of  the i n l e t i n d i c a t e s t h a t at l e a s t i n t h i s l a y e r the d e n s i t y  w i l l be p r i m a r i l y d e f i n e d by the s a l i n i t y . b)  D i v i s i o n o f i n l e t s by location)* Those i n l e t s In c o n n e c t i o n w i t h the n o r t h e r n c o a s t a l  waters show i n t h e i r deeper waters a h i g h e r s a l i n i t y and lower temperature (temperature o f 6*5° C. and a s a l i n i t y o f 32*5 p a r t s per thousand) as compared t o t h a t i n the i n l e t s south o f Knight (which show temperatures o f 7.5° C. and s a l i n i t i e s o f 30.5 p a r t s per thousand), while  K n i g h t remains intermediate  between the two. c)  D i v i s i o n of i n l e t s by s i l l  depth.  There are only a few i n l e t s on the B.C.  coast which-,  l i k e many o f the Norwegian ones, have such h i g h s i l l s the  that  s i l l s prevent the i n t r u s i o n o f h e a v i e r water t o r e p l a c e the  deeper water of the i n l e t , which on t h i s account becomes s t a g nant. of d)  However the m a j o r i t y o f i n l e t s seem t e have f r e e  exchange  t h e i r deeper water w i t h t h a t o u t s i d e . Seasonal v a r i a t i o n s i n the p r o p e r t i e s * I n l e t s a l s o d i v i d e n a t u r a l l y i n t o those i n l e t s whose  r u n o f f i s dominated by d i r e c t d i s c h a r g e from r i v e r s of p r e c i p i t a t i o n f a l l i n g as r a i n i n t h e i r watershed w i t h a maximum  im  s p r i n g and f a l l , and o t h e r s with r u n o f f composed o f the summer m e l t i n g o f p r e c i p i t a t i o n which, f a l l s as snow i n t h e i r  watershed,  with some i n l e t s combining some c h a r a c t e r i s t i c s o f b o t h . In too  i n l e t s where the mixing d u r i n g the s p r i n g i s not  g r e a t , the e f f e c t o f a c c l d winter can be seen u n t i l  late  i n t o summer as a c o l d wedge o f water, s e v e r a l degrees c o l d e r  i n . t e m p e r a t u r e t h a n any surrounding w t o r , featiera  A • similar d i s t r i -  .of' ossygesi h a s also- fee@B. r«$ o r t o d a n d h a s b e a n . ^ a t t r i b u t e d ••'  i© i n t r u s i o n o f low oatygsa. weter f r o t a r e g i o n s o f ^.-fairly  high, r e d u c t i o n ,  r e g u l a r esehaago. o f a i r l - d a p t h i * a t o r -.-aoacsa-'  p a s s i e s the/. :jtas3iisa i s runoff'*  S h e 'exchange e f d e e p e r w a t e r i s '  :  h o w v e r > .'sioit' i r r e g u l a r : - a n d &ppooxs t o t a k e .plaoe. b y i n , t ^ u s i o a s o f d e n s e r water*. •©•).  .  ;  S h o r t ' j>03F4oa i r r e g u l a r motion- of. «&tor.-* ,. •"  •  '.•There i s l i t i l o - i n f o r m a t i o n - a b o m i s u c h p e r t u r b a t i o n s  •to:.-;tho r e g u l a r s y s t e m a s a h e a v y r a i n f a l l o r v e r y strong- 'Sisd w h i c h m a y s t r i p away. tho. s u r f a c e w a t e r . o f a n i s l e t -19§2),or  (Fieldstad,  t h e -response o f t h e d e e p e r , w a t e r s o f a n i s l e t - t o a  -turbidity' c u r r a n t o r t o t h a t i d e *  These a r e f a e t o r s :  rasioh  s a y g i v e a quit© e r r o n e o u s i d e a o f th© n o r m a l s i t u a t i o n s d u r i n g , a o-iie»=>day""c^mi»e' t o suofe' a ' r e g i o n * ;  2)  -gji&ao-  :  , : ;  "."•*•"• Tr'All" g r o c e s a e a that-'- ia&a jfl&ca .at t h e boundaries o f t h e o c e a n 'ara i n f l u e n c e d t o a g r e a t e r o r l e s s o r e x t e n d b y v  oceanic tides*  fe  lakes and s e a s  9  however . the response i s s  s m a l l d u o t o t h e l i a i i t a t i o i j t t h e b o u n d a r i e s impose © n wave length*  "Is-iBost e a s e s I t a s o s d e s o f t h e b a s i c t w l v © s a d  t w e n t y — f o u r ' hour o s c i l l a t i o n s oe0as'ic""tide to  s  will  s  t h e dominant c o m p o n e n t s o f th©  o c c u r * ' Lofeos' ejad. s e a s r e s p o n d s o r e . r e a d i l y  i m p u l s e s o f wind o r o t h e r boundary  f o r c e s , as. t h e n a t u r a l  p e r i o d " o f 'a w a t e r body, which i s d e t e r m i n e d b y t h e rove l e n g t h , (a  f u n c t i o n o f t h e l e n g t h o f l a k e ) a n d t h e wave v e l o c i t y " ( a  f u n c t i o n ' o f t h e depth.) i s u s u a l l y crack s m e l l e r t h a n t h e  p e r i o d '&$ t h e • tide-generating'''forces*'. ;  ,.; > vi,-  • « i ' • S©i©h$s;^»a>s...i&eae' o s c i l l a t i o n s determined, by.,the  -.dimensions o f t^;;^t«*'^odgr- i&r'©-. ^e&j^ffj,, .Qtiefu? as ajrospoaoo to. wind? wave,,- or. curfce&t ia-^bays and,,gulf s., co.naected, t o tho ;  opea oc-eaa.0 ^T/h&s© soicbessGorr.espondv.plosgly'.i^L period, t o tbatybtdh,  'a bay would haver-it i^'";^%f;;cop3^1©t©ly .>i^|og«d<... . :  (  • Th©refor@v-it-'lsv&© b© expected thai' the resp0a.se generating  forces  will  the/'.'-tido^. .  be '.'small*;-,1|& .#i©v'offiior. ^oasd;-&h©, :/  ,  BO- . •  • c a l l e d c o ^ o s c i i l a t i o a t o t h e ©.esaal^-.t'ide. i s by no^ M^ans.: s m a l l * Th© response.- s a y be, .•increased i f :tSe; l e n g t h . o f ,th©. gjil^:ris- some  impropriate- f r a c t i o n Of the-;^v4,-.. length*,, th,©. s a ^ ^ . / c r / i t ^ r i a as J  .-for 'e closed" body o f watorf .nmsttfty t h a t the, wave ro.flec;tod • frosi' a tiound&ry ..roinf ore© the . n ^ ^ i & c o r o ^  •  -';-" •'"•^.'••'fhel By6,*:',:i-nle/fe)B.i i n .spite of, their_ .considorable :  loag-&-»»rd'6i- ni^ •.support;>'ilarg© i  .resonant responses to. the-tldoo -..  I n ah;lnlfet'.'.:w ith an average de^ihv-df 80O ;  i  metor.s th© maximum  ;spioeid---fo«'-lb'i^e^lis^l^.^ud^ .'shallow,water •:wave. is,;©G'.sieters per :s^'c'pnd'>o.^. one"hundred 'and eighteen, k i l o m e t e r s p^r .;hOiUg <. • ;  ;  ;  >  ior^an>;4jal ^!^f one^;hun%ed 'and- 'S^ty,\&ilpm^t©rs;.(l0O;..g$ie8) ;  the i iia'tur'ai' period' • %i about .2' hour e, j.,;. very, s h o r t j-compared, to .. • :  a' t i d ^ ^ ^ t ^ ' & w a v e . o f IS-liOurs'-'geriod'; w i t h the v e l o c i t y of 60;' 'm'e^'fei'.f:.  ; ''seoottd',h&s' a w&v©: l e n g t h -ot- .over, .g^'Oprkilpsotor s :  ;  e  fails'*-©?'. • ti;4©/''^1,1 be./prpppgated. up .ass-, i n l e t so- gu'ickly'that i t r^taia^' ''almost the.'s-asjo- phase,-throughout,- the, ialet, '.s- length.,, ,. ;  !  ?  fh'is>'i''^ ^i^QFdl' the .<c«s£. _ Throfrgh'-\th©. 80 . k ^ ^ © t © r s ^ ^ j p ^ , a ^ i ^ y  Alo3bt'' Bay''just o u t s i d e the .-mouth, of E a i g h t I n l e t , end @l@n.dal'©" ;  •Cove near' i t s - m i d p o i n t t h e r e - i s " a change of fiir© degrees i n ;  the s e m i - d i u r n a l .component o f the-tide«  Although presumably  cbaag£-ag;-tli'©;''sattir.© o f t i e f l o o d OT tibhj t h e s i l l does n o t s i g n i f i c a n t l y r e t a r d i t , Similarly there i s a s h i f t o f t e n degrees' i n ' t h i s ' eoapoaeiit 'between F 6 i n t • A t k i n s o n i n the':Str©'i't''; ;  o f G e o r g i a and f a d d i n g t e n Harbour a t t h e head of' B u t e , a. d i s - •• tanoo'" of- a^pr'oxiraately '"twice t h a t 'In-'Shigkt.  .'  '.""In 'the p r e s e n c e o f l a t e r a l b o u n d a r i e s g e o s i r ^ p h i e :  force's'''have';40' o t h e r e f f e c t o n a /steady f l o w t h a n t o cause th© l e v e l " s u r f a c e s t o s l o p e up from' l e f t t o r i g h t o f t h e d i r e - , ;  c t i o n o f f l o w i n t M Northern, gemi'sphera. . Shio i s i n ' a ftnaor' s i m i l a r t o 'that du© t o c e n t r i f u g a l " f o r c e a t a, bend i n th© f l o w , e x c e p t t h a t , t h e r e i s so secondary h e l i c a l f l o w a s s o c i a t e d w i t h ©orlolls'force i n a s t r a i g h t c h a n n e l , s i a e e t h e d i s p l a c e m e n t o f t h e levels"'' i s t h e ease t h r o u g h o u t t h e length©'of t h e f l o w * On the" o t h e r hand' a t i d e t h r o u g h a n y . s e c t i o n w i l l cause-a -' per i o d i c a l l y ' r e v e r s i n g - f l o w w h i c h w i l l e x p e r i e n c e f o r c e p r o p o r t i o n a l t o it's v e l o c i t y * secondary;flow  i s to be expectedj  a Coriolia  t h u s some c o n s i d e r a b l e  sweeping t h e p r o p e r t i e s f i r s t  one way' a c r o s s t h e i n l e t , t h e n t h e o t h e r , as t h e t i d e ebbs and flows.' " A t ' i n t e r n a l s u r f a c e s t h i s e f f e c t w i l l be.considerably enhanced: i s th© presence' o f any s t r a i i f i c a t i o n . 7  These' e f f e c t s  have'not been e x t e n s i v e l y s t u d i e d i n B-.C., i n l e t s though, i t i s ka®«a.'tha,t''ia t h e S t r a i t o f G e o r g i a t h e t i d e d e f i n i t e l y f l o o d s ;  along, one" s i d e and ebbs o n t h e o t h e r . X ^ r i c t i o n can m o d i f y t h e r e s o n a n t  characteristics of  a t i d a l wave, p r i m a r i l y by i t s a c t i o n on t h e amplitude.* w h i c h r e s u l t s in''only p a r t i a l support o f the incoming wave by t h e 1  r e f l e e t o d one.  Thus a node d i s a p p e a r s  t o foe r e p l a c e d by a s  area of-ffiisiffiuia . a m p l i t u d e  and the.abrupt change o f phase a t  ?  the 'node;-.reduces- to a g r a d u a l one.as tho,for® ©f the co-rosci!-* .. latioa.-.approadhoa .that..of &.progressive decay o f p a p l i t u d o . . -.•  wave with.an;.exponential ....  -\\ . .';  ••<f.-Vr,;*^n>.^8tu«*ia8 where the . r e t a r d i n g e f f e c t s arafthas'd  ;  produced'' by :i|ie' outflow- o f a r i v o r and .the p r o g r e s s i v e . ..decrease :  v  :  i n d"epthi£-:;tha='-tide. has a s h o r t e n e d p e r i o d $ f f l o o d .with,;..-.respect v  to- tho- shore.;,-. B e l a t i v e iOi-the river., o f course.), tho. p e r i o d i s the-'-aaiBes as' "the t i d e a t i t s mouth, :  the., shapo; o-f • tho peak, of'.... -  'tho ' f l o o d - i s •••steepened as? the h i g h e r amplitude parts, o f t h o .... wavo "overt-site" the e a r l y f l o o d * ^hos.© wav© v e l o c i t y i s a l s o . d e c r e a s i n g • with' depth.  I f the h y d r a u l i c head o f the f o l l o w i n g  water' is-" s u f f i c i e n t t o i n c r e a s e the. v e l o c i t y above t h a t of. a n inertiol:"WavO'in t h o some depth o f water.* .®. h y d r a u l i c jusap { t i d a l ' box©) may-develop* • Bue to- the- e f f e c t i v e drag; o f t h e bottosr the'-volo'City-of t h e t i d a l current's i n - i t s v i c i n i t y a r o s h i f t e d i a phase With r e s p e c t to. the l a y e r s above, and saay i n -fact''"b©"opposite - i a d i r e o t i o a to those at. th© su'$faoe» . •••*•• •• •'-••-l't"-ia not u n l i k e l y • that* socio or.'all o f theoo o f f o o t s -occur;-at'-'some'-point i n .the passage o f a-tide, into- tm, i n l e t * . ; • M'mo.gt"' ail'-'tho i n l e t s -are - separated front- the - c o a s t a l waters :.,, •' :  o f - t h e ooeaa by depths o f l e s s t h a n a - hundred • meters..  la  ;  'lsiigM''aad-';'B\Sst0 l a l a t s t h i s does l i t t l e - t o a l t e r the phase o r :  the amplit:udo.' :  s  though th© amplitude- i s i a e r e s o e d b y © f o o t .or- .  two probably.'due  t o a small c o - o s c i l l a t i o n e f f e c t ,  Bu-tv sosa©  ialotgs aro approached- by. entrance paswago-s- o f such:-small' , ;  d i m e a s i o a i r t h & t tho flow, aay a l l . b u t -cease- to-be :  iaertia-1.  and mav.be. m a i n t a i n e d i n s t e a d by t h e h y d r a u l i c head. between i t s two. ends* . fhorapsoa. aad Barkey,/(195$5 r e p o r t , that, at-'the ;  ;  eatrane©./channel, t o the/-Hugent, T e l i a e * ' a n d  Seymour-, cotoplejsh .  . o f • i a l e t s , .the coa@triet.ioa;. i s ouch., that- t h o t i d e s r u a o*a,the f l o o d and'-ebbc a t a'...rate.,of. twenty..knots.? ;oao.of :thio.--fei-gfee«fe.---i.'. ,  ;  ;  t i d a l . ,v#3^i.t'i©s ^^asnsaeyo, i a tfe.e, ^d.rld». I t i s . i a e o a c o i v s i b l o ;  ..that safch/-&:;-C;paqtric^i3o.a. w i l l h.ave rao,' effect o a ;tae-^ha$© o f :  the, •^do.st':^.'|%oea Its'i'tw© ends.*;. ;;•;';The-\eurroats': w h i c h ecceapany t h o t i d e s a r e - . b a s i c a l l y governed"by'rjtho. rospoaso'.sf t h e w a t e r s - i a t h e for®, of••  1-oag . <  i n e r t i a ! waye"^ . I o t i n . t h e i r .t.ur.a. the. currants;, may i a o d i f y t h o foro' of: 'th-a ' t i d e .through... t h e i r , seas a tiv.-ity.,-to gees t r o p h i c ep&\ ;  f r i c t i o a a l , f o r c e s * , ,X®%- th© t i d a l ro.sgase of, th©; inlets"'cannot.be e n t i r e l y ,.i'a-.ertial , f o r ; t h e . . t r e v o l . tirae< a a l o a l ^ t o d f o r the.". -;;; s  distf^c'a";-botwe©a.; A l e r t Boy .and GlendaiOrCov© f o r a wave t r a — ' •  :  v e i l i n g ;o.a ^:bottom o f 860 m e t e r s depth, '.(greater t h a n 'moat -©f ;  the r e p o r t ^ a ^ a e p t h t h e tidQ :tablos*. v  S t r a i t ' of'Georgia,  i n . . t h i s ; section).- i s t w i c e t h a t - r e p o r t e d - in. The• sama.is tru@->for th® two s t a t i o n s in*tl*©' :  Thus as. s u g g e s t e d by Dawson (1920) t h e  fl.ood" tid©/'&ots . l i k e , a . p i s t o a on,'th© .aoatSa o f • t h o i n l e t ; • f o r - ' " cia-g. .the' t i d e up a t a. r a t e much i a .excess, -of t h a t t o be e x p e c t e d o f a a i n e r t i a ' ! ..wave*. T h i s , would iadi-eate that';tho tid© a^t.ed :  r a t h e r l i k e one- i n am -estuary . and' t h a t the- p r o f i l e would b© !  3  steepened o a t h e f l o o d ,aad c o u l d &©•• longer-toe-t r e a t e d a s a ;  s i n u s o i d a l " o s c i l l a t i o n f o r which- t h o f l o o d and ebb a r e syaaaetric.  - io 3)  -  The R e l a t i o n of Tides to the D i s t r i b u t i o n o f Qceanographie P r o p e r t i e s The  simplest theory of the r o l e of t i d e and of r i v e r  d i s c h a r g e i n the exchange of p r o p e r t i e s i n and out of an i s t h a t of the t i d a l prism.  The theory of the t i d a l  inlet  prism  which i n v o l v e s d i v i d i n g the l e n g t h of t he i n l e t i n t o segments w i t h i n which there i s complete v e r t i c a l and h o r i z o n t a l mixing, was  o r i g i n a l l y d e v i s e d f o r use i n shallow bays and e s t u a r i e s  (Ketchum, 1951)*  However o b s e r v a t i o n s ( T u l l y , 1949)  the p r i n c i p a l exchange of the deep B.C.  show t h a t  i n l e t s takes p l a c e above  a depth of e l e v e n meters, a depth p o s s i b l y s u b j e c t to f u r t h e r l i m i t a t i o n by s i l l  depth*  A p p l i c a t i o n of the theory of the  t i d a l prism to the l a y e r above t h i s depth, where the segment i s determined  by the r i v e r discharge i n one  p e r i o d , and each subsequent volume i s determined  initial tidal  by the  inter-  t i d a l volume of the p r e v i o u s ones, has l e d to q u a l i t a t i v e agreement f o r the s u r f a c e l a y e r .  A typical i n i t i a l  segment  l e n g t h f o r a coast i n l e t such as Knight i s one m i l e , each subsequent segment i n c r e a s i n g by roughly one-twentieth p r e v i o u s one.  of the  In the f i f t y mile l e n g t h of the i n l e t there  would then be t h i r t y - f i v e prisms.  T h i s i s a l s o the number of  t i d a l c y c l e s f o r which a property discharged a t the head would s t a r t being removed from the mouth. nique i n which a mixing  A refinement of the t e c h -  l e n g t h i s determined  under the assump-  t i o n of complete h o r i z o n t a l advection g i v e s a f a i r l y  accurate  d i s t r i b u t i o n f o r the s u r f a c e p r o p e r t i e s o f the i n l e t s (Arons & Stommel, 1951).  - i i The simplest type of exchange between the upper l a y e r and t h a t beneath i t w i l l depend on the r e l a t i v e s t a b i l i t y between the two l a y e r s , which i n the f i n a l  sheer analysis  depends on the d e n s i t y and the t r a n s p o r t of the r u n o f f compared to  the t i d a l f l o w inward under t h i s l a y e r *  (Keulegan, 1949) between two  Model  show t h a t there e x i s t s a c r i t i c a l  experiments velocity  such l a y e r s above which the lower l a y e r w i l l  e n t r a i n e d f r e e l y i n t o the upper.  be  T h i s i s c h a r a c t e r i z e d by the  b r e a k i n g i n t o the upper l a y e r of i n t e r n a l waves propogated i n the  surface of separation*  Above t h i s c r i t i c a l v e l o c i t y an  e x p r e s s i o n f o r the volume of entrainment i n terms o f the t i c a l v e l o c i t y , and the r e l a t i v e v e l o c i t y o f the upper  cri-  layer  d e r i v e d from a simple model o f h y d r a u l i c flow, approaches v e r y c l o s e l y the observed v a l u e s .  A more s o p h i s t i c a t e d model of  e s t u a r i n e f l o w which takes account o f entrainment through an a r b i t r a r y form o f eddy d i f f u s i o n , p r o v i d i n g t h a t i t i s F i c k i a n , i n s p i t e of not p r e d i c t i n g the decrease of depth o f the upper l a y e r toward the mouth, does p r e d i c t the observed  critical  v e l o c i t y of the flow, and to a good approximation the observed density d i s t r i b u t i o n (Pritchard, In  1952).  a s i n g l e twelve hour p e r i o d the t i d e f i l l s  and  empties an average i n l e t o f a volume of water equal to the average r u n o f f i n a month.  The passage o f t h i s volume through  a c o n s t r i c t i o n , such as at the s i l l  i n Knight I n l e t , would  g i v e an average v e l o c i t y across the whole c r o s s s e c t i o n o f t h i r t y centimeters per second.  For a r e g u l a r s i n u s o i d a l v e l o -  c i t y t h i s g i v e s a maximum v e l o c i t y o f f o r t y - f i v e centimeters  - 12 per second throughout sill  the cross s e c t i o n .  Observations  a t the  ( P i c k a r d & Rogers, 1959) suggest t h a t the v e l o c i t y may be  n e i t h e r uniform  across the i n l e t nor through  i t s depth, but i s  concentrated near the center somewhat below the s u r f a c e , with a maximum v e l o c i t y o f over 120 centimeters per second.  If  the t i d e enters and leaves the i n l e t as a prism;, the o n l y apparent mechanism o f exchange f o r water below the s u r f a c e i s that of d i f f u s i o n .  X e t with h i g h v e l o c i t i e s and non-uniform  p r o f i l e i t i s q u i t e p o s s i b l e t h a t the f l o o d w i l l be c a r r i e d by its  momentum w e l l up t h e i n l e t i n the form o f a m o d i f i e d j e t  to mix and r e t u r n i n some other manner on the ebb.  T h i s may  i n i t i a t e some c o n s i d e r a b l e exchange w i t h waters o u t s i d e the inlet.  Should the waters below the s i l l  stratified,  i n the i n l e t be s t r o n g l y  waters t h a t enter i n a j e t w i l l be h e l d by t h e i r  buoyance above t h i s l a y e r , and t h i s form o f i n t r u s i v e j e t would be i n c r e a s e d i n extent.  Should the water o f the i n l e t be l e s s  dense than the water s p i l l i n g over the s i l l ,  i t w i l l be r e p l a c e d  by the h e a v i e r water and d r i v e n out o f the i n l e t on the ebb t i d e . Chapter I I The Oceanographic S t r u c t u r e o f Bute and Knight  Inlets  In the study o f the t i d a l processes o f the i n l e t s i t is  important  to e s t a b l i s h the r e g u l a r i t y o f the d i s t r i b u t i o n  of p r o p e r t i e s , i f a t a l l p o s s i b l e .  When a synoptic survey i s  attempted, i t i s hoped t h a t the v a l u e s o f these p r o p e r t i e s w i l l remain r e l a t i v e l y constant during the p e r i o d i n which the i n l e t is  sampled.,  X e t the time taken t o observe  at stations at f i v e  m i l e i n t e r v a l s through t h e l e n g t h of a f i f t y mile i n l e t may be  «• 13 ** a matter o f one to one and a h a l f days.  I f the s t a t i o n s are  r e l a t i v e l y evenly spaced i n t e r v a l s , the t i d a l i n f l u e n c e may become apparent as a p e r i o d i c displacement o f i s o p l e t h s as they are  plotted against  location.  On the other hand, i f a s e r i e s o f readings i s taken at  one s t a t i o n , the t i d a l  e f f e c t s w i l l be observed as p e r i o d i c  displacements o f i s o p l e t h s i n a time s e r i e s p l o t . When only a s i n g l e s t a t i o n i s taken, i t i s v i t a l t o the  i n t e r p r e t a t i o n o f these displacements (as h o r i z o n t a l ,  v e r t i c a l , or t u r b u l e n t movement o f the water) to know the g e n e r a l f e a t u r e s o f the h o r i z o n t a l d i s t r i b u t i o n o f p r o p e r t i e s . Once the main c h a r a c t e r i s t i c s have been e s t a b l i s h e d , an attempt can be made t o c o r r e l a t e the t i d a l movements with the p r i n c i p a l f e a t u r e s o f the i n l e t s . Among many i n l e t s on the c o a s t , Bute and Knight ( P i g . l ) have been s t u d i e d more e x t e n s i v e l y than the r e s t .  Bute  Inlet,  with a l e n g t h o f 41 m i l e s , width o f 2 and mean depth o f 500 meters, i s the :southernmost  o f the two.  I t possesses a smooth  bottom, which slopes i n easy stages from the head to a depth o f over 730 meters, erne d i s t a n c e behind a s i l l depth.  o f 250 meters i n  The waters o f the i n l e t are connected over t h i s  with the northern waters o f the S t r a i t o f Georgia.  Some connec-  t i o n with Johnston S t r a i t i n the north may a l s o p o s s i b l y the  deeper waters o f the i n l e t ,  sill  influence  the r u n o f f , which i s a l i t t l e  more than average f o r an i n l e t o f Bute's s i z e , o r i g i n a t e s (as i n most i n l e t s ) from the r i v e r s a t the head, the Homathko and the Southgate.  To the normal r u n o f f o f the p e r i p h e r a l streams along  - 14 its its  -  l e n g t h i s added t h discharge of the O r f o r d R i v e r c l o s e t o midpoint. Knight  is a little  longer than Bute, w i t h a l e n g t h of  f i f t y - f i v e m i l e s , average width o f 1,6 o f 400 meters.  m i l e s , and average depth  The bottom has the same r e g u l a r c h a r a c t e r  Bute with a maximum depth of about 600 meters. two  as  Between the  s i l l s , the inner of which i s only 65 meters i n depth, the  depth averages some 200 meters and the l e n g t h i s i n t e r s e c t e d by Tribune  Channel.  The outer s i l l  forms a narrow c o n s t r i c t i o n  of 60 meters i n depth and between f i v e and ten m i l e s i n l e n g t h . The  e f f e c t of the inner s i l l  w i l l be shown to be t h a t o f b l o c k -  ing  water o u t s i d e i t and below i t s l e v e l .  the deeper water between the s i l l s  On  the other hand  i s s a l i n e enough? t o i n d i c a t e  t h a t a p o s s i b l e exchange takes p l a c e between i t and Queen C h a r l o t t e S t r a i t . I f b l o c k i n g i s the case f o r the outer  sill,  exchange c o u l d take p l a c e only through Tribune Channel, which in  s p i t e of i t s great extent appears to be not much l e s s than  200 meters i n depth. in  The  deep water of Knight I n l e t i s midway  i t s c h a r a c t e r i s t i c s between those of the northern  inlets  d i r e c t l y connected with the c o a s t a l water, and those of the south connected with the S t r a i t of Georgia, whose waters are l e s s s a l i n e than those of the coast due  to the  considerable  discharge of the F r a s e r R i v e r . Thus the most s i g n i f i c a n t d i f f e r e n c e s between the two  i n l e t s a r e s ( i ) the s i l l  depth, e f f e c t i n g the degree o f  exchange o f deeper water, and  ( i i ) the l o c a t i o n , which d e t e r -  mines the nature of the deeper water exchanged.  •,/ • '- 15 - ' With the exception o f Knight I n l e t ( i n 1954), both i n l e t s have been v i s i t e d at l e a s t once a year since  1951.  Prom the r e s u l t s o f each c r u i s e l o n g i t u d i n a l p r o f i l e s o f temp e r a t u r e , s a l i n i t y , and <7  t  have been p l o t t e d .  During 1957  and 1958 some e i g h t c r u i s e s were made to Bute i n l e t , s e n t i n g most phases of the seasonal v a r i a t i o n .  repre-  Thus although  c r u i s e s i n Knight I n l e t normally were only made i n J u l y , i t i s p o s s i b l e to deduce the seasonal changes nf water s t r u c t u r e from Bute I n l e t i n s o f a r as they are common to> both*  To permit t h i s  comparison i s o p l e t h s have been drawn side by s i d e f o r each i n l e t and each y e a r . The temperature d i s t r i b u t i o n i n both i n l e t s i s chara c t e r i z e d d u r i n g the e a r l y p a r t o f the y e a r by a d i s t i n c t l y wedge-shaped s t r u c t u r e l y i n g at a depth o f approximately 100 meters, w i t h i t s t i p to the mouth o f the i n l e t and i t s c o l d core a g a i n s t the head.  Xet q u a n t i t a t i v e l y d i f f e r e n c e s do  appear between the two, i n p a r t i c u l a r the t h i c k n e s s and the sharpness which d e f i n e s the wedge's upper and lower surfaces.. However the temperature o f the c o l d core i s the same i n both inlets.  For example, the r e g i o n s bounded by the 9° C.  iso-  therm f o r the two i n l e t s from the diagrams of 1953 and  1956  may  be compared.  The t h i c k n e s s and l e n g t h i n Bute are 20  meters and t h r e e - q u a r t e r s of the i n l e t ' s l e n g t h ; i n K n i g h t some 100 meters and t h r e e - q u a r t e r s of the l e n g t h t o the inner sill.  Above the wedge the v a l u e s of temperatureeand  their  r a t e of change appear to be mueh the same i n both i n l e t s . Below the wedge the v a r i a t i o n of temperature to the deepest  - 16 p o i n t i n Knight  i s only 0.5 C . ° i n Bute 2 C . ° .  The g r a d i e n t  9  of temperature i s much b e t t e r d e f i n e d i n Bute, and i s l i m i t e d to  o n l y a few meters j u s t below the wedge,  ( F i g . 2)  An e x p l a n a t i o n o f the d i f f e r e n c e s i n the temperature s t r u c t u r e between the two i n l e t s c o u l d p o s s i b l y be found i n a theory o f the formation or decay o f t h i s wedge.  The water* o f  the wedge core i s c o l d e r , i n J u l y , than any surrounding e i t h e r o f the surface o r the connecting  water,  channels from which  an. exchange o f water c o u l d be expected to take p l a c e w i t h the inlet. On the other hand the formation o f the temperature wedge can be accounted f o r only by a c o o l i n g process  associated  with a boundary, such as the winter c o o l i n g o f surface water or the i n t r u s i o n over the s i l l some other s u r f a c e .  o f water cooled i n t h i s way a t  A number o f observations  indicate that  t h i s temperature minimum o r i g i n a t e s a t the s u r f a c e ; extent o f the wedge i n Knight  the l a r g e  i n s p i t e o f i t s shallower  sill,  the formation o f a c o l d l a y e r a t the surface i n Bute during; the s p r i n g o f 1953, and the very c l o s e connection  o f the f o r -  mation and character o f the wedge with the weather p a t t e r n (Tabatai & P i c k a r d , 1957),. The  decay o f the wedge appears to be from mouth t o  head, as the s e r i e s o f p r o f i l e s taken from c r u i s e s through Bute I n l e t d u r i n g 1957 and 1958 shows so c l e a r l y ( F i g . 3).. Remains o f the previous year's wedge are s t i l l  present i n  March and May o f 1958, as signs o f the new one appear near the surface.  - 11 The most important i m p l i c a t i o n from the occurence and v e r y slow d i s s i p a t i o n o f t h i s s t r u c t u r e are the l i m i t a t i o n s i t sets on the p a t t e r n o f c i r c u l a t i o n .  The presence" o f the wedge  f o r a l a r g e p a r t o f the year w i t h no source o f replenishment i n d i c a t e s t h a t the temperature over r e l a t i v e l y short p e r i o d s i s v e r y n e a r l y c o n s e r v a t i v e , thus e s s e n t i a l l y d i v i d i n g , the c i r c u l a t i o n above from t h a t below i t .  .On the other hand the decay o f  the wedge sets a l i m i t to the Use o f temperature as a t r a c e r f o r water movement, p a r t i c u l a r l y near the t i p where changes seem t o take p l a c e on every t i d a l  cycle.  In the upper l a y e r o f the i n l e t , energy C o n s i d e r a t i o n s i n d i c a t e t h a t f r e s h water d i s c h a r g e from r u n o f f should remain at the s u r f a c e , i n c r e a s i n g i n s a l i n i t y by the mixing o f more s a l i n e water from o u t s i d e or entrainment from l a y e r s  below.  I s o h a l i n e s below some 15 meters remain almost h o r i z o n t a l , t e r m i n a t i n g o n l y at the head o f the i n l e t ( F i g . 4 ) . T h e r e f o r e the mixing process appears t o be l i m i t e d to the s u r f a c e 15 meters, l e t a r a p i d i n c r e a s e o f temperature to form the upper surface o f the wedge a t some t w e n t y - f i v e meters i n Knight and f i f t y  meters  i n Bute, could be the r e s u l t o f slower a d v e e t i o n o f s a l i n e , warmer water from o u t s i d e the i n l e t , above the wedge and below the l a y e r o f most intense mixing.  That some s o r t o f exchange  of deeper water occurs with the o u t s i d e i s i n d i c a t e d ,  since  the lower surface o f the wedge does not extend to the lbottom of e i t h e r i n l e t .  The d i f f e r e n c e between the degree o f exchange  i n the two i n l e t s i s probably the r e s u l t o f the marked d i f ference o f s i z e between the s i l l s , .  The shallow s i l l  i n Knight  - 18 would l i m i t the exchange and thus the n e a r l y homogeneous nature of  the deep water would probably be made more n e a r l y so by some  iaixing mechanism a s s o c i a t e d w i t h the t i d e s . The changes i n bottom water seem t o be i r r e g u l a r i n p a t t e r n , and c o u l d be caused by an i n t r u s i o n o f more s a l i n e , warmer, h i g h e r oxygen water. In Knight and Bute the s a l i n i t y in the of  the i n l e t i s nowhere g r e a t e r than t h a t a few meters below outer edge of the s i l l ,  i n d i c a t i n g an almost t o t a l b l o c k i n g  water below t h i s l e v e l ( F i g .  4)*  E x c e p t i o n a l motion o f the  t i d e s might w e l l be s u f f i c i e n t to produce an i n t r u s i o n o f t h i s blocked water over the s i l l .  The low s i l l  i n Bute would  facil-  i t a t e the i n t r u s i o n o f more s a l i n e water, which i s a l s o warmer, to  mix with and r e p l a c e the c o l d e r , l e s s s a l i n e water produced  by the mixing down of the lower edge of the wedge, which forms the  s h a r p l y d e f i n e d lower edge i n Bute. The T,S diagram i s o f t e n used to determine the degree  of  mixing o f water masses ( F i g .  7).  The data from a s e r i e s o f  s t a t i o n s taken i n Knight d u r i n g J u l y of 1956, when drawn up in  t h i s manner, show, i n the upper s t a t i o n s o f the i n l e t , a  g r e a t e r s i m i l a r i t y of water type above and below the wedge than w i t h the wedge i t s e l f *  This i n d i c a t e s t h a t more mixing than  would normally occur through d i f f u s i o n processes has taken place. the of the  The water o u t s i d e the s i l l  rest*  shows l i t t l e  S t a t i o n 4 c l o s e i n s i d e the s i l l  well-mixed water below 50 meters.  s i m i l a r i t y to  shows c h a r a c t e r i s t i c s  I t i s important t o note  d e f f e r e n c e between s t a t i o n s 5a and 5b taken only a matter of  two days apart and a t much the same phase o f the t i d e *  Two  s e r i e s o f temperature and c u r r e n t readings were made a t t h i s station..  Y e t c l o s e to the t i p of the wedge, t h i s r e g i o n shows  a c o n s i d e r a b l e change of c h a r a c t e r i s t i c s a t a l l l e v e l s , i n s p i t e of the shallow s i l l  which might be thought t o i n h i b i t  motion a t any great depth. C l o s e l y a s s o c i a t e d w i t h s a l i n i t y i s d e n s i t y , which in  the B.C.  i n l e t s depends on i t t o a much g r e a t e r degree than  temperature.  T h i s i s s i g n i f i c a n t i n the i n t e r p r e t a t i o n  o f the  dynamic motion, which i s only p r o p e r l y r e p r e s e n t e d by deductions made from the form o f the i s o p y c n a l s of isopycnals exhibit  <r  e  .  Diagrams o f  a v e r y d e f i n i t e change o f l e v e l a t most  s t a t i o n s , c l o s e l y a s s o c i a t e d with the phase of the t i d e  (Pig.5).  Nowhere i s t h i s so marked as near the s i l l , where there  may  occur a drop o f as much as 130 meters from one s i d e o f the  sill  to the o t h e r . 2)  S e r i a l D i s t r i b u t i o n of Properties In times of low r u n o f f , the t i d e s at the s i l l may  be  s u f f i c i e n t to r e v e r s e the d i r e c t i o n of the f l o w i n the upper layer.  Indeed i t may  e f f e c t s at the s i l l in  be the p r o p a g a t i o n up i n l e t o f the t i d a l  which causes the d i s t r i b u t i o n o f p r o p e r t i e s  t h i s surface l a y e r  to depend on the l e n g t h o f the i n l e t  r a t h e r than on the d i s t a n c e from the head f o r i n l e t s o f comparable runoff.  The mode o f f l o w of the t i d e over the  sill  c o u l d be o f some importance i n determining the i n t r u s i o n o f more s a l i n e water i n t o the deeper waters of the i n l e t . asymmetric  e f f e c t of the t i d e as shown at Knight 3-1/2  might be s u f f i c i e n t to r e l e a s e some o f the more s a l i n e  The i n 1955 water  - 20 blocked behind the s i l l  ( F i g . 8 ) . Though the p r o f i l e s o f i s o -  therms a t t h i s same l o c a t i o n i n the f o l l o w i n g year g i v e no i n d i c a t i o n o f t h i s i n the well-mixed p r o p e r t i e s o f the water below 30 meters, near the end o f the s e r i e s there i s some l i t t l e i n d i c a t i o n o f an inhomogeneity.  Simultaneous readings o f s a l i -  n i t y would have helped immeasurably  i n interpreting  this.  At s t a t i o n s where there i s a s u f f i c i e n t l y marked v a r i a t i o n o f temperature with depth, a comparison o f h o u r l y temperatures (which are more s p e e d i l y sampled than s a l i n i t y ) over s e v e r a l t i d a l c y c l e s may, i f t h e changes are s t r i c t l y  Cyclic,  i n d i c a t e the dynamic motion o f the t i d e a t depths below the s u r face.  A b a s i e change o f shape from t i d e to t i d e c o u l d , on the  other hand, i n d i c a t e the extent o f the mixing a s s o c i a t e d w i t h each t i d a l c y c l e .  A t K n i g h t 5a (7|- m i l e s behind the i n n e r  sill)  there i s a t low water s l a c k a pronounced minimum, which as the t i d e f l o o d s becomes broader and l e s s pronounced u n t i l a t h i g h water s l a c k the water below the surface l a y e r appears almost homogeneous ( F i g . 9 ) .  T h i s makes the isotherms i n t h i s p e r i o d  of two or three hours almost impossible t e f o l l o w .  As the t i d e  ebbs, the minimum reappears, but net to the same degree. 1  Com-  p a r i s o n o f the minima a t low water s l a c k , when the water o f the wedge would be f u r t h e s t advanced, i n d i c a t e s a f a i r l y  consistant  mixing process which takes the form o f a broadening, and d i m i n i s h i n g o f the minimum o f temperature.  T e t a s t a t i o n a t the  same l o c a t i o n two days l a t e r shows lower temperatures by h a l f a degree.  T h i s c o u l d o n l y be due to an advance o f the wedge,  i n d i c a t i n g e i t h e r the d i f f e r e n t extent o f the t i d a l  excursion  - 21 or an outward a d v e c t i v e process a t t h i s l e v e l .  At a s t a t i o n  i n Bute c l o s e t o the t i p o f the wedge a s i m i l a r proeess i s observed, while some d i s t a n c e along the wedge the minimum r e mains much the same throughout the whole t i d a l c y c l e , so t h a t the v e r t i c a l displacement i n t h i s case would seem t o be due e n t i r e l y to the displacement o f the water l e v e l .  I n the ease  of mixing or some s o r t o f sheer f l o w i t i s p o s s i b l e t h a t the p o i n t s o f i n f l e c t i o n o f the minimum might b e t t e r d e f i n e the boundaries o f the wedge than the boundary isotherms o f the peak of the minimum.  An a n a l y s i s o f the d e r i v a t i v e o f the bathy-  thermograms taken a t  Knight 5a was d i s a p p o i n t i n g ( F i g . 9)..  the maxima and minima which correspond t o th© i n f l e c t i o n p o i n t s of the o r i g i n a l t r a c e s have l i t t l e r e l a t i o n t o one another, and even l e s s t e the t i d e s . C h a r a c t e r i s t i c o f a l l the p r o f i l e s o f isotherms i s the i n c r e a s e o f the range i n the v e r t i c a l o s c i l l a t i o n s t o a maximum a t some depth not i n f r e q u e n t l y c l o s e t o the l o c a t i o n o f the temperature minimum ( F i g . 11),.  Comparison with the t i d e  shows t h a t the v e r t i c a l displacement from the mean l a g s the peak f l o o d and ebb and i n c r e a s e s with depth.  On the ether hand,  o b s e r v a t i o n s a t Knight 5a show at c l o s e agreement w i t h the c u r r e n t s a t a l l depths.  The l a t e r a l extent o f these o s c i l l a t i o n s  i s apparent from simultaneous s e r i e s taken a t two s t a t i o n s i n Bute I n l e t *  The v e r t i c a l o s c i l l a t i o n s d i f f e r i n phase by  appro-  x i m a t e l y 180 degrees and t h e i r magnitude has been c o n s i d e r a b l y d i m i n i s h e d i n the 21 k i l o m e t e r s separating, the s t a t i o n s . In s e r i e s o f bathythermogram c a s t s with h a l f hour  - 22 intervals,  -  there appears, superimposed on the longer  period  o s c i l l a t i o n s , v e r t i c a l o s c i l l a t i o n s which, because o f  their  short p e r i o d of only about two hours, do not appear i n the series  taken at h o u r l y i n t e r v a l s .  Comparison of t h i s p e r i o d  with t h a t of a f r e e o s c i l l a t i o n i n the g i v e n d e n s i t y  gradient  (Brunt frequency) i n d i c a t e s t h a t t h i s f r e e p e r i o d i s too  short,  as i t ranges o n l y from a minute or so near the s u r f a c e to  less  than an hour a t 300 meters, to e x p l a i n the observed o s c i l l a t i o n s , ( F i g , 12).  A l s o the a c t u a l o s c i l l a t i o n s appear to have much the  same p e r i o d throughout the upper depths of the i n l e t and i n many cases c o i n c i d e .  But they are i r r e g u l a r ,  as the absence o f  any term o f t h i s p e r i o d i n the harmonic a n a l y s i s i n d i c a t e s .  A  p o s s i b i l i t y i s t h a t these superimposed o s c i l l a t i o n s are the r e s u l t of s e i c h e s . hours, and  The  n a t u r a l p e r i o d of Bute  the o s c i l l a t i o n s appear to occur  I n l e t i s about i n b u r s t s of  p e r i o d , with o c c a s i o n a l p e r i o d s of calm t y p i c a l o f Unfortunately  two  this  seiches*  the presence of these short o s c i l l a t i o n s ,  which o f t e n have a f a i r l y c o n s i d e r a b l e  amplitude, makes the obser-  v a t i o n o f i s o p l e t h s over short p e r i o d s of d o u b t f u l v a l u e , and  the  o b s e r v a t i o n o f t h e i r h o r i z o n t a l d i s t r i b u t i o n taken along the i n l e t , ambiguous.  Such a s e r i e s of f i v e bathythermogram c a s t s  taken a f t e r an anchor s t a t i o n  i n Bute*  of s i g n i f i c a n t amplitude Were recorded,  Short p e r i o d revealing a  was  oscillations considerable  change of depth i n the i s ©therms i n a matter of h a l f an hour's s a i l i n g time.  I t i s d i f f i c u l t to judge whether these were d i s -  placements of isotherms with time at any given l o c a t i o n permanent p r o f i l e a s s o c i a t e d with the water body.  or  A l l the  the  - 23 evidence o f these l a s t two s e c t i o n s seems to favour the f i r s t of these two p o s s i b i l i t i e s . 3)  Harmonic A n a l y s i s Perhaps the best q u a n t i t a t i v e approach to the a n a l y s i s  o f a s e r i e s o f v a l u e s i s an attempt to match i t a g a i n s t known f u n c t i o n .  some  The most u s e f u l o f these are the s o - c a l l e d  ortho-  gonal f u n c t i o n s which can be d e f i n e d by a d i f f e r e n t i a l r e l a t i o n ship and which, when i n t e g r a t e d over a s u i t a b l e i n t e r v a l ,  vanish t  when taken as a product with any other s o l u t i o n but i t s e l f . The simplest any  o f these are the sine and cosine f u n c t i o n s by which  well-behaved f u n c t i o n can be f i t t e d *  orthogonality  By the nature o f t h e i r  p r o p e r t i e s , the c o e f f i c i e n t s o f t h i s s o - c a l l e d  F o u r i e r s e r i e s can be evaluated  by the i n t e g r a t i o n o f the unknown  f u n c t i o n over the r e g i o n o f d e f i n i t i o n *  I t i s p o s s i b l e to show  t h a t such a F o u r i e r s e r i e s i s the best f i t to any curve,  a pro-  p e r t y i t has i n common with the r e s u l t s o f the Gaussian l e a s t squares method which i s more r e a d i l y adapted f o r use with d i s c r e t e series of readings. entirely  I n f a c t the two processes can be shown t o be  equivalent* A harmonic a n a l y s i s , as t h i s process i s c a l l e d when  the c i r c u l a r f u n c t i o n s the r e p r e s e n t a t i o n  o f a s e r i e s by the f i r s t few terms o f a s i n e  s e r i e s whose p e r i o d s ther.  are used f o r the r e g r e s s i o n , w i l l l e a d to  bear an i n t e g e r r e l a t i o n s h i p to one ano-  The amplitudes when d i s p l a y e d as a spectrum! can be com-  pared t o o t h e r s to determine any c o r r e l a t i o n between t h e i r representations  as p e r i o d i c terms*  uated and the s y n t h e s i s  The s e r i e s can then be e v a l -  compared to the o r i g i n a l data and any  _ 24  -  aperiodic e f f e c t s isolated*. The  s y n t h e s i s of s e v e r a l analyses  t i o n of the mean depth of the two  6*7°C.  of the h o u r l y p o s i -  isotherms d e f i n i n g the  lower minimum- of temperature a t Knight 5a. when p l o t t e d a g a i n s t a  the o r i g i n a l , shows t h a t the b a s i c p e r i o d i s b e s t f i t t e d by fundamental harmonic a f a p e r i o d o f 25 hours. by  The  representation  s i x components shows only a s l i g h t l y b e t t e r d e f i n i t i o n o f  peaks than when represented  by four components ( F i g . l l ) *  the  The  peaks show the same d e v i a t i o n from the o r i g i n a l as i s charact e r i s t i c o f t i d a l curves when the impulsive  e f f e c t of wind i s  superimposed on the r e g u l a r p e r i o d i c i t y of the t i d e s . d i f f e r e n c e between the o r i g i n a l and  the  synthesized  Thus the  curves, when  p l o t t e d a g a i n s t time shows a r e g u l a r a p e r i o d i c form., which i n the c u r r e n t data has  been shown to be r e l a t e d q u a l i t a t i v e l y  the wind a c t i o n at the s u r f a c e More exhaustive  to  (Rodgers, 1959).*  a n a l y s i s of the t i d e s , h o r i z o n t a l  c u r r e n t s , and v e r t i c a l o s c i l l a t i o n s , as represented  by movements  of isotherms and  significant  h o r i z o n t a l c u r r e n t s , show a r a t h e r  r e l a t i o n s h i p among t h e i r s e m i - d i u r n a l of d i s c r e t e readings  components.  a method i f i s o l a t i n g the dominant b a s i c  frequency i s to run a s e r i e s of harmonic analyses number of terms.  In a s e r i e s  The  n i f i c a n t frequencies,  with a  spectrum o f the components w i l l , f o r  r i s e of the i s o l a t e d f r e q u e n c i e s measure of i t s s i g n i f i c a n c e . during  sig-  show i s o l a t e d peaks a g a i n s t a background  of a b r o a d , continuous spectrum c h a r a c t e r i s t i c o f n o i s e .  a t A l e r t Bay  Varying  The  above the background i s then at  Thus i n the a n a l y s i s of the t i d e s  s t a t i o n K n i g h t 5a, the f o u r t h component,  * 25  -  which i s c l o s e to the twelve hour one,  does not i n c r e a s e  signi-  f i c a n t l y to i t s maximum i n the a n a l y s i s of 50 terms* but  the  envelope of the smaller background components decreases t o a^ marked extent. (3?ig. 13). also very  strong.  The  The  second ( d i u r n a l ) component i s  i n c r e a s e of the t h i r d component f o r a%  smaller number of terms i s assumed t o be due o f these two The  t o the  overlapping  l a r g e r ones as t h e i r peaks become l e s s w e l l d e f i n e d *  a n a l y s i s seems to i n d i c a t e t h a t the l u n a r s e m i d i u r n a l  com~  poaent o f 25 hours i s the dominant p e r i o d f o r the t i d e s during the p e r i o d of Knight unproductive data was  5a;  For t h i s reason and to a v o i d a r a t h e r  excess of labour, the a n a l y s i s o f the  r e s t r i c t e d to a b a s i c p e r i o d o f 25 hours.  remaining; Any  very  gross change from a 25 hour b a s i c p e r i o d would appear i n the d i s t r i b u t i o n of the harmonics, and i t appears f a i r l y c l e a r from the q u a l i t a t i v e data t h a t the i n t e r n a l modes o f motion are c l o s e l y r e l a t e d to the t i d e s at l e a s t i n p e r i o d . An a n a l y s i s of the v e r t i c a l o s c i l l a t i o n s showed, as might be expected, a c l o s e r e l a t i o n s h i p to the t i d e , except at Knight  5b ( i i ) , where i n spit© of the marked dominance of the  s e m i d i u r n a l component, the corresponding  o s c i l l a t i o n a t thuee  meters i s p r a c t i c a l l y absent, s i n c e i t i s r e p l a c e d by a very s t r o n g twenty-five hour component ( F i g , 15). p o s s i b l y be due The  This effect  may  to strong winds r e p o r t e d d u r i n g t h i s p e r i o d .  s e m i d i u r n a l component appears always to i n c r e a s e with depth  to a maximum somewhere i n the v i c i n i t y of the wedge of c o l d Water, w i t h a continuous  change of phase with depth.  dominant component (the semidiurnal one)  seems to vary  The  other  -  26  -  e r r a t i c a l l y with depth i n both phase and amplitude ( F i g . 18). At Knight 5a the s e m i d i u r n a l component appears t o be r a t h e r c l o s e l y r e l a t e d to the temperature v a r i a t i o n s .  Close  to the s u r f a c e the temperature shows a marked d a i l y v a r i a t i o n which decreases w i t h depth, t o r i s e s h a r p l y i n the r e g i o n o f the lower temperature minimum ( F i g . 14). lower depths may  The v a r i a t i o n at  be some s o r t o f advective e f f e c t connected  perhaps with th© change o f shape o f the minimum;, which tends to have a d a i l y r a t h e r than a h a l f - d a i l y p e r i o d .  The behaviour  of the semidiurnal component o n l y emphasizes t h a t the v a r i a t i o n o f t h i s component must be due to a d i f f e r e n t cause, f o r the component of temperature v a r i a t i o n bears l i t t l e r e l a t i o n t o t h a t of the v e r t i c a l amplitude (Table  l).  Comparison o f s p e c t r a a t two simultaneous s t a t i o n s i n Bute I n l e t i n d i c a t e s t h a t the semidiurnal component dominates, and t h a t t h e r e i s a change o f phase of t h i s component of 170 degrees between the two s t a t i o n s ( F i g . 17).  A comparison o f  the r e l a t i o n to depth o f the phase shows a r e g u l a r i t y only i n the s e m i d i u r n a l components The c u r r e n t s were observed over a more r e p r e s e n t a t i v e range of depths than was p o s s i b l e f o r the v e r t i c a l  oscillations  by the method o f f o l l o w i n g d i s t i n g u i s h a b l e isotherms,  It i s  i n t e r e s t i n g to note the mean v a l u e s f o r the c u r r e n t s , which i n d i c a t e a mean f l o w out from the c e n t r a l r e g i o n o f the i n l e t between one and two hundred meters.  T h i s i s compensated  by a  f l o w of the same order up i n l e t at a depth o f three hundred meters, f i f t y meters from the bottom of K n i g h t I n l e t , and a t  - 27  -  f i f t y meters from t h e s u r f a c e i n the r e g i o n between the s u r f a c e m i x i n g a r e a and the temperature wedge.  These s e r i e s r u n  o n l y f o r p e r i o d s o f a few d a y s , and t h u s the means may  only  be t r a n s i e n t e f f e c t s * v A l l t h e s t a t i o n s show t h i s tendency t o a g r e a t e r o r l e s s e r degree.  However a t K n i g h t 5b ( i ) t a k e n  two days a f t e r K n i g h t 5a, t h e f l o w i s out a t f i f t y meters and i n a t two hundred m e t e r s , y e t the p r e v i o u s p a t t e r n i s resumed on t h e f o l l o w i n g day a t K n i g h t t S h ( i i ) , as i t i s on t h e two day s e r i e s t a k e n i n t h e p r e v i o u s J u l y , K n i g h t 5c ( F i g * 1 8 ) . At  a l l s t a t i o n s t h e s e m i d i u r n a l component i s dominant  at two hundred meters and a l s o a t t h r e e hundred e x c e p t a t KMight Sc where t h e background almost envelops i t .  The s i z e e f t h e com-  ponent a t K n i g h t 5c i s worth n o t i n g as i t i s t h e more r e l i a b l e , because o f c o n t i n u i t y o f r e s u l t s .  The s e r i e s a t K n i g h t Sa and  K n i g h t 5b were m o d i f i e d from t h e i r o r i g i n a l form* i n which some r e a d i n g s were m i s s i n g , by a d d i n g i n t h e i r p l a c e dummy r e a d i n g s c a l c u l a t e d from t h e two a d j a c e n t ones.  I t was f e l t t h a t , i n  s p i t e o f t h e i n a c c u r a c y t h i s would i n t r o d u c e , some i n d i c a t i o n of  t h e o s c i l l a t i o n o f the c u r r e n t a t t h e s e depths would r e s u l t ,  and t h e method o f a n a l y s i s would n o t p e r m i t empty r e a d i n g s * T h i s a r b i t r a r y method o f a s s i g n i n g terms would i n e v i t a b l y l e a d to a p a r t i c u l a r l y l a r g e background, though i t c o u l d h a r d l y a l t e r the  t r e n d s o f t h e main terms.  A p o s s i b l e explanation of the  v e r y l a r g e v a l u e s a t t h r e e hundred meters i n K n i g h t 5a i s t h a t t h e y a r e t h e r e s u l t o f some form o f i n t r u s i o n . considered l a t e r *  T h i s w i l l be  The v e r y h i g h background a t one hundred meters  i n a l l e x c e p t 5b i s more d i f f i c u l t t o i n t e r p r e t , and the r e a d i n g s  a t f i f t y meters appear t o have no d i r e c t r e l a t i o n t o the t i d e i n t h e i r general s t r u c t u r e ,  fhough the s e m i d i u r n a l component  i s l a r g e , the dominant components a t K n i g h t 5a, are the 8,  4,  and 2k hour p e r i o d s p o s s i b l y a s s o c i a t e d w i t h some  form o f s e i c h e m o t i o n , 4)  for instance,  ,  Theorem o f C o n t i n u i t y Tracer  substances are o f g r e a t use i n the i n t e r p r e t -  a t i o n , o f dynamics of l a r g e b o d i e s of water*  J u s t as dye  can  be o f use i n s h a l l o w r i v e r s or bays t o the degree t h a t i t f o l l o w s the movement o f the water and i t s r a t e o f d i f f u s i o n i s s l o w i n the time c o n s i d e r e d , so p r o p e r t i e s which change l i t t l e i n the time s c a l e c o n s i d e r e d  and are w e l l d i s t r i b u t e d i n v a l u e  through-  out a water body can be used t o d i v i d e the water by s u r f a c e s c o n s t a n t v a l u e ; t h a t i s , by i s o p l e t h s , i n t o masses t h a t e s s e n t i a l l y separated  one from the o t h e r .  are  For no t r a n s p o r t  t a k e p l a c e through such a s u r f a c e , as t h i s would imply  of  can  the  m i x i n g o f t h e p r o p e r t y and t h e r e f o r e i t s e s s e n t i a l l y non-conservative nature.  Observations  of p r o f i l e s of such s u r f a c e s  over some d i s t a n c e , or a p e r i o d o f t i m e , can l e a d t o an i d e a o f the k i n e m a t i c s o f th©  system*  More p a r t i c u l a r l y i f the  equi-  l i b r i u m p o s i t i o n o f the s u r f a c e i s known, t h e n any d e v i a t i o n from i t can be i n t e r p r e t e d q u a n t i t a t i v e l y as a ra©v©a$eat; I n such a c a s e , and i f the motion i s known t o be g e n e r a t e d by wave m o t i o n o f g i v e n v e l o c i t y and d i r e c t i o n , the a s s o c i a t e d h o r i z o n t a l c u r r e n t s ( u ) are d e f i n e d i n d i r e c t i o n and magnitude at every d e p t h by the v e r t i c a l g r a d i e n t o f t h e d i s p l a c e m e n t  i^,)  and the wave v e l o c i t y ( c f ) under the assumption t h a t d e n s i t y i s  c o n s e r v a t i v e , thus:  When a s e r i e s of readings are taken at a number of i s o l a t e d depths, i t i s f r e q u e n t l y i m p o s s i b l y to f o l l o w the movement of a g i v e n v a l u e of a p r o p e r t y through i t s v a r i a t i o n with depth.  I f the p r o p e r t y can be shown to be h o r i z o n t a l l y  homogeneous and to be c o n s e r v a t i v e i n time, the theorem o f c o n t i n u i t y f o r t h a t p r o p e r t y can a g a i n be a p p l i e d i n the E u l e r i a n form t o get:  where  p  i s the d i f f e r e n c e from the e q u i l i b r i u m v a l u e P  the g i v e n depth j from t h i s depth.  it  and  for  r^ty i s the v e r t i c a l displacement  I t i s of importance t o note t h a t both these  ^ r e l a t i o n s are s t r i c t l y a p p l i c a b l e o n l y where mixing i s n e g l i ggiible i n the p e r i o d considered* In  p a r t i c u l a r the T*S c h a r a c t e r i s t i c of water i n  Knight has been shown f o r J u l y o f 1956,, masses w i l l appear  As s i m i l a r water  as groups of a s s o c i a t e d p o i n t s , there ap-  pears to be a d e f i n i t e s i m i l a r i t y of water type f o r s t a t i o n s h i g h e r i n the i n l e t .  P r o f i l e s of c h a r a c t e r i s t i c s show t h a t  they change o n l y slowly through the seasons.  Although v a r i -  a t i o n s from one s t a t i o n to another occur over the t i d a l c^eUe, it  i s e v i d e n t , a t l e a s t away from the r e g i o n o f the s i l l ,  they .are i n the nature of displacements, f i l e s i n Bute through the y e a r s of 1957 of  the c h a r a c t e r i s t i c temperature  from the  sill.  that  fhe s e r i e s of p r o and 1958  show the decay  p a t t e r n takes p l a c e up  inlet  - 30 An examination i n some d e t a i l o f a s e r i e s o f p l o t s o f temperature  a g a i n s t depth over a p e r i o d o f a, day and a h a l f  at Knight 5a together with t h e i r g r a d i e n t s , and d e v i a t i o n s the mean, shows t h a t l i t t l e  from  s i m i l a r i t y e x i s t s w i t h the deep  c u r r e n t s over the same p e r i o d ( F i g s . 9 and 10).  Study o f the  p r o f i l e s f o r t h a t p e r i o d i n d i c a t e s t h a t the s t a t i o n l i e s a t a p o s i t i o n c l o s e t o the most i n t e n s e decay o f the temperature s t r u c t u r e , near the t i p . A q u a n t i t a t i v e a n a l y s i s o f p e r i o d s shows a remarkably l a r g e v a r i a t i o n o f phase with depthj t h i s can p a r t l y be e x p l a i n e d negative temperature 180 degrees*  as n e g a t i v e amplitudes i n r e g i o n s o f  gradient  and the phase can be changed by  When t h i s i s done however, the phase a t lower  depths s t i l l proceeds t h a t o f the amplitudes c a l c u l a t e d from the movement o f the c h a r a c t e r i s t i c p r o f i l e , by almost 90 degrees.  exactly  I t i s p o s s i b l e then t h a t these temperature  vari-  a t i o n s are more c l o s e l y a s s o c i a t e d with mixing o f the surf&ee t i d e s than to the displacement o f the water body. Amplitudes when c a l c u l a t e d from the movement o f v e r t i c a l p l o t s show a r e g u l a r change o f phase with depth i n t h e i r semi-diurnal one hundred meters.  component and a d e f i n i t e maximum o f about T h i s should correspond t o a minimum  in  the h o r i z o n t a l c u r r e n t p r o f i l e i f they eaa be simply r e l a t e d through a s i n g l e wave.  There i s a s u g g e s t i o n o f t h i s , a l s o  an i n d i c a t i o n t h a t the s i t u a t i o n i s somewhat more c o m p l i c a t e d . U n l i k e t h a t i n K n i g h t I n l e t simultaneous s t a t i o n s i n Bute I n l e t show l i t t l e v a r i a t i o n o f t h e i r v e r t i c a l  structure  throughout the t i d a l c y c l e , so t h a t the i n d i c a t i o n o f p e r i o d i c  *** 3 %. ,** motion with a change of  phase o f 180 degrees and a drop i n  amplitude o f 60$ between the s t a t i o n s can be accepted w i t h perhaps more credence as the a c t u a l r e s u l t o f v e r t i c a l  dis-  placement o f the water mass. S e v e r a l e l t e r a a t e hypotheses p r e s e a t themselves as an ©xploaatioa o f th© i n f e r r e d movement o f the s u r f a c e s def i n e d by isotheriaals i n these two i n l e t s * of  l a on assymmetry  movement i a aad out o f the i n l e t o f the t i d e caused by  .geostrophic e f f e c t * the t i d e f l o o d s along one s i d e o f the i a l e t aad ebbs along the o t h e r .  Th© respoase o f i a t e r a a l  s u r f a c e s o f a s t r a t i f i e d f l u i d to such a motion would be g r e a t l y exaggerated*, aad so<-c a i l e d c r o s s i a l e t h e l i c a l c u r r e n t s would develop*  A s i m i l a r e f f e c t would be encountered  through c e a t r i f u g a l fore© oa th© sharper beads o f the i n l e t * . Tot  t h i s would a o t e x p l a i n the v e r y d e f i n i t e phase l a g with  depth aor the maximum o f amplitude a t aa i n t e r m e d i a t e depth of  the v e r t i c a l o s c i l l a t i o a .  Another e x p l a a a t i o a which  suf-  f e r s from the same d e f e c t suggests t h a t th© raoveaeat i a and out  w i t h th© t i d a l prism o f the temperature s t r u c t u r e c o u l d  w e l l account f o r th© observed v a r i a t i o n s ,  This i s a possi-  b i l i t y at the s t a t i o a s i a K a i g h t f y e t a p u r e l y adveeMve movemeat would b© expected to b© th© same ©a th© f l o o d aad ebb* At  a p o s i t i o n aear th© s i l l  i t i s possible that a  coabia&tion o f the above e f f e c t s c o u l d account f s * the observed v a r i a t i o n .  For i f th© t i d e were to f l o o d aad ©bb i n  a d i f f e r e n t maaner over the s i l l ,  accompanied  by a c e r t a i a  amount o f m i x i a g , an e f f e c t which aeed a o t m i r r o r the f l o o d oa  -  82  -  the ebb c o u l d occur with a change of phase w i t h depth due t o the d i f f e r e n t for© o f f l o o d and ebb, ©n the other hand t h i s c o u l d not occur a t p o s i t i o n s f a r from the s i l l where the temperature  structure i s well esta-  b l i s h e d and the mixing t h e r e f o r e minimized.  An h y p o t h e s i s  whieh accounts f o r not only the change of phase with depth, but i t s change from s t a t i o n t o s t a t i o n , as w e l l as the maximum o f amplitude a t an i n t e r m e d i a t e depth, i n the absence o f mixing, i s t h a t o f an i n t e r n a l i n e r t i a l mode o f o s c i l l a t i o n .  The aim  of the next chapter i s t o examine s e v e r a l hypotheses based on t h i s from a more q u a n t i t a t i v e p o i n t o f view. Chapter I I I 1)  The Equations o f  lotion  I n t e r n a l Waves  ( i ) The s o l u t i o n f o r a continuous d i s t r i b u t i o n o f d e n s i t y . C o n s i d e r a t i o n o f the r e l a t i o n o f r a t e o f change o f momentum t o p r e s s u r e , g r a v i t a t i o n a l p o t e n t i a l , o r other i n t e r n a l f o r c e s , g i v e s r i s e to a d i f f e r e n t i a l equation o f motion, which d e f i n e s the response o f a water body to these f o r c e s i n the presence o f d e f i n i t e geometric boundaries.  The s o l u t i o n o f t h i s  equation w i l l u s u a l l y depend on the t h r e e s p a t i a l c o o r d i n a t e s and time. When s p e c i a l i z e d to p e r i o d i c motion o f periodo,, the equations reduce to a s o l u t i o n o f p a r t i a l d i f f e r e n t i a l equations i n the s p a t i a l c o o r d i n a t e s o n l y .  Upon the a p p l i c a t i o n o f t h i s  to a c a n a l o f c o n s t a n t depth, and motion which proceeds along i t w i t h no secondary e f f e c t s , the equation then w i l l i n v o l v e o n l y the  - 33 v e r t i c a l coordinate z and equilibrium  (Fjeldstad,  -  d e f i n e the v e r t i c a l displacement from  1933).  The  d i f f e r e n t i a t i o n of t h i s  with r e s p e c t to time, a f t e r interchange of order of  tiation,  differen-  r e s u l t s i n an equation i n v e r t i c a l v e l o c i t y more e a s i l y  f i t t e d to the boundary c o n d i t i o n s at the These r e q u i r e , c a l v e l o c i t y be  bottom surface*  f o r i n t e r n a l modes of o s c i l l a t i o n , that the zero*  upper s u f f a e e , but crepancy i s  top and  This condition  i s not met  w i t h r e s p e c t to the  verti-  s t r i c t l y at  i n t e r n a l motion the  the  dis-  negligable*  A s o l u t i o n i s then d i f i n e d , to the order of an  arbi-  t r a r y constant m u l t i p l i e r , i n terms of the v e r t i c a l s t a b i l i t y and  depth, by the d i f f e r e n t i a l equation and  tions*  I f the product of the  the boundary c o n d i -  square of the wave number and  average d e n s i t y i s small at a l l depths with r e s p e c t to the d i e n t of average d e n s i t y with depth, t h i s term can be i n the  ^  i s the  the  acceleration  i n v e r s e of the wave v e l o c i t y , and  neglected  of  gravity  <f>-~^ " 5 ^ ~ * ' °  V  stability. Should <j>  depth, an a n a l y t i c sought.  gra-  equation which then becomes:  where w i s the v e r t i c a l v e l o c i t y , g the and  the  h o l d a simple f u n c t i o n a l r e l a t i o n s h i p  s o l u t i o n of the  I f t h i s i s not  the  system of equations can  l a y e r only i n the  s u r f a c e (Cameron, 1951), a numerical  method of s o l u t i o n can be a p p l i e d t i a l l y involves  be  case, as i n the B«C* i n l e t s where  a n a l y t i c d i s t r i b u t i o n s have been f i t t e d to the immediate v i c i n i t y of the  to  d i v i d i n g the  (Fjeldstad,  1933).  T h i s essen-  i n l e t v e r t i c a l l y i n t o homogeneous  lamina© which are then f i t t e d to one another and the boundary c o n d i t i o n s by a form o f a n a l y t i c c o n t i n u a t i o n .  T h i s process  has i n l a t e r y e a r s been j u s t i f i e d (Benton, 1956)  by showing t h a t  the s o l u t i o n i n c l o s e d form f o r a f i n i t e number o f laminae goes over i n the l i m i t o f l a r g e numbers of laminae to the s o l u t i o n f o r a continuous d i s t r i b u t i o n o f d e n s i t y .  Through a p p l i c a t i o n o f  t h i s method the a s s o c i a t e d h o r i z o n t a l c u r r e n t s are  determined  with the v e r t i c a l ones to the order of an a r b i t r a r y constant mult i p l i e r , where i t i s assumed, f o r the d e r i v a t i o n o f the equation, t h a t c o n d i t i o n s are s u i t a b l e f o r the a p p l i c a t i o n of the theorem of C o n t i n u i t y . Thus the procedure,  i n a p p l y i n g the method to f i n d the  p o s s i b l e i n t e r n a l modes i n some s p e c i f i c s i t u a t i o n , i s t o d e t e r mine by t r i a l a v a l u e of the parameter A*a  which f i t s the boun-  dary c o n d i t i o n when used f o r the numerical i n t e g r a t i o n , of the equation*  A first  t r i a l parameter i s found by a p p l y i n g the  first  step o f the W^KUB* method, which i s e q u i v a l e n t t o determining average v a l u e f o r the numerical f u n c t i o n  an  , aad then f i n d i n g  the a n a l y t i c s o l u t i o n t o the system (determiaed by the d i f f e r e a t i a l equation) i n which t h i s i s a constant*  The f i r s t few  ences can be c a l c u l a t e d by use of the T a y l o r s e r i e s , and by a l t e r n a t e use of the d i f f e r e n t i a l equation aad  differ-  continued  difference  formula r e l a t i n g the second d i f f e r e n c e o f the f u a c t i o a w toethe secoad d e r i v a t i v e and i t s second d i f f e r e n c e a t v a r i o u s steps of th© calculation.  The numerical v a l u e s o f <f>  must be t a b u l a t e d f o r each  depth o f i n t e g r a t i o n aad chaaged i n accordance size  used*  w i t h the  interval  The  35  -  r e s u l t s o f the i n t e g r a t i o n g i v e the p o s s i b l e modes  o f o s e i l & a t i o a o f the system represented tion  by t h e numerical  func-  <(> i n terms o f t h e i r wave v e l o c i t y , and a r e p r e s e n t a t i v e  p r o f i l e o f v e r t i c a l and h o r i z o n t a l p a r t i c l e v e l o c i t y *  There i s  t h e o r e t i c a l l y an i n f i n i t e sequence o f these, but i t i s u s u a l t o take the f i r s t few modes o n l y , and to t r y t o f i t the a r b i t r a r y constant m u l t i p l i e r s o f the s o l u t i o n s w t o t h e a c t u a l d i s t r i b u t i o n o f amplitude and v e l o c i t y a t the given depths f o r each h o u r l y s t a t i o n , p i c k i n g out those modes which appear to f i t b e s t . To determine t h i s best f i t , the orthogonal  i t i s p o s s i b l e to take advantage o f  p r o p e r t i e s o f the s o l u t i o n s w and u t o determine  t h e i r c o e f f i c i e n t s when r e p r e s e n t i n g an a r b i t r a r y f u n c t i o n i n terms o f them, i n a manner i d e n t i c a l to t h a t o f F o u r i e r a n a l y s i s . T h i s i n v o l v e s i n t e g r a t i n g over depth, which i s n o t p o s s i b l e i n t h i s case because the Values o f the amplitudes are not S u f f i c i e n t l y w e l l d i s t r i b u t e d i n depth.  An e n t i r e l y e q u i v a l e n t  pro-  cedure i s to make a r e g r e s s i o n a n a l y s i s o f these s o l u t i o n s w a g a i n s t the v a l u e s o f the amplitude. used are obtained  C o e f f i c i e n t s f o r each mode  f o r each hourly s t a t i o n *  The harmonic a n a l y s i s  o f these permits the r e p r e s e n t a t i o n o f the v e r t i c a l  oscillations  i n terms o f the i n t e r n a l modes o f motion, under the given hypothesis. An a l t e r n a t i v e process  i s t o make a r e g r e s s i o n o f the  w's a g a i n s t the product o f the harmonic amplitudes and t h e s i n e and  cosine o f the phase angle r e s p e c t i v e l y .  Although t h i s i s  c e r t a i n l y s p e e d i e r , i t does not have the advantage o f d e t e r mining the other p o s s i b l e p e r i o d s besides  the one chosen f o r  - 36 the a n a l y s i s . used,-  .;  Therefore the former r a t h e r t e d i o u s process  wa£  •  • •'  \  '  .  At Knight 5 the s t a b i l i t y c o u l d o n l y be  determined  \il(  from a s i n g l e c a s t , and i s t h e r e f o r e by no means r e p r e s e n t a t i v e of  the average  ( F i g , 19),  S i m i l a r l y a t Bute ( F i g s . 20, 21),  ^ ',[*  a l t h o u g h f i v e readings were taken d u r i n g the two day s t a t i o n , they extended  o n l y to a depth of 90 f e e t *  \  Lower depths were r e p * . . ' • v~  r e s e n t e d by an average of s i x or seven s t a t i o n s taken i n the n i t y d u r i n g t h a t month.  The range among these was  and no s i n g l e deep c a s t was original station. be hoped f o r *  ;  vici-  rather large,  taken on the exact l o c a t i o n of the  To t h i s extent, o n l y q u a l i t a t i v e r e s u l t s can-  F o r t u n a t e l y th© v a l u e s of s t a b i l i t y a t lower depths  are v e r y small and thus not c r i t i c a l } a l s o i n the d e t e r m i n a t i o n of  the c h a r a c t e r i s t i c s of the wave between the two  4 and Bute B  f  s t a t i o n s Bute  i t i s r a t h e r an advantage than otherwise to have a  s t a b i l i t y r e p r e s e n t a t i v e of the surrounding waters.  Thus i n spit©  of  the above r e s e r v a t i o n s , the r e s u l t s from Bute 4 may  to  be more r e p r e s e n t a t i v e than those c a l c u l a t e d from the s i n g l e  cast at  Knight 5,  The maximum v a l u e s o f the numerical  be  expected  function,  are some hundred times those i n p r e v i o u s i n t e g r a t i o n s where the v a l u e has been g i v e n ( F j e l d s t a d , 1933), (Munk, 1941)*  On  the  other hand the depths have been somewhat l e s s and the deeper waters a p p a r e n t l y l e s s In  stratified.  order to t e s t the hypothesis f o r th© observed  t i o n s , an i n t e g r a t i o n was made f o r both the f i r s t f o u r modes ( F i g s . 22 & 23).  sta-  Knight 5 and But© 4 f o r A r e g r e s s i o n o f th© accom-  .  - 37 paaying v a l u e s of w a g a i n s t the observed v a l u e s o f the v e r t i c a l amplitude  i n the p a r t i c u l a r l e a s e i s somewhat q u e s t i o n a b l e , s i n c e  the f i t can o n l y be made i n the top one hundred meters, l e a v i n g open the p o s s i b i l i t y t h a t a s i n g u l a r i t y of the determinant the covariance matrice may  occur.  of  X e t probably because the major  d i f f e r e n c e among the four, harmonics occurs i n t h i s upper l a y e r * the d i f f e r e n t modes may  v e r y w e l l be s u f f i c i e n t l y w e l l separated  by t h i s p r o c e s s , sinee n o o s i n g u l a r i t y does occur*  A possible  a l t e r n a t i v e method i s to r e s t r i c t the numerical i n t e g r a t i o n t o the upper l a y e r , f i t t i n g i t a t the bottom to the boundary c o n d i t i o n s f o r a homogeneous bottom l a y e r ( F j e l d s t a d , 1033). Knight  5a At the s t a t i o n i n Knight  I n l e t hourly readings of  c u r r e n t were accompanied by bathythermograph c a s t s , which enabled both c u r r e n t s and amplitude® to be observed a t t h i s s t a t i o n f o r a p e r i o d of two days or f o u r s e m i d i u r n a l c y c l e s *  Values of  were c a l c u l a t e d from a s i n g l e b o t t l e c a s t near the end of the s t a t i o n ( F i g . 19).  T h i s may  be compared t o s t a b i l i t i e s  calcu-  l a t e d f o r other s t a t i o n s along the l e n g t h of the i n l e t ( F i g * 6 ) . I t i s as w e l l to note t h a t the v a l u e of <f> d i f f e r s from t h a t of ^Xio  *  The former i s ten times g r e a t e r .  Results of  numerical i n t e g r a t i o n g i v e the v e l o c i t i e s of propagation o f the f i r s t f o u r i n t e r n a l waves as 102, per second*  (Table 2 ) .  55*6, 33*2, and 26*0 centimeters  R e g r e s s i o n a n a l y s i s of the f o u r s o l u t i o n s  a g a i n s t the observed v e r t i c a l o s c i l l a t i o n s (Table 4) shows t h a t f o r a l l but the t h i r d wave, which i s s m a l l f o r a l l p e r i o d s , the s e m i d i u r n a l component dominates.  Although the c o e f f i c i e n t f o r the  — 38 -» f i r s t mode i n the d i u r n a l component i s l a r g e enough to i n d i c a t e a p o s s i b l e response o f t h i s form, i t i s not s i g n i f i c a n t the s e m i d i u r n a l c o e f f i c i e n t s *  beside  The r e p r e s e n t a t i o n o f the v e r t i c a l  o s c i l l a t i o n L i n terms o f the f i r s t  f o u r i n t e r n a l waves o f semi-  diurnal period a i s ; L a 8.12 sin(at/l^t,+2,55)*^  ^ 5.09 s i n ( a t - k g X 4 0.54)w  2  -Y 2.63 s i n C a t - k g X -I. 2»21.)«g. • £ 13.09 s i n ( a t «. k ^ x + 6..i7)w^ where the v a l u e s w'have been t a b u l a t e d (Table 3 ) . The c o e f f i c i e n t s of the f i r s t  three waves h o l d much the same r e l a t i o n to one ano-  t h e r as has p r e v i o u s l y been r e p o r t e d f o r waves i n Norwegian f i o r d s ( F j e l d s t a d , 1952), but the f o u r t h wave i s remarkably l a r g e and dominates the whole motion, i i n c e the f i r s t two waves have tially  essen-  o p p o s i t e phase. The  s y n t h e s i s o f t h i s e x p r e s s i o n when subjected t o a  harmonic a n a l y s i s can be compared to the o r i g i n a l data (Table  5).  A comparison o f the magnitude o f the v e r t i c a l o s c i l l a t i o n t o t h a t o f the observed d a t a shows o n l y q u a l i t a t i v e agreement ( f i g . 2 5 ) . The v a l u e s i n the s u r f a c e l a y e r are o f the order o f e i g h t meters too  l a r g e , probably  t o f o r c e the deeper readings down to the c o r -  r e c t order o f magnitude.  The phase f o l l o w s the observed v a l u e s  more c l o s e l y , but agree mueh b e t t e r i n shape w i t h the s t a t i o n s Knight  5b ( i ) and ( i i ) i , A s y n t h e s i s i s made u s i n g the d e r i v a t i v e s of the w  ( i . e . , the u) and the same c o e f f i c i e n t s as f o r the p r e v i o u s one; t h i s i s compared to the components o f the harmonic a n a l y s i s a t the same depths (Table 6 ) . Although these c o e f f i c i e n t s a r e o n l y e v a l uated  from v a l u e s i n the top hundred meters, e x t r a p o l a t i o n t o two  and t h r e e hundred meters shows c l o s e agreement i n phase, although b e t t e r agreement with the shapes of the v a r i a t i o n with phase e x i s t s with Knight 5b ( i ) and 5c ( F i g . 26).  On the other hand  the magnitude a t none of the s t a t i o n s can be c o n s i d e r e d to be compatible with t h a t expected from t h i s type of o s c i l l a t i o n . Bute 4 and 6 i n t e g r a t i o n w i t h use o f the averaged v a l u e of the v e r t i c a l s t a b i l i t y ( F i g . 21) leads t o v a l u e s of the wave v e l o c i t y of 106, 70.7,  40.8,  31.2  centimeters per second(Table  2)* I t i s  a o t s u r p r i s i n g i n view of the g r e a t e r s t a b i l i t y i n the upper l a y e r s of the i n l e t t h a t these Wave v e l o c i t i e s should have g r e a t e r v a l u e s than the corresponding ones i n K n i g h t .  Eegressioa analysis  (Table 4) i n d i c a t e s t h a t , although on the whole the s e m i d i u r n a l component i s dominant, a very l a r g e c o e f f i c i e n t f o r the f o u r t h mod© o f the d i u r n a l component explanation.  .. cannot be d i s m i s s e d without  The harmonic a n a l y s i s o f the temperature  variations  at Knight 5a i n d i c a t e s t h a t there i s a p a r t i c u l a r l y l a r g e d i u r n a l component a s s o c i a t e d with the d a i l y h e a t i n g aad c o o l i a g of the surface.  But the h i g h e r modes of o s c i l l a t i o n " have t h e i r g r e a t e s t  v a l u e s i n the upper l a y e r , and thus w i l l tend to f i t v a r i a t i o n s o f t h i s layer i n a regression analysis* f o u r t h component may of the temperature  Thus the l a r g e v a l u e s o f th©  be a t t r i b u t e d to a aon-eonservative  variation  a t the s u r f a c e , and can be h a r d l y expected to  r e p r e s e n t the o s c i l l a t o r y motion of a wave. The r e p r e s e n t a t i o n of the v e r t i c a l o s c i l l a t i o n L by f o u r i n t e r n a l waves of s e m i d i u r n a l p e r i o d a i s ;  L -s 13.4 s i a ( a t  kjX  + 2.7 s i n ( a t - k x +- 1.03)w g  -h 9,2 s i n ( a t - k x  0.94)^  g  3  3*.96)w  2  8,2 s i n ( a t -k^x -f- 2«>98)wg  where the c o e f f i c i e n t s w a r e t a b u l a t e d  (Table  3 ) , The  synthesis  o f t h i s (Table 7) compares r a t h e r unfavourably ( i n the shape o f i t s d i s t r i b u t i o n o f magnitude with depth) t o the observed bution,  although the phase agrees r e l a t i v e l y w e l l .  mode alone i s f i t t e d t o the semidiurnal fit  distri-  When the f i r s t  a n a l y s i s * a remarkably good  i s made ( P i g . 27), The  distance  wave v e l o c i t i e s a r e used to compute the phase f o r the  o f 21 k i l o m e t e r s between the two simultaneous s t a t i o n s i n  Bute, and the s y n t h e s i s changes (Table Bute 4.  i s performed u s i n g the corresponding phase  8) and the r e g r e s s i o n  Here the f i t i s no b e t t e r  l a r g e i n v a l u e f o r the magnitude*  coefficients calculated f o r  i n shape and c o n s i d e r a b l y too Whea the s i a g l e mode used a t  Bute 4 i s t r e a t e d i a t h i s way, aad m u l t i p l i e d by a s e a l i n g f a c t o r o f 0,4, there? i s a much b e t t e r f i t .  T h i s * coupled with the obser-  v a t i o n t h a t the c a l c u l a t e d wave v e l o c i t y (106 centimeters per second)  o f the f i r s t mode i s the same as the a c t u a l v e l o c i t y o f 10'I  centimeters per seooad f o r a 12-§- hour wave t o t r a v e l the 21-| k i l o meters betweea the two s t a t i o n s with a phase change o f 170 degrees, seems t o coafirm  t h a t the o s c i l l a t o r y motioa i a t h i s p o r t i o a o f  the  i n l e t i s composed o f the f i r s t and p o s s i b l y the second i n t e r -  aal  waves.  is  However* the change o f phase betweea the two s t a t i o n s  somewhat l e s s thaa t h a t t o be expected from the t h e o r e t i c a l  wave, aad though t h i s i s w i t h i a the p o s s i b l e e r r o r o f the c a l c u 1ation,  i t may a l s o be accounted f o r by a decrease i a depth  betweea the two s t a t i o a s , which c o u l d have the teadeacy t o  • 41 decrease the v e l o c i t y .  On the other hand, the average s t a b i l i t y  tends to i n c r e a s e , which would tend t o compensate f o r t h i s * I t i s i n t e r e s t i n g t o note t h a t the phase a t Bute 4 l a g s the t i d e by a phase angle  s l i g h t l y l e s s than the d i f f e r e n c e o f  phase between Bute 4 and 6, although the d i s t a n c e i s somewhat g r e a t e r (34 k i l o m e t e r s as opposed to 21 k i l o m e t e r s ) *  Bute 6- i s  taken as some 22 k i l o m e t e r s from the approximate head o f the i n let.  Thus a p r o g r e s s i v e wave generated a t the s i l l  d e c r e a s i n g v e l o c i t y through the l e n g t h o f the i n l e t ,  t r a v e l s with T h i s might  be due t o the dependence o f the wave v e l o c i t y on depth and s t a b i l i t y or t o the e f f e c t o f eddy v i s c o s i t y on the wave number. These q u e s t i o n s among others w i l l be d i s c u s s e d f o r s p e c i a l  distri-  b u t i o n s i n the next s u b s e c t i o n , (ii)  Approximate forms I n the p r e v i o u s d i s c u s s i o n i t was i n d i c a t e d t h a t the  r a t h e r l a r g e v a l u e s o f the r e g r e s s i o n c o e f f i c i e n t s f o r the f o u r t h i n t e r n a l wave were probably due t o surface e f f e c t s n o t a s s o c i a t e d with a c t u a l i n t e r n a l o s c i l l a t i o n s , and t h a t f o r t h i s reason c o u l d w e l l be d i s c a r d e d *  they  As the t h i r d component i s i n a l l cases  v e r y s m a l l , i t seems n o t improbable t h a t the f i r s t two i n t e r n a l waves c o u l d g i v e a good r e p r e s e n t a t i o n o f the motion, p a r t i c u l a r l y as t h e f i r s t one alone i s shown t o give an adequate representation^ i n Bute  Inlet.  Thus approximations which f i t the f i r s t two waves  w e l l c o u l d probably  be used w i t h some success to r e p r e s e n t the  a c t u a l motion. The for  comparison o f the f i r s t two modes w i t h the r e s u l t  a three l a y e r system ( F j e l d s t a d , 1933) shows t h a t a two l a y e r  - 42 system i n which the lower l a y e r i s homogeneous and the upper l a y e r has a constant g r a d i e n t might g i v e a good approximation.  I f the  upper l a y e r i s taken as one hundred meters and the g r a d i e n t c a l c u l a t e d from the average  s t a b i l i t y for this layer, a velocity of  181  centimeters per second f o r l u t e and 148 centimeters per second f o r Knight i s found f o r the f i r s t i n t e r n a l wave. too l a r g e .  These v e l o c i t i e s are  I f the system c o n s i s t s of o n l y one l a y e r , with a s t a -  b i l i t y equal to the average over the whole depth, v e l o c i t i e s of 153 for  and 101 centimeters per second are c a l c u l a t e d r e s p e c t i v e l y the two  inlets.  Though the v a l u e f o r Bute i s s t i l l too l a r g e ,  t h a t f o r Knight o f 101 centimeters per second i s v e r y c l o s e t o the one c a l c u l a t e d u s i n g numerical  integration,  A b e t t e r r e p r e s e n t a t i o n f o r the s t a b i l i t y appears the l o g a r i t h m i c p l o t s ( F i g . 19 &; 2 l ) a s t r a i g h t l i n e as a rough mean. of  the s t a b i l i t y i s  A ( x )  from  which appear t o l i e about  Thus an a n a l y t i c r e p r e s e n t a t i o n  where % i s the slope of the mean  and A the i n t e r c e p t o f the l i n e with the y equal t o one a b s c i s s a Table 9 ) •  The  s o l u t i o n of the wave equation, when t h i s a n a l y t i c  e x p r e s s i o n i s used f o r the s t a b i l i t y , i s a B e s s e l f u n c t i o n from which the v a l u e s o f the wave v e l o c i t y can be found by f i t t i n g t o the boundary c o n d i t i o n s *  When t h i s i s done f o r a s i n g l e l a y e r  system, r e s u l t s f o r the f i r s t two modes a t Bute 4 are 266, 55 centimeters per second, and a t Knight 5, 96, and 51 per second,  and  centimeters  The v a l u e s i n Knight seem i n f a i r agreement w i t h those  c a l c u l a t e d by numerical i n t e g r a t i o n , but the v e l o c i t y o f the  first  wave i n Bute i s c o n s i d e r a b l y too l a r g e , i n d i c a t i n g a g a i n t h a t t h i s s i t u a t i o n c o u l d be b e t t e r represented by a m u l t i - l a y e r system*  - 43 the modulus o f decay o f a long wave f o r a system of two homogeneous l a y e r s ( R a t t r a y , 1954)  i s found to depend on the  eddy v i s c o s i t y , d i f f e r e n c e of d e n s i t y , and the depths o f the l a y e r s * the p e r i o d , and the l a t i t u d e .  two  I f t h i s approximation i s  good f o r Bute I n l e t , the wave v e l o c i t y can a l s o be r e p r e s e n t e d i n terms of the d i f f e r e n c e of d e n s i t y between two homogeneous l a y e r s and t h e i r depths*  I f the depth o f the top l a y e r i s as-  sumed to be the depth of maximum amplitude f o r the f i r s t computed i n t e r n a l wave a t t h i s s t a t i o n ( f a b l e 2 ) , the d i f f e r e n c e o f d e n s i t y i n the formula f o r the modulus of decay can be s u b s t i t u t e d f o r i n terms of the wove v e l o c i t y , and the depth o f the two d e f i n e d i n t h i s way.  layers  When the e x p r e s s i o n i s evaluated f o r eddy  v i s c o s i t y i n terms of the decay of amplitude between s t a t i o n s Bute 4 and 6 f o r a twelve hour wave i n the l a t i t u d e o f 51  degrees  n o r t h , a v a l u e r e s u l t s f o r the eddy v i s c o s i t y some 16 times l a r g e r than a n t i c i p a t e d by R a t t r a y and twice as l a r g e again as v a l u e s observed i n the i n l e t s ( P i c k a r d & T r i t e s , 1957). approximation which was  The  designed f o r use on the c o n t i n e n t a l  shelf  seems u n r e a l i s t i c i n a number o f ways when a p p l i e d t o the i n l e t s * I t assumes a constant eddy v i s c o s i t y f o r a l l depths, whereas the eddy v i s c o s i t y i s shown to have a c o n s i d e r a b l e dependency on depth.  But perhaps more s i g n i f i c a n t , i t does not take i n t o account  the r a t h e r p e c u l i a r s t r a t i f i c a t i o n of the i n l e t s , which we have i n d i c a t e d may  be r a t h e r b e t t e r f i t t e d by a power f u n c t i o n and  s o l u t i o n s i n the form of B e s s e l f u n c t i o n s . The importance of the approximate s o l u t i o n i s the two way  forms o f a n a l y t i c  r e l a t i o n they i n f e r between the oceaho-  graphic c o n d i t i o n s and the o s c i l l a t o r y motion s t u d i e d . we have i l l u s t r a t e d , the oceanographic parameters may  For as be used  i n a numerical a n a l y s i s to e v a l u a t e the modes of the i n t e r n a l waves p r e s e n t , and thus t h e i r presence i n a survey may be compensated f o r . But i f an approximate form such as R a t t r a y ' s can be shown to be an adequate r e p r e s e n t a t i o n of the s i t u a t i o n , i t may indeed be p o s s i b l e to i n f e r the d i s t r i b u t i o n of the more d i f f i cult-to-measure parameters from the mode o f the o s c i l l a t o r y motion or i t s decay, as has been attempted q u a l i t a t i v e l y i n t h i s sectidn.  To t h i s end perhaps the most f r u i t f u l endeavour may  be  as has a l r e a d y been suggested, the use o f a power s e r i e s r e p r e s e n t a t i o n f o r the s t a b i l i t y and a s o l u t i o n i n terms o f B e s s e l functions* 2) (i)  (See a l s o Benton  1956).  Other Forms o f O s c i l l a t o r y Motion S o l u t i o n f o r f i n i t e l e n g t h and v a r i a b l e depth* I n c o n t r a s t to the t h e o r y of a p r o g r e s s i v e  internal  wave i n an i n f i n i t e channel of constant depth as t r e a t e d i n the p r e v i o u s s e c t i o n , a b a s i n of v a r i a b l e depth imposes  boundary  c o n d i t i o n s on a system, with which the s o l u t i o n of the equation of motion as a s i n g l e p r o g r e s s i v e wave i s i n c o m p a t i b l e . Further i t can be shown i n g e n e r a l that the only mode of o s c i l l a t i o n compatible with these c o n d i t i o n s f o r such a b a s i n i s a standing wave (Munk, 1941)* A method has been d e v i s e d by Munk f o r f i n d i n g numeric a l l y the modes of a g i v e n b a s i n ( a proeess used some f i f t e e n y e a r s p r e v i o u s l y f o r the surface t i d e s (Defant, 1925).  The  method c o n s i s t s o f assuming f o r a l l the s t a t i o n s a s i n g l e  trial  ~ 45 parameter, which i s used to o b t a i n a v a l u e o f w and u a t the bottom by the same numerical i n t e g r a t i o n technique as used by F j e l d s t a d , assuming f o r t he boundary c o n d i t i o n s a t the s u r f a c e , w equal to zero and the product of i t s d e r i v a t i v e u by some s c a l i n g constant equal to one. modes.  T h i s i s repeated f o r other  The boundary c o n d i t i o n s a t the bottom, t h a t i s o f no  motion normal to the boundary, i s a p p l i e d to form a s e t of l i n e a r equations i n these c a l c u l a t e d v a l u e s o f w and u summed i n accordance  with the v a r i o u s modes*  The c o r r e c t choice o f  parameter ( i . e . p e r i o d e f motion) then corresponds t o a m i n i mum  i n the v a l u e of the determinant  corresponding set of equations.  of the c o e f f i c i e n t s i n the  In t h i s way  f r e e long, p e r i o d  motions were i n t e r p r e t e d to be a resonant response of the G u l f of C a l i f o r n i a , C o n s i d e r i n g the v e r y c l o s e p e r i o d of a l l observed o s c i l l a t i o n s to t h a t of the dominant t i d a l component, i t i s u n l i k e l y t h a t they are f r e e standing waves determined the boundaries.  o n l y by  However the o s c i l l a t i o n s observed a t Bute 4  and 6 d i f f e r i n phase by almost  180 degrees.  The occurence  the node o f an i n t e r n a l c o o s c i l l a t i n g t i d e between the two  of sta-  t i o n s c o u l d f u r n i s h an a l t e r n a t i v e e x p l a n a t i o n to the p r e v i o u s one of p r o g r e s s i v e waves* tude between the two  In t h i s case the decrease o f ampli-  s t a t i o n s would i n d i c a t e t h a t Bute 6  c l o s e r to the v i c i n i t y of the node. c i t y of 106  was  Taking the p r e d i c t e d v e l o -  centimeters per second as the v e l o c i t y of an i n t e r n a l  wave i n the i n l e t , the f i r s t node of a c o o s c i l l a t i o n i a response to the s e m i d i u r n a l component of the t i d e would be some 12 k i l o -  meters from the head o f the i n l e t , a p o s i t i o n 1 1 k i l o m e t e r s f u r t h e r from Bute 4 than i t i s from Bute 6 . The next node would occur some 3 6 k i l o m e t e r s from the head of the i n l e t , a p o s i t i o n approximately f i v e k i l o m e t e r s from Bute 4 , and 1 7 from Bute 6 (Table 9 ) .  The v e l o c i t y at. Bute 4 which was used f o r t h i s  calcu-  l a t i o n i s probably the g r e a t e s t v e l o c i t y which such a wave would a t t a i n as the depth decreases from t h i s p o s i t i o n t o the head ( P i g o  5)j  and the i n c r e a s e i n s t a b i l i t y would probably n o t be  s u f f i c i e n t to compensate  forthis;  However, any decrease i n  v e l o c i t y would s h i f t the p o s i t i o n o f the node c l o s e r t o Bute 6 , which would b e t t e r e x p l a i n the smaller amplitude a t t h i s C h a r a c t e r i s t i c o f a standing c o o s c i l l a t i o n i i  station.  the u n i f o r m i t y o f  phase between nodes; thus, i f t h i s were a d i r e c t response t o t h * t i d e s , the phase between any two nodes would e i t h e r be the same as the t i d e s or 1 3 0 degrees out o f phase, or some other constant v a l u e s , i n c o n t r a s t to a p r o g r e s s i v e wave which can be expected to have a c o n t i n u o u s l y v a r y i n g phase throughout the l e n g t h o f the i n l e t .  Thus i n the case o f Bute 4 and 6 constant phase Would  be expected between the p o s s i b l e l o c a t i o n o f the nodes a t 1 2 , 3 6 , and 6 0 k i l o m e t e r s from the head.  C o n d i t i o n s at other times might  be expected to v a r y somewhat i n the p o s i t i o n o f the nodes and even the phase r e l a t i o n to the t i d e s , due to the dependence o f the wave v e l o c i t y on the oceanographic s t r u c t u r e , and a p o s s i b l e change i n the d r i v i n g mechanism.  However the mean phase o f the  semidiurnal component of a harmonic a n a l y s i s o f f i v e  stations  between the p o s i t i o n s of Bute 4 and Bute 6 (Table 1 0 . ) do not show any c o n s i s t a n t r e l a t i o n t o the t i d e ,  I n f a c t , the g e n e r a l  - 47 g r a d a t i o n o f amplitude and phase seems to support the h y p o t h e s i s of a p r o g r e s s i v e wave.  ¥et, as the s t a t i o n s are spread over a  p e r i o d o f two y e a r s , t h i s i s by no means c o n c l u s i v e evidence* Only an adequate  oceanographic  survey, i n c l u d i n g anchor  stations  at i n t e r v a l s throughout the i n l e t or s e v e r a l s w i f t s e r i e s o f bathythermograms over the l e n g t h o f the i n l e t ,  sufficiently  spacedj would d i s t i n g u i s h between the two cases, (ii)  The e f f e c t o f a f i n i t e b a r r i e r a t the mouth o f an i n l e t . The o s c i l l a t o r y motion o f the deeper waters o f the  i n l e t i s most p l a u s i b l y a s s o c i a t e d w i t h the a c t i o n o f the t i d e over the s i l l , inlets.  a s t r u c t u r e c h a r a c t e r i z i n g the mouth o f most B.G.  The assumption  i s i m p l i c i t l y made i n the numerical  i n t e g r a t i o n s and other approximations to the form o f the motion, t h a t the depth i s g r e a t with r e s p e c t t o the amplitude, and t h a t the approximation o f a s i n u s o i d a l wave i s j u s t i f i e d ,  A recent  study (Long, 1953, 1954, 1955) shows fro® theory and mode! experiment  t h a t s i n u s o i d a l waves which r e s u l t from an i n f i n i -  t e s i m a l b a r r i e r are not n e c e s s a r i l y present f o r a f i n i t e amplitude b a r r i e r .  For a two l a y e r system, a h y d r a u l i c jump i s  l i k e l y to occur i n the s u r f a c e s e p a r a t i n g the two f l u i d s ,  except  f o r a s m a l l b a r r i e r and small approach v e l o c i t i e s ( F i g , 28). I n the f l o w o f a c o n t i n u o u s l y s t r a t i f i e d f l u i d l a r g e eddies and t u r b u l e n c e are common i n the l e e o f the b a r r i e r , while j e t s may form upstream  i n the case o f c o n s i d e r a b l e b l o c k i n g ahead o f the  b a r r i e r ( F i g . 29). The method i s to perform the a n a l y s i s f o r an i n f i n i t e s i m a l o b j e c t and then to extend t h i s c a l c u l a t i o n t o the f i n i t e  «a  48 •*  amplitude case by deforming the bottom  streamline.  The c a l c u -  l a t i o n s a r e then a p p l i e d t o a b a r r i e r o f the d e s i r e d h e i g h t and l e n g t h , but o f a shape d e f i n e d i n t h i s way.  The f l o w i s c h a r a c -  t e r i z e d by the v a l u e o f the Froude number (which i n c l u d e s the d e n s i t y g r a d i e n t ) , the r a t i o o f b a r r i e r h e i g h t to t o t a l depth, and f o r ' t h e two f l u i d ease t t h e r a t i o o f the i n i t i a l depth o f the  lower f l u i d to the t o t a l depth.  For the case o f continuous  g r a d i e n t of d e n s i t y a constant g r a d i e n t i s used f o r the Froude number, and a l s o the h a l f l e n g t h and the i n f i n i t e s i m a l h e i g h t are  specified, In  i t s progress up an i n l e t the t i d e achieves a r a t e  of progress almost twice t h a t o f the t h e o r e t i c a l l o n g wave f o r the  same depth.  Even when the f i n i t e h e i g h t o f the wave i s  taken i n t o account, t h i s i s not compatible with an i n e r t i a l wave, but must progress as some s o r t of shock wave s i m i l a r t o an h y d r a u l i c jump.  At the s i l l  i t encounters a b a r r i e r  which  may b l o c k as much as 5/6 o f the channel, as i s the case i n i t s approach to Knight I n l e t , o r 1/3 t o 1/5, i n the case o f Bute, I f the main stream moves i n the surface l a y e r , i t i s p o s s i b l e t h a t the s i l l  a t Bute might appear as an i n f i n i t e s i m a l b a r r i e r .  In Knight I n l e t t h i s i s most improbable. I t i s o n l y p o s s i b l e a t present t o make q u a l i t a t i v e i n f e r e n c e s from Long's work, as two c o n d i t i o n s hamper i t s application.  In the f i r s t p l a c e the t h e o r e t i c a l work makes  the  assumption o f steady s t a t e .  Secondly, i t i s assumed t h a t  the  depth i n f r o n t o f the b a r r i e r i s the same as t h a t behind. The passage o f the t i d e over the s i l l  w i l l occur  w i t h a continuous i n c r e a s e i n v e l o c i t y which w i l l i n time r e a c h a maximum and f i n a l l y reverse*  During t h i s t r a n s i t i o n the f l o w  w i l l probably pass through s e v e r a l o f the steady s t a t e regimes of motion, and t h e r e f o r e w i l l be ^indefinable i n terms of the c r i t e r i a of Long's t h e o r y .  Perhaps the best c r i t e r i o n t h a t can  be p i c k e d i s the v a l u e o f the Froude number corresponding to< the  maximum v e l o c i t y a t the apex o f the s i l l ,  some i d e a o f the regime to whieh  as t h i s may give  '>the motion may develop, low-  ever, as t h i s i s a t r a n s i e n t p r o c e s s , t h e r e e i s no knowing the if  Whether  s t r u c t u r e o f the motions i s the same as the steady s t a t e , or so, how long i t takes t o develop* Because o f the o s c i l l a t o r y nature o f the t i d e s over  the  sill,  the s t r u c t u r e which d e f i n e s the Froude number o f the  f l o w w i l l dppend on the flow d u r i n g the p r e v i o u s h a l f c y c l e .  An  asymmetry; o f the s i l l w i l l , q u i t e apart from any d i f f e r e n c e o f mixing on e i t h e r s i d e o f th© b a r r i e r , determine d i f f e r e n t  forms  of motion f o r the ebb and f l o o d by g i v i n g a d i f f e r e n t r a t i o o f b a r r i e r h e i g h t t o approach depth f o r these two phases o f th© t i d e * Thus i t i s q u i t e l i k e l y t h a t the f l o o d and ebb t i d e behave q u i t e d i f f e r e n t l y a t the s i l l .  The p r o f i l e s o f p r o p e r t i e s  of Knight I n l e t show almost complete b l o c k i n g o f the f l o w below the  l e v e l o f the s i l l  on the f l o o d .  Model experiments show t h a t  t h i s s i t u a t i o n may r e s u l t i n the r i s i n g o f the l e v e l behind the sill* ber  and e v e n t u a l s p i l l i n g over o f the f l u i d i f the Froude num-  o f approach i s s u f f i c i e n t l y h i g h ( F i g .  2 8 ) , Thus, abnormally  h i g h t i d e s a s s o c i a t e d w i t h storms o r s p r i n g t i d e s , may l e a d t o i n t r u s i o n s i n t o the deeper waters o f the i n l e t .  Profiles of  - 50 p r o p e r t i e s i n d i c a t e a form o f h y d r a u l i c jump i n tlie l e e o f the b a r r i e r i n Knight  and p o s s i b l y a l s o i n Bute (Pig* 5^) .  with l a r g e b a r r i e r s and a continuous  Experiments  d e n s i t y g r a d i e n t ( F i g . 2S)  show t h a t t h h presence o f such h y d r a u l i c jumps i s a s s o c i a t e d with tumbulence i n l a r g e eddies The  i n the l e e o f the s i l l .  apparent mean f l o w i n a t the bottom; and out a t mid  depths r e p o r t e d i n the harmonic a n a l y s i s o f the c u r r e n t s a t Knight 5 (Table 5) could p o s s i b l y be explained by the d i f f e r e n c e o f the mean flow o f f l o o d and ebb i n the presence o f the s i l l .  Model  experiments show ( F i g . 29) t h a t f o r a high b a r r i e r a j e t tends to  form upstream and above the l e v e l o f the b a r r i e r , With s t a g -  n a t i o n p o i n t s above and below i t .  The l a t t e r may develop i n t o  negative v e l o c i t i e s with r e s p e c t to the mean flow,  A mean deep  f l o w i n on the f l o o d and a f l o w out a t mid dppth on the ebb i s q u i t e compatible  with the dynamics o f such a system, and may  indeed give r i s e to the e x t r a o r d i n a r y v a r i a t i o n i n the magnitude of the h o r i z o n t a l c u r r e n t f l u c t u a t i o n s with depth. Gonelusions It  i s suggested i n standard t r e a t i s e (Sverdrup, 1942)  t h a t t i d a l motion i s c o n f i n e d to regions o f the i n l e t above the l e vel  o f the s i l l .  Studies o f the f l u c t u a t i o n s i n the h o r i z o n t a l  c u r r e n t s and v e r t i c a l o s c i l l a t i o n s o f isotherms  indicate that  motion o f t i d a l p e r i o d takes p l a c e at much g r e a t e r depths.  The  manner i n which t h i s takes p l a c e i s a s s o c i a t e d with the h y d r a u l i c flow over the s i l l .  I n the presence o f a low s i l l  the motion  appears to be o f an i n e r t i a l type, changing phase up i n l e t to lag. the t i d e by as much as a whole p e r i o d *  T h i s motion can be a t t r i -  * 51 —  buted If  t o e i t h e r a p r o g r e s s i v e i n t e r n a l wave o r a s t a n d i n g wave.  t h e m o t i o n were d e f i n e d by t h e bottom and l a t e r a l b o u n d a r i e s ,  t h e s t a n d i n g wave would be t h e o n l y one p o s s i b l e . close to a s i l l  At a p o s i t i o n  o f v e r y g r e a t h e i g h t , the m o t i o n a t depth does  n o t agree w i t h t h a t o f an i n e r t i a l o s c i l l a t i o n , b u t appears t o be d e f i n e d by some form o f h y d r a u l i c jump g e n e r a t e d a t t h e s i l l . T h i s i s n o t i n c o m p a t i b l e w i t h s t a b i l i t y c o n d i t i o n s as d e f i n e d by i s o p l e t h s o f d e n s i t y drawn from s t a t i o n s t a k e n i n t h e same and o t h e r y e a r s . P i t t i n g o f a n a l y t i c s o l u t i o n s of the equations o f i n e r t i a l motion t o t h e i n l e t s show t h a t t h e w a t e r s behave toward such a motion i n a manner s i m i l a r t o a two l a y e r system, t h e lower o f the two b e i n g a p p r o x i m a t e l y  homogeneous.  A power f u n c t i o n approa-  c h i n g a homogeneous s t a t e a t t h e bottom i s shown t o be a b e t t e r approximation  t o the a c t u a l d i s t r i b u t i o n o f s t a b i l i t y .  Motion  o f S>hh deeper water a s s o c i a t e d w i t h a p r o g r e s s i v e i n t e r n a l wave in  such a homogeneous l a y e r should be a s s o c i a t e d w i t h c u r r e n t s ,  and subsequent m i x i n g , throughout t h e l e n g t h and depth o f t h e layer.  S t a n d i n g waves w i l l on t h e o t h e r hand be a s s o c i a t e d w i t h  p o i n t s o f s t a g n a t i o n near the p r i n c i p a l l o o p s .  Distribution of  p r o p e r t i e s i n Bute seems t o suggest t h e f i r s t p o s s i b i l i t y , s i n c e the deeper l a y e r i s w e l l d e f i n e d from below t h e bottom o f t h e minimum, and t h e water appears t o show good communication w i t h that outside the s i l l . The motion i n t h e l e e o f a steady s t a t e h y d r a u l i c jump or t h e e q u i v a l e n t t o i t i n a c o n t i n u o u s l y s t r a t i f i e d f l u i d i s n o t s i n u s o i d a l , as t h e h i g h l o s s o f energy t e n d s q u i c k l y t o d  - 52 damp the motion with i t s progress h o r i z o n t a l l y (Long,  1958).  Thus such an impulse c o u l d not be propagated f a r from i t s source.  However due to the p e r i o d i c nature o f the t i d e over  the s i l l *  the f o r m a t i o n and disappearance o f the jump on  each c y c l e of the t i d e c o u l d generate an i n e r t i a l  wave t h a t .  would t r a v e l with a s u i t a b l e change o f phase throughout the e n t i r e l e n g t h o f the i n l e t .  Thus i n s p i t e o f the i n t e n s e  mixing and t u r b u l e n c e i n the r e g i o n o f the s i l l , at  which extends  l e a s t as f a r as Knight 5 (seven m i l e s ) , the c o n d i t i o n ^  f u r t h e r from the s i l l high s i l l  can be expected t o be f a i r l y s t a b l e . The  i n Knight b l o c k s , t o a much g r e a t e r extent than the  one i n Bute, the entrance o f p r o p e r t i e s from o u t s i d e , l e a d i n g to  a l e s s w e l l d e f i n e d , more permanent low temperature wedge,  which under the a c t i o n o f the i n t e r n a l o s c i l l a t i o n s tends to spread srell i n t o the bottom water. Although the a n a l y t i c d e f i n t i o n stratified is  o f the motion o f a  f l u i d moving p e r i o d i c a l l y over an asymmetric  barrier  w e l l n i g h i n t r a c t a b l e , numerical i n t e g r a t i o n and model  s t u d i e s i n a t i d e b a s i n c o u l d show r e s u l t s f o r a p a r t i c u l a r case which might be o f g r e a t v a l u e i n the i n t e r p r e t a t i o n o f motion a s s o c i a t e d with and a r i s i n g from the s i l l .  P r o f i l e s of  the oceanogrpphic p r o p e r t i e s i n Knight I n l e t suggest t h a t a complete b l o c k i n g o f f l u i d o u t s i d e and below the l e v e l o f the sill  i s n o t always the case.  The f l u i d appears t o s p i l l  over  on o c c a s i o n s to f o l l o w the main f l o w deep behind the s i l l *  Model  s t u d i e s f o r the case o f steady s t a t e i n d i c a t e t h a t f o r a c o n t i nuously s t r a t i f i e d  fluid,  such a motion i s accompanied  by  - 53 boundary l a y e r s e p a r a t i o n and t u r b u l e n c e i n the l e e o f the b a r rier.  Study o f t u r b u l e n c e i n such a r e g i o n , as w e l l as checking  t h i s c o n j e c t u r e , may  a l s o r e v e a l what the e f f e c t o f a sudden:  expansion o f a p e r t u r e would have on the s c a l e o f motion i n a stratified flui.d  r  a c o n s i d e r a t i o n o f some importance to the  study of eddy c o e f f i c i e n t s i n an i n l e t .  High t u r b i d i t y might  be expected i n a s s o c i a t i o n with a bottom swept by such motion, a l s o a s e t t l i n g as sediment i n r e g i o n s o f s t a g n a t i o n . The h i g h degree o f mixing i n the r e g i o n o f the  sill  makes i t d i f f i c u l t to determine the motion by f o l l o w i n g any particular characteristic. is the  Thus a b e t t e r method i n t h i s r e g i o n  a s e r i e s o f c u r r e n t s t a t i o n s c l o s e to and over the s i l l inlet.  A s i n g l e s t a t i o n c l o s e to the i n s i d e o f the  of  sill  with s u f f i c i e n t l y c l o s e depths o f r e a d i n g s would be most r e vealing.  A study of the v a r i a t i o n of g r a i n s i z e o f bottom  samples c o r r e l a t e d w i t h t u r b i d i t y might a l s o h e l p determine the  more common forms of motion. Should i t be p o s s i b l e to determine the motion o f the  t i d e over the s i l l for  i n parameters s i m i l a r to those used by Long  the steady s t a t e , and i t s a s s o c i a t i o n w i t h the i n t e r n a l  o s c i l l a t i o n s o f t i d a l p e r i o d , i t would be p o s s i b l e i n terms of the  the topography of an i n l e t , i t s r u n o f f , the weather, and waters w i t h which i t i s i n c o n t a c t o u t s i d e the s i l l , t o  p r e d i e t the oceanographie s t r u c t u r e of any p a r t i c u l a r i n l e t a t any s p e c i f i c time o f y e a r .  ~ 54  -  O b s e r v a t i o n s of the f l u c t u a t i o n s of oceanographic p r o p e r t i e s over s e v e r a l t i d a l c y c l e s i n d i c a t e t h e i r l a r g e t e n t and the inadequacy o f t a k i n g i s o l a t e d s t a t i o n s to sent the seasonal p r o p e r t i e s of any  l o c a t i o n i n the  repre-  inlets.  For o n l y with continuous surveys through the whole l e n g t h an i n l e t , c o n f i n e d  i f p o s s i b l e to a s i n g l e p a r t of the  c y c l e , i s i t p o s s i b l e to e s t a b l i s h the c o n t i n u i t y of  ex-  of  tidal readings  necessary to smooth out t t h e e f f e c t of t i d a l v a r i a t i o n s , which are on o c c a s i o n s - g r e a t e r i n a whole year*  i n a few hours than the seasonal  ones  55 Bibliography Arons, A.B. and H. Stommel (1951). A mixing l e n g t h theory o f t i d a l f l u s h i n g . Trans. Amer, G e o p h y s i c a l Union, 32(3): 419 - 421.. Benton, G.S. (1956). A g e n e r a l s o l u t i o n f o r the c e l e r i t y o f long g r a v i t a t i o n a l waves i n a s t r a t i f i e d f l u i d . F l u i d Models i n Geophysics. U.S. Government P r i n t i n g O f f i c e , Washington 25, B.C. Cameron, W.M. (1951), On the dynamics o f i n l e t c i r c u l a t i o n s . D o c t o r a l D i s s e r t a t i o n , S c r i p p s I n s t i t u t i o n o f Oceanography, U n i v e r s i t y o f C a l i f o r n i a , Los Angeles, C a l * Defant, A. (1925). Gezeitenprobleme des Meeres i n landnahe. Probleme der kosmischen p h y s i k , VI* Hamburg, pp. 80. Dawson, W.B, (1920), The t i d e s and t i d a l streams with i l l u s t r a t i v e examples from> Canadian waters. Queen*s P r i n t e r , Ottawa. F j e l d s t a d , J * E . (1933), I n t e r n e w e l l e n , G e o f y s i s k e P u b l i k a s j o n e r , 10(6), F j e l d s t a d , J.E. (1952)* Observations o f i n t e r n a l waves. G r a v i t y Waves. H a t i o n a l Bureau o f Standards. C i r c u l a r 521. Ketchum, B.H, (1951)* The exchange o f f r e s h and s a l t water i n t i d a l e s t u a r i e s ^ J . Mar, Res, 10: 18-38. Keulegan, G.H.(1949)* I n t e r f a c i a l i n s t a b i l i t y and mixing i n a s t r a t i f i e d f l o w . J . Tes. N a t l . Bur. Stand, 43, PR 2040 j 487 - 500, Long, R.R. (1953), Some aspects o f the f l o w o f s t r a t i f i e d f l u i d s . I . (A t h e o r e t i c a l i n v e s t i g a t i o n ) . T e l l u s , 5(1)s 42-58. (1954) , Some aspects o f the f l o w o f s t r a t i f i e d f l u i d s * I I . (Experiments with a t w o - f l u i d system). T e l l u s , 6(2) : 87 - 115. (1955) , Some aspects o f the f l o w o f s t r a t i f i e d f l u i d s * I I I . (Continuous d e n s i t y g r a d i e n t s ) . T e l l u s , 7(3) : 341-357. Munk, W.H. (1941), I n t e r n a l waves i n the G u l f o f C a l i f o r n i a . J o u r . Mar, Res, 4 : 81 - 91. P i c k a r d , G.L. (1955), B r i t i s h Columbia I n l e t s * p h y s i c a l Union 36(5) s 897 - 901.  Trans. Amer. Geo-  (1956). P h y s i c a l f e a t u r e s o f B r i t i s h Columbia Trans. Roy, Soc* Canada, 50, Ser. 3: 47-58.  inlets*  ~ 56' P i c k a r d , G.L. aad R.W. T r i t e s (1957). F r e s h water t r a n s p o r t d e t e r m i n a t i o n from the heat budget with a p p l i c a t i o n s to B r i t i s h Columbia i n l e t s . J o u r . Fish.Res, Bd, Canada, 14(4) s 605 - 616. P i c k a r d , G.L. arid K. Rogers (1959). Current measurements i n Knight I n l e t , B r i t i s h Columbia. J.Fish.Res.Bd.Canada, 16 (5) 635 - 678.  j  P r i t c h a r d , D.W. (1952), E s t u a r i n e hydrogrpphy. Advances i n Geophysics. V o l I , pp. 243-280, Academic Press I n c . , New York, N.X. R a t t r a y , M. (1954). P r o p a g a t i o n and d i s s i p a t i o n of l o n g i n t e r n a l waves. Tech, Rep. 27. U n i v e r s i t y o f Washington Department o f Oceanography, S e a t t l e , Washington. Sverdrup, H.U., H.W, Johnson, R.H. Fleming (1942). The Oceans, t h e i r p h y s i c s , chemistry and g e n e r a l b i o l o g y . P r e n t i c e H a l l , Inc., Englewood C l i f f s , N.J. Tabata, S. and P i c k a r d , G.L, (1957), The p h y s i c a l oceanography o f Bute I n l e t , B r i t i s h Columbia. J . F i s h . Res, Bd. Canada, 14(4) s 487 - 520. Thompson, T.G. and K.T. Barkey (1938), Observations on f j o r d waters. Trans. Amer, Geophys* Union, 19 : 254 - 260. T r i t e s , R.W. (1955). A study o f theooceanographic s t r u c t u r e i n B r i t i s h Columbia i n l e t s and some o f the determining factors. Doctoral Dissertation, University of B r i t i s h Columbia, Vancouver* T u l l y , J.P. (1949), Oceanography and p r e d i c t i o n o f pulp m i l l p o l l u t i o n i n A l b e r n i I n l e t . F i s h , Res. Bd. Canada, B u l l . No. 88, pp. 169.  Table 1 Comparison  o f amplitudes c a l c u l a t e d from c o n t i n u i t y  theorem  w i t h d e f l e c t i o n s o f isotherms. Amplitude from temperature a n a l y s i s  Depth (meters)  magnitude (meters)  phase (radians)  1,2 4.6 7.3 48.8 30,4 38.1 38 l 35,6 25.9 30,4  9,1 13,7 18.3 30.4 45.7 76.2 91,5 106 *7F 122.0 152.4  f  Deflections isotherms phase (radians)  magnitude (meters)  (4,6) (4.5) (4.2) (3.9) (0.7) (2.3) (1.7) (2.1) (4.3) (4.9)  1.2 3.4  (4.2) (3.7)  9.1 13 i 4  (2.5) (2,1)  16.5  (1.2)  19,8  (0,8)  Table 2 Wave v e l o c i t i e s and depths o f maximum amplitude. Station  Mode  Wave V e l o c i t y (cm/sec)  Depth o f Maximum Amplitude (meters)  Bute 6 (observed)  101  75  Bute 4 (observed5  101  80  106 71 41 31  120 140 280 320  (calculated)  K n i g h t 5a (observed) (calculated)  I II III IV  70 130  Max I Max I I I II III IV  102 56 33 26  65 100 ISO 140  Table 3 (See Table o f Contents) Knight 5a Depth (meters)  *1 0.405 0.569 0.953 1.324 2.058 2.181 2.427 2.473 2.383 2.163 1.960  4*2 5.8 10.1 14.9 32.9 38.1 48.6. 51*7 98.0 125.9 148.4  u  50 100 200 300  W  2  W  -0.420 —0.662 -0.908 -0*971 0.269 0,648 1.344 1.501 2.088 1.991 1*834  l  u  -1.462 0.711 0.954' 0.993  :  2  3  W  0,846 0*857 0*360 -0.440 -0.736 -0.623 -0.1S6 -0.020 -1.334 1*512 1.471 n  3  *-5,107 0.108 .849 .977  -5*291 -1.160 0.553 0.929  2  *3  4  -0*120 -0.103 0.012 0.S35 -0.238 -0,345 *-0.359 -0.299 0.948 1.230 1.254 u  4  -2.043 -1.600 0.377 0,398  lute 4 Depth 8.4 10.4 13.9 21.2 45.2 80.6 67.5 76.6i 80.1 83.8 99.1  (metersf  W  1.271 1*465 1.747 2*298 3.574 4*188 4.408 4.651 4.734 4.841 5.017  -1.473 -1.414 -1.244 -0.748 1.068 2.157 2.569 3.077 3.253 3*414 3.940  -0.131 -0.419 -0.739 -1*464 -1.505 -0.885 -0.413 -0*002 C0*204 0.418 1.208  *4 0.166 0.258 0.325 -0.318 -0.286 -0.576 -0*619 -0*602 -0.585 -0.528 -0*245  Table 4 Regression  Coefficients (I)  8.33 Hour 6.25 Hour D i u r n a l (2) Semidiurnal phase amp phase amp amp phase amp phase (radians) (radians) (radians) (radians)  Mode  Unight 5a  w"  (0.18) (3.82) (0.14) (3.42)  28.3 16.7 8.3 42.9  (2.55) (0.54) (2.21 (6.17  4.7. 2.4 3.0 10*9  (2.80) (0.33) (3.37) (4.88)  13.0 (4*15) 13.4 (1.52) 5.2 . (2.76) 35.0 (2.12)  44.0 30.1 8.8 26*8  (0.94) (3 *96) 1.03)  8.5  ;o.55j ,3.68J [4.82 3.57,  16.9 8.1 9.1 3.4  6*3 7.2 5.7 7.6  (5.53) (2.65) (5.96) (2.83)  Bute 4  *4  2*99)  9*9  1.4 22 • 2  1) The c o e f f i c i e n t s should only be compared with those o f the same: s t a t i o n as the s c a l i n g o f the s o l u t i o n ws i s d i f f e r e n t f o r the two s t a t i o n s , when f i t t e d t o the c o e f f i c i e n t s the readings are i n f e e t . 2) T h i s i s the l u n a r s e m i d i u r n a l component and has a p e r i o d o f 25 hours. Table 5 Comparison o f computed and observed v a l u e s o f amplitude a t Knight 5a. Depth (meters) 4.2 5.7 10.0 14*6 32.5 37,7 48,0 51.1 96.8 124.3 146.6 Tide  Observed Amplitude Phase (meters) (radians)  :4.1s;  1.2 1.6 3.4 4,6 e.2 il.o 13.5 14.0 16.6 19*9 20.8  (2,13) "jl.19) 0.80) ,0*49)  1.3  (3*25)  ,3.78' ;3*70 3.29 2.50J 2*47)  2.11)  Calculated J Amplitude Phase / (meters) (radians)!> 6*5 8.3 10*5 11.7 15.5 17.0 19.9 20*4 19,1 18,1 16.6  |2*84 2*84 2.90) 2*93) ;2.57) 2*49) ,2.32) (2.28) ,1.77) ,1.52) ,1.51)  Table: # Synthesis of currents Depth (M) 50 IOC)  2000 300  Knight 6  Observed Amp Phase (cm/sec) (rad) 2.3 6.0 10*5 5.8  (3*30) (2*76) (1.88) (1.73)  Predicted Amp Phase (cm/sec) (rad)  S y n t h e s i s Bute 4 Observed Amp Phase Amp (rad)  (Ml  8,4 10.4 13.9 21.2 45.2 60.6 67*5 76.6 80*2 83.8  1.1 1*4 2.0 3.1 6*6 6.7 6.9 7.2 7.5 7.7  (1.56) (1.71) (1.59 (1.36. (0.99 (0.93] (0*91f (0,84; (0*74 (Q.83J  Tide  2.2  (2,83)  Calculated Amp Phase (M) (rad) 4.8 5.0 5.4 5.0 7,7 5,6 5.9 0.6 5.6 5.6  (0.91) ( 0 . 8 66) ,; (0,87; 10,88 (0.83] (0.83) (0.84) (0.86) (0.86) (0*87)  Table 8 S y n t h e s i s Bute 6 Depth i»ep 7.3 9.4 18.2 31.6 47.9 57.8 63.4 72.9 7711 80.7 89.4 109.5  Tide  Observed Phase Am (rad) 1.0 1.2 1.5 1.9 1.9 2.6 2.9 3.8 3.3 3.0» 3.3 2.8  (4.43) (4*42] (4*19 (4*42 (3.76 (4.21 (4.28 (3.87] (3.92 (4.05 (3.83] (3.69)  2,2  (2.83)  Amp (M)  Predicted Phase (rad)  3*6 4.0 4.8 5*5 8.1  8*1 8.7 9*0 9*5 10*9  (cm/sec) -1.9 1.8 0*6 -0.8  20*4 8.7 8.0 8*0  Table- 7  Depth jjep (M)  Mean  5.46) 5.43) 5.39)  Table 9 Values f o r Constants o f the approximate form f o r the s t a b i l i t y (from f i g u r e s 19 & 21) Station  -N S t a b i l x t y *» Ax • Depth A (meters)  N  Depth o f s u r f a c e homogeneous l a y e r (meters)  Bute 4  700  10,000  2.47  4  Bute 6  500  85,000  1*89  7  K n i g h t 5a  350  2,000  1.89  4  • -£able 10 Depth o f maximum amplitude and r e l a t i o n o f average phase t o t h a t o f the t i d e f o r anchor s t a t i o n s which have been given h a r monic a n a l y s i s . Series  Date  Bute 4  3/7/53  34  43  7.jf  90  (283)  Series 2  8/6/52  37  40  5.0  88  (129)  S e r i e s 3 13/8/52  39  38  5.8  84  ($07)  S e r i e s 1 31/5/52  46  31  2.7  80  (182)  3/6/53  56  21  3.9  72  (72)  Bute 6  Distance Maximum amplitude from s i l l from head Magnitude depth (Km) (M) (Km) • (M);  Phase to t i d e (degrees  STATION  LOCATIONS  ANNUAL TEMPERATURE S T R U C T U R E C O KNIGHT  JUNE  1951'  BUTE  Fig.  2o  ANNUAL T E M P E R A T U R E  KNIGH1  STRUCTURE (CONT.M'C)  Jl'LV I9S6  BUTE  Fig.  JUNE 30,I9»6  2b  FEBRUARY 1958  MAY 1958  MARCH 1958  JUNE 1988  SEPTEMBER  1957  ANNUAL  DENSITY  STRUCTURE  (a.)  FJO.S  t  KNIGHT GRADIENT STATION 0  |  2  I  3  4  5  /  o> a*  E  1  200X  »a. UJ  Q  300-  - 5 00  0  5<30 1 0 0 0 I  , 1 -1  0  10  , 1  •  0  A b ove 6 0 m  20 i Be low 6 0 m  6  ( ~ 7  7  100-  ••—  DENSITY  T  ) 6t  10  [  / •  60  k.  OF  1  {  T,S DIAGRAM, KNIGHT INLET  K N I G H T - 5 o  TIME  SERIES Of  PLOTS  KNhGHT-5a AVERAGE 7  F i 9 , ,  TEMPERATURE 8  50  CO  a> +- 1 0 0  Fl RST 36 HOURS  X  a. LU  a  F I RST 24 HOURS  1501  200  250J-  °  TIME SERIES KNIGHT—5d  TIDE (ALERT  BAY. OBSERVED)  KNIGHT-5Q I  I  B U T E - 4  Period (minutes) I  I  L.  1  1  1  '  1  1  Fig.13  TIDES. HARMONIC  Alert  Bay  ANALYSIS ( S P E C T R A 1  Period I  4 - 6 J u l y , 19 5 6  Hour  R e a d i n g s  4 8  L  S T A .  KNIGHT-5 a  T e m p e r a t u r e  25  Oscillcrtior  R e a d i n g s (I h r. apart)  [ M  S T A , K N I GH T-5a  Vertical 0 t c i l l a t ions 50 R e a d i n g s (I hr. a p a r t ) HiO.O) c [6  - M  91 ™ *  L  (72) 4.6 m (9..°C)  32 5  L _ _ L  16.7)  1  1  (7.6)  13.7 (7.,)  1  -L  78  ( )" °C  9 .I  Fig.l4  J  L  37 6 (MIN.) L  1  1 .  48  0  (MIN.) L  111., 30.5 (6.6)  51.1 (6.7)  L  L  J  L  45.7 (6.6) L 610 76.2  1  1  j  1  1  1  1  1  1  1  1  (6.6)1  SLA  I  (6.5)  IQ6.7  1  96.8  I  (6.4) 12 4.3 (MIN.)  I Z\.9 (6. 3)L  J  L  Iff 2. 4  16T5)L. 18 2.9 fe .7) c 289 I (6.7j L  146.5 m (6.7*  C)  1  l  F i g . 15 VERTICAL Knight-5b(i) (lO.O) (8.0)  1 1  17.5) 18.0 1  28 READINGS ( I HR. A P A R T ")  10  1 1  K n i gh t - 5 b (i i)  (10.0) 9.6  1 1  OSCILLATIONS  (8.0) 16.4  1 .  (7.5) 20.2  1 m e *t e~r s  0  (7.0)  J  34.9  (7.0), 34.3 L  J L ( )  - o centigrade -  Meters  l  6  5  )  810  (6.5) 79.2 '  (MIN.)  _LLCL7_  J  (MIN.) 115.0  (6.5), 136.7  T I DE u  (6.5) 139.8 TIOE  u  L.  I  V E R T I C A L B U T E - 4  { ) - o  meters  in nl'  TIDE  hr.  (1/2  IO 4.  I  1  1  1  1  (lO.O) l39l  1 1  1  1  0 meters  .  . 1  . .  .  1  1  1  .  1  1  (9.4 9.4  (I0 0)l IB ? l  31 B  '94) 1  1  ,  ,  1  1  1  1  •  1  1  ,  I  1  1  1  1  1  1  1  1  (94)  21.21  apart)  c  • 1  '  V  Readings  - M '  -a^-l  3  B U T E - 6 IOO  - 0  F i g . 16  O S C I L L A T I O N S  1  1 1  1  1  ,  1  ,  (8.9) 9  47  M  45.2l  11  1  i  1  .  1  (B.3)  5 7.8 (7.8) 63.4  (8.3) 6 0 Gl  1 1  1  (7 8) 6 7.51  | 1  1  .  1  ,  1  ,  !  1  M  72  Hi  1  1  1  J_l  8  I(MIN; 77.1  (MIN!) 80.2l  PA  80.7L  M B3.R1  (7.8) 99-'  89.3  (9.4) J09.5 L  I  L  J  L  ( — U PSTREAM)  _e Depth  L  m.  100  m.  200  m.  3 0 0 m.  5b(i)  3  0 50  KNIGHT 5a  C URRENTS  CM./SEC.  - 9  9  6  6  3  3  -L  -i  L  I I  5c  i  r  6  - 3  o c my SEC.  0  II  CM./SEC.  J _ i  1 I  L  DOWNSTREAM)  5b(H)  -0 CM../SEC  I i_  ( +  J  i L  J_L  HARMONIC  ANALYSIS  (DEPENDENCE  Amplitude  ON  F l a . 18  DEPTH)  Phase  KNIGHT-5  T. zs  sa it i I  I.  —o.»1  SCALES  1  I 1 II  T« 6  »»  »b i  T  .  2  «•  -L  i  S  • 1 1  1  1  •  .1 ••e  60  oo  00  o»  oo  o  oo  0 — 0  o o  I .1  J  .1-  1  28  . A .o  I I  ; i  l  0  T« 8  o  —  —  '  0  °  B  a  .  °  a  T »I2.S  1  . 1  o « ° o  >••  1  »•»''  .  1  1  1  l  1  T.28  , . l  o  o  *  •  S  B  •  T«6  .1  o o o  e  o o  o  o  o  e  e  T • I2.S  ... 1 .  .. T « 6  II  - 3  1  •  o  • _ _ .»  . * •  T(«if«ratur« B t  1  2  1  1  . 1 1  .  o  .»__o___  Il  .  .  .  U  I  I  .  T«lt.»  000  O  0  O  o  o  10  I *-  -i—I  100  15  20 I  '  1  r-  25  BUTE-4 DENSITY  T  -i  1  100  K  )  200  L_  5  L_ 2 00  E  300  300 Q. UJ  LU Q  Q  L_ 4 0 0  500  6  00  L_  400  \— 5 0 0  600  1  r  10  BUTE  i'  P H A S E  A M P L I T U D E  REGRESSION  Fig.24  ANALYSIS  BUTE  -  4 T= 25  w,  w,  w  s  w, T-I2.5L  T * 25  T • 12.5  T « 8  T « 8  I 1  1  T» 6  I1  1  .  1  I — .5  ' —  1 T « 6  KNIGHT -  25  L  T = I2.5 T-12.5  T«  8  T "  6 ,  L  |  -  180'  1—  0  J  360'  5a  T«  T«25  r—  I  I  T »  8  T«  6  0 ° i  KNIGHT-5 SYNTHESIS AMPLITUDE  (meters)  FOR I N T E R N A L  WAVES  T E M P E R A T U R E (°C)  PHASE  (degrees)  V E L O C I T Y  - T . 3  — r  .2  P H A S E  6  5  -  I 80  ( d e g r e e s )  1  360  KNIGHT-5 SYNTHESIS  X o  \  100  cm./sec.)  4  CURRENTS  D E P T H ( m e t er s)l  (  \  \  \ \  \  5a(observed )  o--o •  \ X  \  \  \  \  • 5 d(calculated  A.—A  5 b(i) ( o b s . )  D — o  5 b(ii) ( o b s . )  x — x 5 c (obs.) \  \  \  /  200  \  l  \ \  \ • \  /  /  /  y / /  /  /  /  3001  I  I  1  V ro  Fig. 2 8  FLOW  O F  S T R A T I F I E D  FLUID  TWO FLUID SYSTEM  ABSOLUTE  SUBCRITICAL  FLOW  ABSOLUTE  SUPER-  CRITICAL  FLOW  ( LOW FROUDE NUMBER) (HIGH FROUDE NUMBER)  M m r n m r , SMALL SINE  BARRIER WAVE  COMPLETE  BLOCKING  LARGE BARRIER HYDRAULIC JUMP  SPILLING OVER  (AFTER  OF  FLUID  BARRIER  LONG  1954)  FIG.  FLOW OF S T R A T I F I E D CONTINUOUS SUPER  CRITICAL  p  REVERSAL AND  DENSITY  —L~  OF  VELOCITY  FORMATION 277-  FLUID  GRADIENT  FLOW  :>  STAGNATION 27T  <  .  (  F  T  EDDIES  OF TURBULENCE  AND  OVERTURN  IT  1  BLOCKING OF BLOCKING  TSV-< F  29  BOUNDARY  <  WITH  FORMATION  JET LAYER  SEPARATION  ^ •*= F < = 2  4lF  '^rrTIflJlMmirt^  ^ (AFTER  LONG  ^  ^  !955 )  7T  ^  ^  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085378/manifest

Comment

Related Items