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A physical study of upwelling flow dynamics in long canyons Waterhouse, Amy Frances 2005

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A Physical Study of Upwelling Flow Dynamics in Long Canyons by A m y Frances Waterhouse B . S c , T h e Unive r s i ty of B r i t i s h C o l u m b i a , 2001 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E i n T h e Facu l ty of Gradua te Studies (Oceanography) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A M a y 25, 2005 © A m y Frances Waterhouse, 2005 Abstract L o n g canyons are topographic features that are responsible for increased upwel l ing along coastal margins . L o c a t e d between Vancouver Is land and Wash ing ton State, J u a n de F u c a C a n y o n is a long canyon that begins at the cont inental slope and continues in to the S t ra i t o f J u a n de F u c a . T h i s canyon is a condui t for significant nutrient flux to the St ra i t of J u a n de F u c a and has been associated w i t h seasonal upwel l ing onto the shelf. A n eddy, vis ible at the surface, forms at the m o u t h of the J u a n de F u c a St ra i t and is an area of increased p lank ton growth . A phys ica l model of this canyon has been constructed i n order to unders tand the upwell ing dynamics i n long canyons. T h e phys ica l model is spun up to an i n i t i a l ro ta t ion rate and the flow is forced by increasing the ro ta t ion rate over the equivalent of several days. F l o w v i sua l i za t ion is used to determine the s t rength and loca t ion of upwell ing, the s t rength o f the deep canyon vor t ic i ty , a n d the deepest depth of upwel l ing. T w o m a i n stages of the flow are observed. T h e first stage involves increased upwel l ing on the shelf close to the canyon mou th . H o r i z o n t a l isopycnals (represented by hor izonta l layers of dye) show increased stretching along the ups t ream w a l l of the canyon. T h e second stage of the flow is indica ted by reduced upwell ing and the format ion of an eddy at the canyon mou th . T h e vor t i c i ty of this eddy is related to the side w a l l vor t ic i ty , as wel l as water co lumn stretching. Parameters from previous short canyon experiments are repl ica ted and show that long canyons have increased upwel l ing under s imi la r condi t ions . T h e R o s s b y scale taken f rom previous short canyon experiments d i d not proper ly characterize the flow as separat ion was observed at the canyon m o u t h i n a l l exper imenta l runs. i i i Contents Abstrac t 1 1 Contents 1 1 1 List of Tables v i i List of F igures v i i i Acknowledgements 3 0 1 1 Introduct ion 1 1.1 M o t i v a t i o n 1 1.2 Geographic L o c a t i o n 2 1.3 Scope 3 1.4 M e t h o d o l o g y 5 2 T h e o r y and Li terature Rev iew 6 2.1 T h e o r y 6 2.1.1 F l o w i n Submar ine Canyons 9 2.2 L i te ra tu re Rev iew 12 2.2.1 R o t a t i n g tanks w i t h no topography 12 2.2.2 T a n k w i t h topography 13 Contents i v 2.2.3 F i e l d measurements and N u m e r i c a l models . . 16 2.2.4 L a b o r a t o r y models 19 3 Methods 23 3.1 T a n k and C a n y o n shape 23 3.2 C a n y o n cons t ruc t ion 24 3.3 Set up of equipment 25 3.3.1 F l o w t racking: Par t ic les 26 3.3.2 F l o w t rack ing: D y e 26 3.4 D a t a A c q u i s i t i o n and Image Ana lys i s 28 3.5 Scal ing 28 3.6 Stra t i f icat ion: Theore t i ca l and R e a l 30 3.7 L o n g canyon vs. Short canyon 32 3.8 Measurement E r r o r s 33 3.8.1 T a n k Osc i l l a t ion 33 3.8.2 Surface W i n d 33 3.8.3 Other E r r o r s 34 3.9 Exper imen t s 34 4 Results 40 4.1 Resul ts from the Hor i zon ta l : T w o Dimensions 40 4.1.1 F l o w away from the canyon 40 4.1.2 F l o w i n the canyon 42 4.1.3 C o m p a r i s o n between different stratifications 45 4.1.4 F l o w Separat ion and the Rossby N u m b e r 49 4.1.5 V o r t i c i t y observed i n the Tank 52 Contents v 4.1.6 Summary : Resul ts from the H o r i z o n t a l (2D) 62 4.2 Resul ts from the Hor i zon ta l : Three Dimensions 70 4.2.1 Par t i c l e T r a c k i n g 70 4.2.2 Summary : Resul ts from the Hor i zon t a l (3D) 84 4.3 Resul ts from the Ver t i ca l : T w o Dimensions 86 4.3.1 Image Ana lys i s : Qua l i t a t ive and Quant i t a t ive 86 4.3.2 S u m m a r y : Resul ts from the Ver t i ca l (2D) 114 4.4 Steady State 118 4.4.1 C r e a t i n g a steady state 118 4.4.2 D y e ups t ream of the canyon 118 4.4.3 Summary : Steady State 123 5 D i s c u s s i o n 126 5.1 S u m m a r y of Resul ts 126 5.1.1 C o m p a r i s o n of hor izonta l dye layers w i t h real da ta 127 5.1.2 Deepest depth of upwell ing 130 5.1.3 Effect of C a n y o n W i d t h 133 5.1.4 C o m p a r i s o n w i t h Prev ious Resul ts (3D) from a Short L a b o r a t o r y C a n y o n . . 135 5.1.5 F l o w upst ream of the canyon 136 5.1.6 Phys ics beh ind the flow i n the canyon 142 5.2 L a b o r a t o r y Resul ts 153 5.2.1 Consis tency of Resul ts 153 5.2.2 Image Q u a l i t y and Resolu t ion 154 5.3 Fu tu re W o r k 154 6 C o n c l u s i o n s 156 Contents v i References 158 A Equat ions Descr ib ing C a n y o n Shape 163 A . 1 C a n y o n D e p t h 163 A . 2 C a n y o n W i d t h 164 A . 3 C a n y o n Func t i on 165 B Image Process ing techniques 169 B . l W h i t e l ight sheet images 169 B . 2 D y e images 169 C Streak images 170 D B o u n d a r y layer m o d e l 172 E D y e D e p t h D a t a 175 v i i List of Tables 3.1 Comple te P h y s i c a l and Non-d imens iona l Parameters 30 3.2 Non-d imens iona l numbers for various chosen velocit ies 30 3.3 Procedure for da ta col lect ion 34 4.1 Difference i n c m between thickness of dye layer over 60 s 89 4.2 Stre tching and Compress ion (in / -un i t s ) 90 4.3 C o m p a r i s o n between s t re tching/compress ion at Pos i t i on C 99 4.4 C o m p a r i s o n between s t re tching/compress ion at Pos i t i on D 105 4.5 C o m p a r i s o n between s t re tching/compress ion at Pos i t i on E(II) 114 5.1 Non-d imens iona l w i d t h 134 E . l Change i n depth over 60 s of the hor izonta l dye layers 176 v i i i List of Figures 1.1 M a p of J u a n de F u c a C a n y o n region 4 2.1 C a n y o n Scales 8 2.2 F l o w i n a Submar ine C a n y o n 11 2.3 Force balance i n the tank 22 3.1 L a b o r a t o r y T a n k Topography 24 3.2 C a n y o n function used i n physical model 25 3.3 R o t a t i n g table and tank labora tory geometry. 35 3.4 V e r t i c a l l ight sheet posit ions along the canyon 36 3.5 Dens i ty Profi le: R e a l vs T h e o r y 37 3.6 Par t i c l e t racks i n tank w i t h filled and par t i a l ly fil led tank 38 3.7 Interpretat ion of part icle tracks i n tank 39 4.1 Ve loc i ty away from the canyon: U — 0.5 c m s _ 1 , N =2 s _ 1 . . . 41 4.2 Streak images for various velocities 46 4.3 Interpretat ion of flow 47 4.4 Streak images for various velocities 50 4.5 Interpretat ion of flow 51 4.6 C a n y o n M o u t h E d d y Format ion : U = 0.5 c m s _ 1 , N =2, 3 and 3.75 s " 1 53 List of Figures i x 4.7 Par t i c l e T r a c k i n g i n C a n y o n M o u t h E d d y 63 4.8 V o r t i c i t y of C a n y o n M o u t h E d d y w i t h N 64 4.9 U p s t r e a m Par t i c l e Tracks : N = 1 - 3.75 s _ 1 65 4.10 U p s t r e a m part ic le veloci ty and associated vor t i c i ty 66 4.11 Ve loc i ty profiles (U and V) i n the Strat i f ied E k m a n layer 67 4.12 Dens i ty profiles i n the stratified E k m a n layer 68 4.13 Wate r c o l u m n stretching 69 4.14 Red-Green -Blue l ight sheet: U = 0.15 c m s" 1 , Ro = 0.08, N = 2 s " 1 73 4.15 Red -Green -B lue l ight sheet: U - 0.3 c m s _ 1 , Ro = 0.14, N = 2 s _ 1 74 4.16 Red -Green -B lue l ight sheet: U = 0.5 c m s _ 1 , Ro = 0.24, N = 2 s _ 1 75 4.17 Red -Green -B lue l ight sheet: U = 0.6 c m s" 1 , Ro = 0.29, N = 2 s - 1 76 4.18 Red -Green -B lue l ight sheet: U = 1.5 c m s" 1 , Ro = 0.71, N = 2 s _ 1 77 4.19 Red -Green -B lue l ight sheet: U = 0.5 c m s" 1 , i?o = 0.24, 5 w = 0.25, N = 1 s _ 1 . . 80 4.20 Red -Green -B lue l ight sheet: U = 0.5 c m s" 1 , Ro = 0.24, 5 u = 0.76, N = 3 s " 1 . . 81 4.21 Red -Green -B lue l ight sheet: U = 0.5 c m s _ 1 , i?o = 0.24, = 0.95, JV = 3.75 s " 1 . 82 4.22 C C D C o l o u r E s t i m a t i o n 84 4.23 Change i n depth over 60 s of the hor izonta l dye layers 88 4.24 D y e layer at pos i t ion A 91 4.25 L o c a t i o n of four t ime series profiles: A 92 4.26 T i m e Series of D y e at pos i t ion A 93 4.27 D y e layer at pos i t ion B 95 4.28 L o c a t i o n of four t ime series profiles: B 96 4.29 T i m e Series of Dye at pos i t ion B 97 4.30 D y e layer at pos i t ion C 100 4.31 L o c a t i o n of four t ime series profiles: C 101 L i s t of Figures x 4.32 T i m e Series of D y e at pos i t ion C 102 4.33 D y e layer at pos i t ion D 104 4.34 L o c a t i o n of four t ime series profiles: D 105 4.35 T i m e Series of D y e at pos i t ion D 106 4.36 D y e layer at pos i t ion E : 5cm from the bo t t om 109 4.37 D y e layer at pos i t ion E : 6cm from the bo t t om 110 4.38 L o c a t i o n of four t ime series profiles: E I l l 4.39 T i m e Series of D y e at pos i t ion E 112 4.40 L o c a t i o n of four t ime series profiles: E( I I ) 115 4.41 T i m e Series of D y e at pos i t ion E( I I ) 116 4.42 S u m m a r y of D y e T i m e Series D a t a 117 4.43 Steady State: dye i n i t i a l l y upst ream of the canyon 119 4.44 Steady State: dye in i t i a l l y mid-canyon 124 4.45 Z o o m of Steady State: dye in i t i a l l y upstream of canyon (200 s) 125 5.1 Cross-sect ion of A s t o r i a canyon from Hickey (1997): M a y 21, 1983 128 5.2 Cross-sect ion of A s t o r i a canyon from Hickey (1997): M a y 22, 1983 129 5.3 Stre tching vor t i c i ty from A s t o r i a canyon (Hickey, 1997): M a y 21, 1983 131 5.4 Stre tching vor t i c i ty from A s t o r i a canyon (Hickey, 1997): M a y 22, 1983 131 5.5 Stre tching across l abora tory canyon 132 5.6 F l o a t tracks for vary ing canyon w i d t h ( H y u n and K l i n c k , 2004) 138 5.7 Resul ts from A l l e n et a l . (2003): Strat i f ied Case 139 5.8 L o n g canyon results for compar ison to experiment from A l l e n et a l . (2003) 140 5.9 Ve loc i ty on the shelf upst ream of the canyon after 30 s 141 5.10 In i t i a l stage of the labora tory flow 148 5.11 Secondary quasi-steady stage of the labora tory flow 149 List of Figures x i 5.12 H o r i z o n t a l ve loc i ty from H y u n and K l i n c k (2004) 150 5.13 Ve loc i ty away from the canyon: U = 0.5 c m s _ 1 , N =2 s _ 1 after 60 s 151 5.14 Ve loc i ty ups t ream of the canyon: U = 0.5 c m s - 1 , N =2 s _ 1 after 60 s 152 A . 1 C a n y o n center depth function 164 C.1 Streak images for various velocities over a fixed t ime 171 Xll Acknowledgements I wou ld l ike to gratefully thank m y supervisor, Susan A l l e n . She has been a wonderful supervisor p rov id ing endless support , enthusiasm, encouragement, guidance and has been a wea l th of great ideas a long the way. Y o u r support has been invaluable and thank y o u for p rov id ing me w i t h such a great work environment and a superb learning experience. I w o u l d also l ike to thank R i c h Pawlowicz for his tremendous enthusiasm, patience, ceaseless questions, showing me how to wr i t e compl ica ted M a t l a b code (al l i n one line) and for p rov id ing me w i t h many great experiences and oppor tuni t ies i n oceanography. T e d Tedford provided me w i t h great ideas and enormous amounts of help i n the lab and I a m extremely grateful and appreciat ive to have had such a great lab mate and friend. M a n y thanks to C h r i s t i a n Reuten 's magic work w i t h the conduc t iv i ty probes tha t enabled me to calculate the density i n m y tank. Others I wou ld like to thank for p rov id ing insightful discussions as wel l as playful dis tract ions: Chr i s , Gaelen , K e d d i e , H a r r y and a l l of the past and present Wate rHole -ographers. I w o u l d like to thank m y D a d , Jennie, and Geoff for g iv ing me their endless support and encouragement throughout m y studies and life. I 'd also like to thank m y D a d for showing me how much fun m a t h (in your head) can be. I dedicate this project to m y m u m w h o is the insp i ra t ion for everything I do. 1 Chapter 1 Introduction 1.1 Motivation T h e coastal ocean is an area of diverse flow dynamics . One impor tan t coastal ocean process is upwell ing; i t is d r iven by several different mechanisms. Upwe l l i ng is often responsible for b r ing ing nutr ient r i ch , oxygen depleted water to the surface (Freeland a n d D e n m a n , 1982). W i n d b lowing up or down the coast causes either an onshore or offshore flow of water due to E k m a n t ranspor t i n the surface layer (Cushman-Ro i s in , 1994). W h e n water is pushed offshore, water f rom below rises to replace i t ; this process is cal led upwell ing. U p w e l l i n g also occurs a round topographic features such as submarine canyons. A s currents pass across the m o u t h of these ba thymet r ic features, water is d r iven up-canyon, enhancing upwel l ing and m i x i n g (Hickey, 1995). T h e unique flow dynamics and upwel l ing i n these regions have resulted i n the observation of h igh concentrations of zooplank ton around canyon heads ( M a c q u a r t - M o u l i n and P a t r i t i , 1996). Submar ine canyons are topographic coastal features that incise the cont inenta l shelf and are responsible for an unknown por t ion of coastal upwel l ing. These canyons va ry i n b o t h shape and size. Short canyons, such as A s t o r i a and B a r k l e y Canyons , feature a canyon head tha t reaches the depth of the cont inental shelf wel l before the coast ( A l l e n , 2000). L o n g canyons, such as J u a n de F u c a C a n y o n , feature a canyon head that does not reach the cont inenta l shelf depth before the coastline, and extend far into the coastal region, where the head often ends i n estuaries (Hickey, Chapter 1. Introduction 2 1995). L o n g canyons have not been studied i n as great as deta i l as have short canyons and their dynamics are less wel l understood. However, many interest ing conclusions have been made i n long canyons bo th from observations and numer ica l models. Internal waves i n Mon te r ey canyon (Kunze et a l . , 2002) and the response to upwel l ing w i n d stress i n Mackenz ie canyon have been stud-ied (Ca rmack and K u l i k o v , 1998). T h e greatest body of work on J u a n de F u c a canyon comes from Freeland and D e n m a n (1982) wh ich w i l l be discussed i n further de ta i l i n Sect ion 2.3 along w i t h details of other long canyon research. Unders tand ing and describing the flow dynamics w i l l not on ly help b u i l d on the current unders tanding of the physics i n long canyons but also describe how loca l flow patterns and b io logy w i l l be affected by these topographic features. 1.2 Geographic Location J u a n de F u c a C a n y o n is located off the west coast of N o r t h A m e r i c a between Vancouver Is land and the most nor ther ly region of Wash ing ton state (Figure 1.1). In the surface layers, this region has a large out-flow of brackish water sourced from the Fraser R i v e r (Freeland and D e n m a n , 1982). J u a n de F u c a C a n y o n and the surrounding region has long been of interest due to the large eddy that appears close to a spur of the canyon (Freeland and Denman , 1982) vis ible f rom satell i te ch lo rophy l l data . T h e increased ch lorophyl l indicate elevated levels of p r i m a r y p roduc t i v i t y i n the region. T h e eddy at the spur of the canyon is formed due a combina t ion of the topography of the canyon, the Ca l i fo rn i a Undercurrent , estuarine flow from the J u a n de F u c a S t ra i t and t i d a l rect i f icat ion (Freeland and D e n m a n , 1982; Foreman et a l . , 2000). T h e topography of the canyon along w i t h large scale coastal current system causes upwel l ing from depths much greater t h a n expected by wind-d r iven upwel l ing (Freeland and Denman , 1982). Therefore, an unders tanding of the dynamics of this region is impor tan t . J u a n de F u c a C a n y o n measures 85 k m i n length before reaching the coastline; i t then continues Chapter 1. Introduction 3 into the Stra i t of J u a n de F u c a for another 70 k m for a to ta l length of 155 k m . T h e average w i d t h of the canyon is 11 k m . T h e canyon consists of two m a i n regions: the first region extends for approx imate ly 30 k m and is a sharply up-sloping region. T h i s region varies i n depth from approximate ly 900 m up to approximate ly 350 m . T h e second region extends toward the coastline and into the St ra i t of J u a n de F u c a where the canyon ends. T h i s region has a re la t ive ly gentle incl ine and varies i n depth between 350 m and 180 m . A m b i e n t currents t ravel i n different directions along the west coast of Vancouver Is land depending on the area and t ime of year. D u r i n g the summer, the surface current off the west coast of Vancouver Is land travels southward whi le the Ca l i fo rn ia Undercurrent , a current at depths greater t han 200 m , travels nor thward . D u r i n g the winter , the surface current off the west coast of Vancouver Is land travels i n the nor thward direct ion. A l s o present i n this region is the Vancouver Is land Coas t a l current, a buoyancy dr iven, nor thward flowing current that hugs the west coast of Vancouver Is land nor th of St ra i t of J u a n de F u c a (Hickey et a l . , 1991). W i n d dr iven upwell ing, as mentioned previously, occurs long the west coast of Vancouver Is land and Wash ing ton dur ing the summer when winds generally b low from no r t h to south . These winds drive off-shore E k m a n layer flow wh ich is replaced w i t h deeper, nut r ien t - r ich water. In winter , the w i n d blows i n the other d i rec t ion and persistent downwell ing condi t ions occur . 1.3 Scope In this experiment , long canyons w i l l be studied i n a l abora to ry tank. T h e l abora to ry canyon is scaled to J u a n de F u c a C a n y o n using the ro ta t ion of the tank, s t ra t i f icat ion and incident ve loc i ty as the scal ing parameters. Exper iments i n this project w i l l consider different velocit ies and strat if ica-t i o n i n order to ob ta in a comprehensive unders tanding of the flow dynamics i n long canyons. T h u s far, l abora to ry experiments i n short canyons have been investigated but no labora to ry experiments of long canyons have been performed. Compar isons between short canyons and long canyon experi-Chapter 1. Introduction -1 Figure 1.1: Juan de Fuca Canyon, which extends into the Strait of Juan de Fuca between Vancouver Island and Washington State, is visible with bathymetric contours from 2 0 0 m to 1 0 0 0 m. Contour lines increase at 2 0 0 m increments and also include 1 0 0 m contour depth. ments will be used to demonstrate the distinct differences in flow dynamics. Despite the prominence and scale of long canyons such as Juan de Fuca Canyon, they have received little attention over the years and further study of their flow dynamics is important to predict their impact on surrounding regions. Important issues that arise regarding any submarine canyon are: Does upwelling occur with geostrophically forced flow? Where does upwelling occur? What drives upwelling if it does occur? How close to the surface does upwelling bring nutrient-rich water? How does the canyon interact with the coastal circulation? These issues are regarded as the motivation for most submarine canyon research. The purpose of this project is to answer these questions and obtain a comprehensive flow map for long canyons. In order to do so, several specific questions will be answered in this study to aid in this purpose: • What is the deepest depth of upwelling? Chapter 1. Introduction 5 • W h a t is the deep canyon vor t i c i ty? • Where is the area of greatest upwell ing? • H o w do short canyons compare w i t h slow d r i v i n g flow i n long canyons? • H o w does the eddy at the m o u t h of the canyon behave? A compar ison to labora tory experiments of long canyons w i l l be a useful t o o l to val idate theoret ical or numer ica l work. 1.4 Methodology T h e flow is t racked b y observing the mot ion of part icles and fluorescent dye i n the water . B o t h qual i ta t ive and quant i ta t ive results can be found using the methods tha t w i l l be described i n the next chapters. Chapte r 2 provides a brief descr ipt ion on the physics of ro ta t ing flows as wel l as a review of pre-vious l abora tory and numer ica l experiments performed i n the s tudy of submar ine canyons. Chap te r 3 describes the methods used i n this project inc lud ing scal ing analysis , the exper imenta l apparatus and exper imenta l errors. Chap te r 4 contains several different sections of results. T h e first explains how the labora tory canyon was shown to be a long canyon. T h e next section discusses the results obta ined using a single whi te l ight sheet followed by a experiments us ing a mul t i -co loured l ight sheet. T h e next section describes the results obta ined i n the ver t ica l plane us ing fluorescent dye using bo th qual i ta t ive and quant i ta t ive methods. A steady state was achieved and the results from this experiment are i n the final section of Chap te r 4. Chap te r 5 provides a discussion on these results and their relevance and suggestions of further work regarding the flow i n long canyons. A short summary of the m a i n conclusions is presented i n Chap te r 6. 6 Chapter 2 Theory and Literature Review T h e s tudy of submarine canyons i n a labora tory environment requires unders tanding submarine canyons, the theory of ro ta t ing flows i n cylinders, as wel l as an unders tanding of the current state of knowledge and research done on submarine canyons. T h i s chapter provides a review of submarine canyons, and ro ta t ing flow theory i n homogeneous and stratified cases w i t h and wi thou t topography. T h e n , contemporary research from the field, numer ica l s imulat ions and other l abora to ry models w i l l be discussed to provide a s tar t ing point for this research into long canyons. 2.1 T h e o r y T h e cont inental marg in is comprised of a coastline followed by the cont inenta l shelf, then the sharply s loping cont inental slope leading to the abyssal p la in . A s ment ioned i n Sect ion 1.1, submarine canyons are topographic features located on the cont inental shelf edge tha t incise the cont inental slope. Canyons have typ ica l scales of 10-30 k m wide and 2 k m deep (Hickey, 1995). There are two m a i n types of canyons: short and long canyons. Shor t canyons make s m a l l indentat ions i n the cont inental shelf (up to ha l f way) whi le long canyons incise the cont inenta l shelf a l l the way to the coast. In order to s tudy and characterize submarine canyons, impor tan t scales are measured for each canyon. T y p i c a l scales used for s tudy ing the flow dynamics i n canyons are the dep th of the shelf break, HS, the length of the canyon, L C , wh ich is the distance from the head to the shelf break and Chapter 2. Theory and Literature Review 7 the w i d t h of the canyon, W, wh i ch is measured at the shelf break depth (Figure 2.1). N a r r o w and wide canyons have also been dis t inguished by their different effect on the flow. A nar row canyon is denned as a canyon whose w i d t h is less t han ha l f the in ternal deformat ion radius , ^/gTJ/f, where g is gravity, D is the depth at the m o u t h and / is the Cor io l i s parameter ( K l i n c k , 1988). T h e radius of curvature of the canyon, R, is the radius of a circle tha t fits in to the curve of the shelf break contour on the ups t ream side of the canyon (Figure 2.1). T h i s scale is used i n ca lcula t ing a Rossby number for the canyon such that where U is the incident ve loc i ty and / is the Cor io l i s parameter . If the Rossby number is large (and the radius of curvature of the canyon is smal l ) , the upst ream corner of the canyon is sharp and flow t ravel ing along the cont inental slope w i l l not be able to easily follow the isobaths at the curve. However, i f the Rossby number is smal l (and the radius of curvature is large), flow w i l l be able to follow the corner of the canyon as the curve w i l l be large and m a y not show any noticeable change i n depth. A n o t h e r non-dimensional parameter used to describe the flow and effect due to submarine canyons is the Froude number wh ich is defined as where N is the buoyancy frequency denned as p dz (2.3) z=Hs where g is the grav i ta t iona l constant, p is the density and z is the ver t ica l coordinate . T h e Froude number describes the impor tance of advect ion to restoring due to gravi ty. If Froude number is smal l (and the buoyancy frequency is large), flow t ravel ing past the canyon w i l l not feel effects of the change i n topography due to the strong strat i f icat ion wh ich keeps the flow i n place. A s the Froude Chapter 2. Theory and Literature Review 8 Figure 2.1: I l lus t ra t ive p l an v iew of the a submarine canyon and the impor t an t scales. T h e shaded region is the cont inental shelf. T h e shelf break depth, Hs, is the dep th ( in the vert ical) of the shelf break contour. T h e canyon length, Lc, is measured from the shelf break depth to the canyon head. T h e canyon w i d t h , W, is measured from the m o u t h of the canyon at the shelf break depth. T h e radius of curvature, R, is the curve of the upst ream side of the canyon at the shelf break depth. number increases, the canyon effect w i l l become stronger causing an effect on the flow due to the canyon. T h e Burge r number is another impor tan t non-dimensional parameter used when descr ibing flow i n submarine canyons and is denned for long canyons as B u = Jw (2'4) For short canyons, the length scale parameter used i n the Burge r number is the length of the canyon, L, rather than the canyon w i d t h ( A l l e n et a l . , 2003). For long canyons, the w i d t h of the canyon is used i n order to remove the dependence on length of the canyon and to provide poss ib i l i ty of an infini tely long canyon w i t h s imi lar effects on upwell ing dynamics . W e hypothesize tha t the canyon Chapter 2. Theory and Literature Review 9 w i l l exert the same amount of upwel l ing regardless of length. If the Burge r number is large (and the w i d t h is smal l ) , then the flow w i l l feel l i t t le affect due to the canyon. However , as the Burge r number increases (and the w i d t h of the canyon increases), flow w i l l be more l ike ly to enter the canyon and possibly be advected due to the topography. 2.1.1 Flow in Submarine Canyons Consider a geostrophic flow t ravel ing along the cont inental slope. A s i t encounters a submarine canyon, this flow, depending on the w id th , radius of curvature of the canyon, and s t ra t i f icat ion may or may not be advected into the canyon and upwell . T h e flow i n canyons is complex and difficult to characterize, however recent advances i n submarine canyon research has denned a general flow pat tern for short canyons. A s geostrophic currents (wi th Rossby, Burger and Froude numbers less t han or close to 1) pass across the mouths of these ba thymet r ic features at (and just below) the canyon r i m depth (upwell ing current arrow i n F igu re 2.2), water is dr iven up-canyon due to an unbalanced pressure gradient caused by the constr ict ions i n the topography (Freeland and Denman , 1982). T h i s effect enhances upwel l ing br ing ing the deepest water onto the shelf (Hickey, 1995; A l l e n , 2004b). F l o w along the cont inental shelf (shelf flow arrow i n F igu re 2.2) w i l l d ip into submarine canyons ( A l l e n et a l . , 2003). T h i s d ip causes vor tex stretching (at loca t ion A i n F igure 2.2), wh ich , due to conservat ion of potent ia l vor t ic i ty , creates cyclonic vo r t i c i ty i n the flow at the upst ream side of the canyon (Hickey, 1997). T h e generation of cyclonic vo r t i c i ty inside the canyon has also been l inked to flow separat ion at the canyon m o u t h wh ich advects into the canyon (Perenne et a l . , 2001a). T h i s flow, as i t travels across the canyon w i d t h , turns toward the head of the canyon and is advected up onto the shelf. Therefore, as this flow exits the canyon, i t is closer to the shore t han i t was i n i ts o r ig ina l pos i t ion on the shelf ( A l l e n , 2004b). A t the downstream r i m of the canyon, compression of the f lu id columns is occur r ing (at loca t ion B i n F igu re 2.2) as flow advects up onto the shelf w h i c h generates ant i -cyclonic Chapter 2. Theory and Literature Review 10 vor t i c i ty ( A l l e n , 2004b). A cyclonic eddy, formed due to this vor tex s t re tch ing/compress ion and flow separation, is observed i n the canyon from the shelf break depth down to the deep layers inside the canyon m o u t h (arrows r i m label led depth eddy and deep flow i n F igu re 2.2) (She and K l i n c k , 2000; A l l e n et a l . , 2001). Due to the complex nature of the flow i n submarine canyons, i t is necessary to s tudy the dynamics of these canyons. Prev ious research has been conducted i n the field, and using b o t h phys ica l and numer ica l models. T h i s project focuses on the s tudy of flow i n long canyons using a labora tory model . In order to continue w i t h this review of submarine canyons, and for the purposes of p rov id ing a background for this project, a short section on labora tory ro ta t ing tanks w i l l now be presented along w i t h previous field, numer ica l and labora tory research conducted on canyons. Chapter 2. Theory and Literature Review 11 Surface Flow Figure 2.2: Flow in a submarine canyon adapted from Allen et al. (2001) and Allen and Hickey (2004a). The surface flow is unaffected by the topography. Shelf flow dips as it crosses the canyon rim and is the advected further toward the canyon head and up onto the shelf. A canyon rim depth eddy is observed. Upwelling occurs from deep, below the shelf break, as flow travels across the slope and is advected up through the canyon onto the shelf. There is a deep cyclonic eddy that forms in the deepest layer. Stretching of fluid columns occurs at location A, and compression of fluid columns occurs at location B generating cyclonic and anti-cyclonic vorticities, respectively. (Reproduced with permission from the author). Chapter 2. Theory and Literature Review 12 2.2 Literature Review 2.2.1 Rotating tanks with no topography No Stratification T h e labora tory tank must spin-up i n order to achieve sol id b o d y ro ta t ion before any experiments can be conducted. Spin-up is the "flow resul t ing when a state of steady ro ta t ion i n an ax i symmet r i c container is d is turbed by changing the angular speed of the container" (Ben ton and C l a r k , 1974). There are three stages of spin-up (Greenspan and Howard , 1963). T h e first is the development of the E k m a n layer, the second is the inv isc id f luid spin-up and the t h i r d is the viscous decay of residual oscil lat ions. T h e E k m a n layer, not on ly drives the second phase, but also plays the largest role of the three stages i n the spin-up process by induc ing a smal l c i rcu la to ry secondary flow. T h e spin-up t ime, T , is where L is the depth of the f luid , v is the k inemat ic viscosi ty and Q is the angular ve loc i ty of the tank (Greenspan and Howard , 1963). In this experiment, when L = 10 c m , v = 1 0 ~ 6 m 2 s - 1 and Q = f/2 = 0.75 s _ 1 , the spin up t ime is approximate ly 100 seconds. D u r i n g spin-up, the surface of the water i n an open tank, such as i n this exper iment , undergoes two separate effects. T h e first is that the interior flow extends to the fluid 's surface. T h e second effect is that , as the fluid changes from the i n i t i a l to f inal state, a pa rabo la forms on the surface induc ing a r ad ia l mo t ion i n the f luid i n addi t ion to that produced by the E k m a n layer on the bo t tom. C o n t i n u i n g w i t h the theory of interior flow i n a contained sp inn ing tank, Wedemeyer (1964) found that the walls produced a secondary flow wh ich has a s t rong influence on the generat ion of spin i n the cyl inder . H e also found that the t ranspor t of angular m o m e n t u m from the walls to the inter ior was convective t ransport rather t han diffusive t ransport . E k m a n t ranspor t at the s idewall boundary of a cy l ind r i ca l tank differs f rom the t ranspor t i n (2.5) Chapter 2. Theory and Literature Review 13 E k m a n layers of a hor izonta l surface. T h e sidewall region is made up of two ver t i ca l shear layers that are intense and complex t rans i t ion regions, one inside of the other (Greenspan, 1968, Sect ion 2.18) A viscous outer layer, closest to the tank wa l l , and a non-viscous inner layer permi t a ver t ica l mass f lux between them and is often the means by w h i c h mass is t ranspor ted f rom one E k m a n layer to the other (Greenspan, 1968). However, the ver t ica l side wal ls do not d i rec t ly affect the near ly inv i sc id core of the f luid. Effect of Stratification T h e m a i n result emerging from the papers of Ped losky (1967) and W a l i n (1969) is tha t spin-up generally does occur i n a stratified fluid but the final state is one of spa t ia l ly non-uni form ro ta t ion (Benton and C l a r k , 1974). Stra t i f icat ion adds buoyancy to the forces i n the tank w h i c h affect E k m a n layers, side-shear layers and inter ior inv i sc id flow (Benton and C l a r k , 1974). T h e spin-up t ime for a stratified f luid over a flat b o t t o m is (Wal in , 1969): where fi is the angular ve loc i ty of the tank, r is the radius of the tank and S is the s t ra t i f icat ion parameter S = (N/20,)2 and N is the B r u n t - V a i s a l a frequency as defined i n (2.3). 2.2.2 Tank with topography After the fluid is spun-up, the ro ta t ion of the tank is increased s l ight ly i n order to dr ive flow i n the tank across the topography. Af ter the i n i t i a l change i n ro ta t ion rate, a homogeneous f luid (neglecting the side walls and b o t t o m layer) is unaffected by this change i n ro ta t ion rate. However , f luid tha t is near walls w i l l develop boundary layers due to fr ic t ion. These bounda ry layers w i l l be acted on by the ro ta t iona l force creat ing an E k m a n sp i ra l (Pedlosky, 1987). In these layers, there w i l l be a net r ad i a l ou tward E k m a n t ransport . T h i s t ransport is balanced by a ve r t i ca l f lux into the E k m a n layer, causing vor tex tube stretching of the interior (Mirshak , 2001). A weak re tu rn flow toward the r (2.6) Chapter 2. Theory and Literature Review 14 center of the tank refills the water loss created by the ou tward E k m a n flux i n the bounda ry layer. A convection-l ike pa t te rn results i n w h i c h vor tex tube s t re tching causes an accelerated spin-up of the tank. However, i n a stratified f luid, the flow along the b o t t o m boundary is more compl ica ted . F l o w , i n geostrophic balance away from the boundary layer, is reduced due to f r ic t ion when close to the b o t t o m slope and the usual E k m a n spi ra l forms. T h e pressure gradient w i l l now be able to drive cross-isobar flow (Garre t t et a l . , 1993) act ing up slope br ing ing dense water up . T h i s upward flux causes a densi ty difference between the upper and lower regions (and an opposing buoyancy force) which opposes the E k m a n t ranspor t (Garre t t et a l . , 1993). Over t ime, this buoyancy force shuts down the E k m a n t ranspor t up the slope ( M a c C r e a d y and Rhines , 1991). A s the t i l t of the boundary layer isopycnals increase, the buoyancy force t e rm becomes as large as the other terms i n the E k m a n balance (Cor io l i s , pressure gradient and viscous forces). T h e lifted isopycnals a long the slope causes a ver t ica l shear i n the i n i t i a l veloci ty wh ich slows the flow close to the b o t t o m w h i c h leaves less work to be done by viscous forces ( M a c C r e a d y and Rhines , 1993). T h i s reduces the s lowing mechanism of v iscosi ty for the along-slope flow i n the boundary layer ( M a c C r e a d y and Rh ines , 1993). T h i s is cal led an arrested E k m a n layer. Forces act ing on the fluid in the canyon In the this section, the force balance i n a ro ta t ing system w i l l be s tudied. A force balance conta in ing the az imutha l velocity, ug, w i l l help expla in the flow dynamics when topographic constraints are encountered (such as a submarine canyon). T h i s can be done by consider ing the forces i n the tank i n two different ro ta t ing frames. T h e first is when the tank is ro ta t ing at a constant rate and the second is when the tank is increased i n ro ta t ion rate. Before there is any change i n ro ta t ion rate, far away from the canyon, and i n the surface water d i rec t ly above the canyon, there is an equ i l ib r ium between the pressure gradient due to the s loping Chapter 2. Theory and Literature Review 15 surface layer ( toward the center of the tank) and the centrifugal force due to the ro ta t ion of the tank (outward from the center of the tank) as depicted i n F igu re 2.3(a). T h e force balance equat ion for this case of constant ro ta t ion of the tank is fi2r = , g (2.7) where fi is f/2, r is the r ad ia l d i rect ion, g is 9.8 m s~ 2 and n is the change i n surface height of the water. T h e change i n surface height, rj, of the fluid can be calcula ted by which for this experiment is approximate ly 7 m m at the edge of the tank. W h e n the ro ta t ion rate of the tank is increased by A f i to fi2, this drives an alongshore (azimuthal) flow i n the tank (Figure 2.3(b)) wh ich is defined by ue = - A f i r (2.9) neglecting the effects of f r ic t ion i n the boundary layer. T h e equat ion of mo t ion i n the ro ta t ing frame is ^ + - V » + gz = - 2 f i 2 x u - fi2 x fi2 x f (2-10) Dt p where the first t e rm on the r ight hand side is the Cor io l i s accelerat ion t e rm and the second t e rm on the r ight is the centrifugal acceleration term. E x p a n d i n g the mate r i a l der ivat ive i n the r ad i a l d i rect ion, convert ing the pressure t e rm to surface height (77), assuming a steady state and t ak ing only the r ad ia l (f) component gives _ ^ + 5 ^ = 2 f i 2 W e + fi2r (2.11) r or Subs t i tu t ing the Cor io l i s parameter, / = 2 f i 2 , gives fue=g^-nlr-^- (2.12) dr r Chapter 2. Theory and Literature Review 16 To check the significance of each term, values are subst i tu ted into (2.12), such as / = 1.5 s _ 1 , ug = 0.3 c m s _ 1 , g = 9.8 m s 2 , dn/dr = 7 m m / 5 0 cm, 2^ = / / 2 , and r = 50 c m . These are values used i n this experiment (see Chap te r 3 for further details) . T h e last t e r m i n (2.12) is negligible sma l l (by two orders of magnitude) compared w i t h the other terms and can be neglected. T h e remain ing balance is the balance that reproduces a geostrophic current i n the ocean. Therefore, far away from the canyon and above the canyon, (2.12) holds true everywhere (ex-c lud ing the boundary layers). However, due to the t ight topography of the canyon, the alongshore flow (ug) is constr ic ted and cannot balance the right hand side of the equat ion. T h e flow, then, accelerates onshore due to this force imbalance. 2.2.3 Field measurements and Numerical models Short canyons A basic unders tanding of submarine canyon c i rcu la t ion has been developed based on field observa-tions from short canyons wh ich is the basis for the flow descr ipt ion given i n Sect ion 2.1.1. T h e flow dynamics i n short canyons such as Car son , A s t o r i a and B a r k l e y C a n y o n have been wel l documented (K inse l l a et a l . , 1987; Hickey , 1997; A l l e n et a l . , 2001) and pa r t i cu la r ly interest ing observations re-garding the effects of w i n d , the effect of canyon w i d t h , and biology are ment ioned below. Upwel l ing , an impor tan t and impressive mechanism occur r ing i n submarine canyons, brings nu-tr ient r ich water of deep or ig in to a shallower depth, such as the shelf break depth . T h i s is especially evident du r ing an upwel l ing favorable w i n d event, as found i n C a r s o n C a n y o n ( K i n s e l l a et a l . , 1987). T ime-var iab le w i n d forcing on A s t o r i a C a n y o n causes significant upwel l ing events w h i c h are evident i n field measurements (Hickey, 1997). H y u n and K l i n c k (2004) s tudied the effect of variat ions i n canyon w i d t h on upwel l ing dynamics using a numer ica l model . T h e results show that when canyons have wid ths much less t han two in ternal r ad i i , a cyclonic c i rcu la t ion inside the canyon is observed. T h i s eddy appears to be coupled Chapter 2. Theory and Literature Review 17 w i t h s t rong inshore t ranspor t and deep water wh ich resides i n the canyon's head. In wide canyons (wid th much greater than two in ternal rad i i ) , a s tagnat ion point is observed o n the downs t ream w a l l of the canyon, a cyclone occurs on the upst ream w a l l and the deepest water prefers the near shore upst ream corner. Intermediate w i d t h canyons show a dis t inct cyclone inside the m o u t h of the canyon. General ly , onshore t ranspor t is reduced as canyon w i d t h decreases. T h e effect of short canyons on biology has been s tudied du r ing an upwel l ing event ( A l l e n et a l . , 2001). B a r k l e y C a n y o n showed influence on the biology up to 10 m below the water surface. Stretch-ing vo r t i c i ty due to shelf water fal l ing into the canyon was sufficient to form a cyc lonic eddy at the canyon r i m depth. T h i s eddy is s trong enough to, i n tu rn , t rap deep passively dr i f t ing tracers such as zooplankton . L o n g canyons Several projects have dealt w i t h long canyons such as the s tudy of in te rna l waves i n long canyons (Kunze et a l . , 2002) and the response of a long canyon to upwel l ing wind-stress (Ca rmack and K u l i k o v , 1998). However, unl ike their shorter counterparts, long canyons have received l i t t le a t tent ion i n terms of the s tudy of the flow dynamics . T h i s section w i l l discuss the observations made i n and around the region of J u a n de F u c a C a n y o n . Measurements have been taken i n the region of the J u a n de F u c a C a n y o n b y C a n n o n (1972), Freeland and D e n m a n (1982) and V i n d e i r i n h o (1998) i n order to unders tand the effect of the J u a n de F u c a C a n y o n on loca l and regional current flow. D a t a from a moored current meter showed that the flow i n a long canyon great ly differed from those of smaller Ca l i fo rn i a canyons and showed that there is a possible in te rac t ion of canyon currents w i t h b o t t o m water i n the St ra i t of J u a n de F u c a (Cannon , 1972) . A more extensive s tudy of the J u a n de F u c a C a n y o n region was carr ied out between J a n u a r y 1979 and June 1981 (Freeland and Denman , 1982). T h e combina t ion of the t ight topography of Chapter 2. Theory and Literature Review 18 J u a n de F u c a C a n y o n , geostrophic pressure gradient and the ambient large-scale c i r cu la t ion drives upwel l ing i n this region (Freeland and Denman , 1982). T h i s in terac t ion allows water to rise from depths much greater than w i t h t yp i ca l wind-dr iven upwel l ing mechanisms. T h e upwelled water is pa r t i cu la r ly dense, low i n dissolved oxygen and r i ch i n nutrients (Freeland and D e n m a n , 1982). Water o r ig ina t ing from the Ca l i fo rn i a Undercurrent was found deposited on the shelf due to the presence of the J u a n de F u c a C a n y o n (Freeland and D e n m a n , 1982). M o r e recent moor ing deployments i n J u a n de F u c a C a n y o n were specifically loca ted at the spur of the canyon wh ich is large devia t ion (sometimes referred to as a second canyon (Freeland and D e n m a n , 1982)) half way into J u a n de F u c a C a n y o n . Be low 200 m , flow is up-canyon w h i c h is induced by the across-canyon flows i n the upper layers (Vinde i r inho , 1998). Tempera ture and sa l in i ty profiles show enhanced upwel l ing (over as much as 200 m depth) i n the canyon compared w i t h the shelf. T h e Ca l i fo rn i a undercurrent was not l inked to upwell ing whi le the shelf break current, w h i c h drives the pressure gradient, is the most impor t an t mechanism for d r i v i n g upwel l ing (V inde i r i nho , 1998). A l l e n (2000) investigates the difference i n dynamics between a long canyon and a short canyon using two separate ana ly t i ca l models (one long and one short) w i t h a s impl i f ied s t ra t i f icat ion. In regions where the topography converges (on the downstream side of the J u a n de F u c a C a n y o n next to the coastl ine), the flow was found to increase i n speed i n order to follow the isobaths. T h e results indicate that geostrophic flow occurs i n a l l regions of a long canyon (except at s ingular points) , whi le i n a short canyon, a-gesotrophic effects dominate inside the canyon. U p w e l l i n g occurs inside the long canyon, a long the right hand (downstream) wa l l near the coast whi le i n the short canyon, no upwell ing occurs for geostrophic flow ( A l l e n , 2000). T h e results f rom these ana ly t i ca l models expla ined the difference i n upwell ing between the two types of canyons; short canyons have moderate , episodic upwel l ing events whi le long canyons experience constant upwel l ing from great depths ( A l l e n , 2000). T h e results from A l l e n (2000) are for a canyon w i t h a flat shelf w i t h no s t ra t i f icat ion. In order Chapter 2. Theory and Literature Review 19 to accurately represent the flow i n a submarine canyon, s t rat i f icat ion needs to be inc luded as wel l as a more accurate representation of the topography. T h e cont inental shelf should be sloped and the change i n dep th between the shelf and the deep ocean should be smooth rather t h a n stepped. These improvements w i l l a id i n the representation of the flow dynamics i n the canyon. T h i s project w i l l use a l abora tory mode l w i t h these above mentioned improvements . T h e next section w i l l provide a review of previous l abora tory submarine canyon experiments i n order to provide a background for the present work. 2.2.4 Laboratory models R o t a t i n g tank submarine canyon experiments Perenne et a l . (1997, 2001a,b) have carr ied out a number of short canyon experiments using a tank w i t h the coastline i n the middle of the tank, the abyssal p l a in a long the edges of the tank, and a cont inental slope jo in ing the two. Perenne et a l . (2001b), using an impuls ive ly s tar ted flow i n the l abora tory mode l and compar ing i t w i t h a numer ica l model , observed an i n i t i a l a long-canyon flow followed by the generation of a cyclonic vor tex inside the canyon. In upwel l ing cases, this cyclonic vor tex develops a long the upst ream edge of the canyon and then advects into the canyon inter ior wi thou t significant l oca l vor tex stretching w i t h i n the canyon. T h e canyon vor tex is observed to be w i t h i n the canyon from the r i m down to the bo t t om of the canyon. T h e in tensi ty of the upwel l ing vor tex is variable and depends on the di rect ion of forcing at shelf level (Perenne et a l . , 2001b). Short canyon lab results from the tank used in this experiment Previous experiments have been carr ied out on the same ro ta t ing table as used for this project (Mi r shak , 2001; A l l e n et a l . , 2003; M i r s h a k and A l l e n , 2005). T h e apparatus involves us ing a 1 m diameter tank tha t contains t yp i ca l ocean ba thymet ry ( inc luding a cont inenta l shelf a long the outside edge of tank, an insert of the submarine canyon topography, a cont inenta l shelf and flat Chapter 2. Theory and Literature R e v i e w 20 abyssal region i n the center of the tank) wh ich is posi t ioned on a ro ta t ing table. T h e tank is spun-up and after so l id b o d y ro ta t ion is achieved, flow is d r iven b y s l ight ly increasing (decreasing) the speed of ro ta t ion to drive an upwell ing (downwelling) response i n the canyon. These labora tory experiments dr ive an incident flow by increasing the ro ta t ion rate over the equivalent to a ful l scale w i n d event of one day causing an incident shelf break current for various degrees of s t rat i f icat ion. T h e lab mode l results show significant upwell ing i n the unstrat if ied case and less significant upwel l ing i n the stratif ied case. Deep flow i n the canyon (half way down into the canyon below the shelf break) shows a t rapped cyclonic eddy i n the canyon. A c t i v e upwel l ing occurs between this cyclonic layer and the unmodif ied surface layer. T h e flow i n this canyon exits a long the downs t ream canyon w a l l and is a combina t ion of water from bo th the shelf and the slope. A l s o , ups t ream of the canyon, over the cont inental slope, weak offshore flow is observed possibly due to vor tex s t re tching resul t ing from shelf flow fal l ing in to the canyon. M i r s h a k (2001) s tudied how velocity, s trat i f icat ion and ro ta t ion affect upwel l ing i n a short canyon. B y compar ing the behaviours of predicted spin-up i n a tank w i t h and wi thou t a canyon, the amount of upwel l ing i n a short submarine canyon can be est imated by recording the flow i n the surface layer of the tank. T h e difference between the two cases (wi th and wi thou t a canyon) is then equal to the force exerted on the water by the canyon. M i r s h a k (2001) predicted tha t i n a s t rong upwel l ing event, the canyon causes an order of magni tude increase i n upwel l ing flux compared to wind- induced upwel l ing over the same length of shelf. For A s t o r i a canyon, the flux onto the shelf can be described by $ = CdHsRo2'zS-1rlU2 (2.13) where C<j = 0.43 is the drag coefficient and Sc = (N Hs)/(f L) is a Burge r number, as defined by M i r s h a k and A l l e n (2005) for a short canyon. In this project , the dynamics i n long canyons w i t h a slow incident flow (low Rossby number) as wel l as flow w i t h increasingly larger Rossby numbers w i l l be described and compared w i t h the Chapter 2. Theory and Literature Review 21 dynamics i n short canyons. Chapter 2. Theory and Literature Review 22 (a) < •> (b) (8) *" ® < Pressure Gradient Force > Centrifugal Force (£22r) Centrifugal Force with new rotation rate ((Q+AQ) 2r) Coriolis Force due to relative flow (fue) "** Centrifugal force on induced flow (u92/r) <S> Flow into the page ® Row out of the page Figure 2.3: I l lus t ra t ion of the force balance i n the tank. T h e surface layer takes the shape of a pa rabo la where the axis of ro ta t ion of the tank is centered a round the midd le and f = 20. and A / / 2 is the smal l change i n ro ta t ion rate to dr ive the upwel l ing response, (a) shows the force balance after spin-up is complete, (b) shows the force balance after the change i n ro ta t ion rate. A n alongshore flow is d r iven th rough the t ank w i t h flow coming out of the page on the r ight side of the tank (dotted circle) and flow going into the page on the left side of the tank (hatched circle) . 23 Chapter 3 Methods 3.1 Tank and Canyon shape T h e tank used i n this experiment is a c i rcular tank, 1 m i n diameter, tha t has a 10-fold exaggerat ion i n the ver t ica l compared to the depth scale of the ocean. T h e exaggerat ion i n the hor izonta l is approximate ly 3 k m i n the ocean for every centimeter i n the tank. T h e t ank topography consists of an upper s loping region (5° ) wh ich is the cont inental shelf, followed by a shorter sect ion w i t h a larger slope (47°) wh ich is the cont inental slope and the middle of the t ank is the flat abyssal p l a in as shown i n F igu re 3.1. T h e tank topography is a combina t ion of two l inear functions; one for the cont inental slope, and another for the cont inental shelf. T h e canyon used i n the lab experiment is designed to resemble the J u a n de F u c a C a n y o n and is bui l t in to a 22° slice from the tank topography described above. T h e canyon, itself, is d iv ided into three regions; the slope at the canyon head, the flatter region i n the middle of the canyon and the slope at the canyon m o u t h (labeled 1, 2 and 3, respect ively i n F igure 3.2). T h e center depth of the canyon is composed of an add i t ion of three hyperbol ic tangent functions, one for each section of the canyon (See A p p e n d i x A for the ful l equations). T h e cross-sectional shape of the canyon is an exponent ia l function to the four th power p roduc ing a "valley" shape. T h e ba thymet r ic contours of the canyon are shown i n F igu re 3.2. Chapter 3. Methods 24 41 cm 100 cm Figure 3.1: Topography of the labora tory tank which is 1 m i n diameter . It consists of a cont inental shelf ( 5 ° ) , followed by a cont inental slope (47°) and the flat abyssal region i n the center of the tank. T h e tank topography is r ad ia l ly symmetr ic except for the canyon insert. T h e submarine canyon topography used i n the experiment is denoted by the gray l ine. T h e depth of the water (when filled) is 10 c m and the depth f rom the shelf break to the b o t t o m is 2,2 cm. Note figure is ver t ica l ly exaggerated. 3.2 Canyon construction F r o m the contour plot i n F igu re 3.2, the phys ica l mode l was constructed using stacked 1/8" pieces of mahogany p lywood . There are 28 contours i n this figure and each contour was d rawn onto a piece o f wood , the w o o d was cut out and then glued together to replicate a negative o f the canyon shape. T h e finished mode l was then plastered using Plas ter of Pa r i s i n order to provide a smooth , continuous slope between the steps created by the w o o d contours. Once the plaster was dry, the model was placed inside a container w i t h the same size perimeter as the canyon mode l and the edges were sealed w i t h whi te putty. F i b e r T e k marble cast ing resin was then m i x e d w i t h the F i b e r T e k M E K P catalyst a long w i t h F i b e r T e k M u l l e d F ibers , inc luded for durabi l i ty , un t i l the res in /ca ta lys t mix ture was a th ick paste. T h i s paste was poured into the container and al lowed to set. T h e cast was then placed inside the tank, and, along w i t h the shelf/slope insert, was sealed us ing polyure thane sealant, wh ich is flexible, waterproof, and paintable. Once dry, the whole area was painted using flat, black paint i n order to reduce the amount of reflection on the shel f /canyon area. Chapter 3. Methods 25 -12 -8.1 -4.1 B 0 >. 4.1 8.1 12 16 1.4 5.2 9 12.8 16.6 20.4 24.2 28 31.8 x Tcml F igu re 3.2: F u n c t i o n used i n phys ica l mode l for l abora tory canyon shape. T h i s funct ion resembles the va r ia t ion i n depth that occurs i n J u a n de F u c a C a n y o n . C o n t o u r dep th is i n centime-ters where 0 c m is the surface of the water i n the tank. T h e three open rectangles are the three locations of the three hyperbol ic tangent functions used to create the canyon center depth ( (A.2) - (A.4) ) . 3.3 Set up of equipment T h e exper imenta l apparatus consists of a computer-control led ro ta t ing table (F igure 3.3). T h e table has electr ical and f luid s l ip rings mounted underneath the tank w h i c h allows the tank to be filled w i t h water and to have electr ici ty on the table whi le ro ta t ing . T h i s allows for electr ical equipment to be mounted and rotate i n the same reference frame as the table. A l i d is also placed on the tank du r ing spin-up i n order to reduce the effects of the ambient air as w i l l be discussed i n Sect ion 3.8.2. T h e video camera is a C a n o n O p t u r a 10 that has a 1 6 X O p t i c a l Z o o m lens, a 1.33 M e g a p i x e l C C D , and low-l ight and manua l focus settings. There are two basic geometries for the camera and Chapter 3. Methods 26 slide projector (Figure 3.3). T h e first (Figure 3.3(a) and 3.3(b)(i)) involves the slide projector being mounted such that the l ight shines d i rec t ly into the middle of the tank. A mi r ro r is placed at the b o t t o m of the tank at an angle to direct the l ight sheet into the canyon insert as a level , hor izonta l plane. T h e video camera then records the particles i l l umina ted by this hor izon ta l plane of l ight . T h i s geometry w i l l be referred to as T a n k Geomet ry I. T h e second geometry (Figure 3.3(a) w i t h the posi t ions of the video camera a n d slide projector switched and 3.3(b)(ii)) involves the v ideo camera being mounted such that the field of view is a imed di rec t ly into the midd le of the tank. A g a i n , a mi r ro r is placed at the bo t t om at an angle i n order to direct the field of v iew in to the canyon insert. In this second geometry, the slide projector shines a ver t ica l sheet of l ight in to the canyon produc ing a cross-sectional perspective from the m o u t h look ing toward the canyon head. T h i s geometry w i l l be referred to as T a n k Geomet ry II. 3.3.1 Flow tracking: Particles Par t ic les are used i n this experiment i n order to quantify the flow. Different part icles were tested to determine wh ich are the easiest to manufacture and use. A combina t ion of P a r o w a x and differ-ent amounts of t i t a n i u m dioxide powder produce particles whose densities are easy to cont ro l and therefore these particles were used i n this experiment. In order to reduce surface tension, K o d a k P h o t o F l o is added to the particles w i t h a smal l amount of water to make a slurry. T h i s we l l -mixed s lur ry is then added to the water i n the tank after spin-up is complete and approx imate ly 5 minutes before da t a col lect ion begins. 3.3.2 Flow tracking: Dye Fluorescence dye was also used for t rack ing flow i n order to describe the flow dynamics i n the canyon. There are a variety of ways the dye experiments were done and the process of inject ing the dye is described below. Chapter 3. Methods 27 T h e first set of experiments involve hor izonta l layers of dye tha t are used along w i t h a ver t ica l plane of l ight . A m a x i m u m of three layers of dye are used i n the exper iment area. Three c o m m o n depths are chosen as the dye depths for a l l experiments and unless otherwise specified are: 8.5 c m , 7 c m and 5 c m depths. Solut ions of fluorescence and salt water at the par t i cu la r densi ty of these three depths are made i n advance. A s the tank fills and the water level reaches one of these three depths, 1 m£ of dye solut ion is injected into the f i l l ing hose. Due to the neut ra l density of the dye at the layer at w h i c h i t is injected, a t h i n layer forms at the injection depth. For the layer dye experiments , the camera and slide projector are arranged i n T a n k Geomet ry II (Figure 3.3). T h e ver t ica l l ight sheet from the slide projector is set i n i t i a l l y at the canyon m o u t h and w i t h each new dye experiment , i t is moved further toward the head of the canyon i n order to ob ta in a three-dimensional image of the flow (Figure 3.4). Ano the r set of dye experiments used i n this project involved pu t t ing dye-fi l led syringes d i rec t ly into the water and releasing the dye a set per iod of t ime after the ro ta t ion change. T h e syringes are arranged i n two possible manners. T h e first is where four syringes are used: two of the syringes are 0 c m and two are 0.5 c m below the shelf break depth. T h e syringes are coupled so that at each of the two locat ions, there is one syringe injecting dye at each of the two levels i n order to wa tch the flow of the dye at the same loca t ion but at s l ight ly different depths. A var ia t ion of this first geometry is to have on ly the two syringes at 0.5 c m depth below the shelf break. These two depths are chosen to observe the effect of upwel l ing from below the canyon r i m to see whether or not the dye is coming from the r i m depth or below the r i m depth. T h e second geometry for these steady state experiments is where a l l four syringes are spread out over the ups t ream side of the canyon, d i rec t ly i n contact w i t h the shelf. W h i l e the tank is sp inning up, the empty syringes are i n the tank and after sp in up is complete, the plungers of the syringes are carefully raised wh ich sucks i n water from the sur rounding area. T h e syringes are removed from the tank, the water is removed from the syringes, m i x e d w i t h a sma l l Chapter 3.. Methods 28 amount of fluorescence and re-inserted into the syringe. T h e dye-filled syringes are then placed back i n the tank i n the same loca t ion and th i r t y seconds after the in i t i a l change i n speed, the plungers are removed from the syringes and the dye freely flows from the syringes at a slow, fixed rate. 3.4 Data Acquisition and Image Analysis Several methods are used to ob ta in da ta on the flow dynamics i n and a round the canyon. T h e first involves using a single hor izonta l whi te l ight sheet posi t ioned at the shelf break depth and i l l umina t i ng the shelf as wel l as the interior of the canyon and offshore region. Par t ic les are seeded i n the water jus t before the ro ta t ion rate is changed. T h e second me thod involves us ing a m u l t i -coloured (red, green and blue) hor izonta l l ight sheet and seeding the water w i t h part icles. T h i s method was employed i n A l l e n et a l . (2003) (using red and green l ight sheets) i n order to ob ta in ver t ica l ve loc i ty measurements. T h e red l ight sheet is posi t ioned between 1 - 2 c m depth, the green sheet between 2 - 3 c m depth and the blue between 3 - 4 c m depths. T h e t h i r d me thod of da ta acquis i t ion is the use of hor izonta l dye layers wh ich are i l l umina ted using a ver t ica l whi te l ight sheet using Tank Geomet ry II . T h e fourth method of flow v i sua l i za t ion uses dye fi l led syringes placed i n different locat ions throughout the canyon using T a n k G e o m e t r y I. Large amounts of images are obtained from these experiments and a me thod of analysis is developed for each one. T h e more compl ica ted image processing routines can be found i n A p p e n d i x B . 3.5 Scaling Table 3.1 displays the values known for J u a n de F u c a C a n y o n and the corresponding values for the phys ica l model . T h e buoyancy frequency for J u a n de F u c a C a n y o n is obta ined from a C T D profile taken at N 48° 2 .35 ' ,W 125° 36.9' on 2004/07 /14 (2004, courtesy of the Inst i tute of Ocean Sciences, Chapter 3. Methods 29 collected by R . E . T h o m s o n , I O S , Sidney, B . C . ) . T h e buoyancy frequency, N2, was calcula ted to be 0.0046 s~ 2 from this profile at the shelf break depth. T h e Cor io l i s parameter , the buoyancy frequency, and the veloci ty are the parameters that w i l l be varied i n the lab experiments and therefore w i l l be calcula ted so that the non-dimensional numbers i n (2.1), (2.2) and (2.4) m a t c h between the real J u a n de F u c a C a n y o n and the scale model . T h e geostrophic case (Ro < 0.145) w i l l require a ve loc i ty tha t is quite s m a l l and i n order to achieve this low veloci ty whi le m a i n t a i n i n g the qua l i t y of results, there w i l l be a lower l i m i t to the veloci ty wh ich must be considered. In order to do this , / is chosen to be h igh . A s an i n i t i a l estimate, the final ro ta t ion rate of the tank is chosen to be / = 1.5 s - 1 . T h e three non-dimensional parameters are matched between the tank and the ocean by va ry ing the incident veloci ty and the strat i f icat ion. In order to ob ta in the best ma tch between the model and the ocean, a ve loc i ty of 0.3 c m s _ 1 and a s trat i f icat ion of 2 s _ 1 is required. A l t h o u g h from Table 3.1, the non-dimensional parameters are s ight ly different, the Rossby number and the Burge r number are very s imi lar whi le the Froude number is the most different. T h e Rossby and Burge r numbers are the most impor tan t parameters and are closer t han the Froude number . T h e Froude number is less than one i n bo th the tank and ocean cases so that the difference between the values is not significant. T h e f inal ro ta t ion rate of the tank after spin-up is 1.5 s - 1 . T h e t ank speed needs to be changed by some ro ta t ion rate, A / , i n order to create a ve loc i ty of 0.3 c m s _ 1 . Since / = 2w, i f A / = 0.025 s _ 1 , then AUJ = 0.0125 s _ 1 . W i t h this increase i n angular velocity, the ro ta t iona l ve loc i ty at the outside r i m of the tank is: u = w • r = 0 . 0 1 2 5 s - 1 • 0 . 2 5 m = 0 . 0 0 3 1 2 5 m s - 1 = 0 . 3 c m s - 1 (3.1) which is the veloc i ty derived from the scal ing above. T h e ro ta t iona l rate of the tank w i l l change from / = 1.475 s _ 1 to / = 1.5 s _ 1 over 27.3 s. T h e t ime per iod over w h i c h the change i n ro ta t ion takes place is equal to several iner t ia l periods which is chosen to resemble a mean, geostrophic flow i n the tank s lowing changing over several days. In order to investigate the change i n dynamics w i t h Chapter 3. Methods 30 S y m b o l J u a n de F u c a L a b o r a t o r y Shelf-break depth Hs 180 m 2.2 c m Shelf length Ls 68.6 k m 22.5 c m C a n y o n length Lc 45 k m 16.5 c m C a n y o n w i d t h (average) W 12 k m 5.8 c m C a n y o n w i d t h (shelf break) wsb 23 k m 6.5 c m R a d i u s of curvature of Hs R 7.7 k m 1.4 c m Cor io l i s parameter f . 1.08 x l 0 ~ 4 s - 1 1.5 s - 1 B u o y a n c y frequency at Hs N 4.6 x l 0 ~ 3 s~l 2 s - 1 ' Incident Ve loc i ty U 10 c m s _ 1 a 0.3 c m s _ 1 Rossby N u m b e r Ro 0.12 0.145 Froude N u m b e r Fr 0.12 0.07 Burge r N u m b e r Bu 0.64 0.5 W i d t h R a t i o W/Wsb 0.52 0.89 W i d t h - L e n g t h R a t i o W/Lc 0.26 0.35 L e n g t h - L e n g t h R a t i o Ls/Lc 1.52 1.36 Table 3.1: Comple te phys ica l variables and non-dimensional numbers for J u a n de F u c a C a n y o n and the phys ica l l abora tory model . "Data from Freeland and Denman (1982) a change i n velocity, several velocities are chosen and their corresponding non-dimensional numbers and change i n frequencies are summar ized i n Table 3.2. C/[cm s- 1] Ro Bu Fr A / I s - 1 ] 0.1 0.08 0.51 0.04 0.0125 0.3 0.14 0.51 0.07 0.025 0.5 0.24 0.51 0.11 0.0375 0.6 0.29 0.51 0.14 0.048 1.5 0.71 0.51 0.34 0.12 Table 3.2: Non-d imens iona l numbers for various chosen velocit ies. 3.6 Stratification: Theoretical and Real T h e Oster (1965) two bucket me thod was used to f i l l the tank. F i l l i n g the t ank (while the table is rotat ing) completes i n approximate ly 90 minutes. T h e tank is left to spin-up for another two hours Chapter 3. Methods 31 to ensure sol id b o d y ro ta t ion . P r o m the calculat ions shown above, the buoyancy frequency i n the t ank is required to be 2 s _ 1 at the shelf-break i n order for the lab mode l flow parameters to ma tch w i t h the full scale J u a n de F u c a C a n y o n . T h e volume of the tank is calculated along w i t h the densi ty profile of the tank (Figure 3.5(a)). T h e theoret ical density is calculated by discre t iz ing the l inear densi ty profile over the hypsography of the tank topography. T h i s density profile is then used to calculate the buoyancy frequency (Figure 3.5(b)). For the buoyancy frequency at the shelf-break to be 2 s _ 1 as desired, the bo t t om density needs to be 1.0499 kg £ ~ x and the surface densi ty needs to be 1.0148 kg £ - 1 . Conver t ing the bo t t om density to percent NaCl .we igh t gives 7.2% N a C l per 100 g of water for i n i t i a l concentrat ion i n the first bucket (Wol f et a l . , 1978). A mic ro -conduc t iv i ty probe was used to cal ibrate the theoret ical densi ty profile. T h e tank was filled and left to sit for 2 hours i n a non-rotat ing state. T h e probes were located off the m o u t h of the canyon approx imate ly 4 c m from the shelf break. Three conduc t iv i ty probes were then lowered in to the tank twice. T h i s da ta were separated into downward and upward casts of the probes and then averaged over depth i n 0.2 c m increments for the entire depth range (Figure 3.5). A s evident from F igure 3.5, the downward and upward casts are not s imi lar i n the fit they make w i t h the theoret ical curve. There are several possible reasons for the shift of the theoret ical and measured densi ty curves. T h e first reason for the shift is that as the conduc t iv i ty probe is raised up th rough the water co lumn m i x i n g between density layers is a problem (not such a problem on the way down as ins t rument has not d is turbed the water below i t ) . T h e second possible reason for the shift is the error associated w i t h the measurement of the salt and water used for the experiment. T h e t h i r d possible reason is a misca l ib ra t ion of the conduc t iv i ty probes which w i l l causes a difference i n measured densi ty for each depth. T h e devia t ion at the b o t t o m of the density profile is possibly due to m i x i n g du r ing the f i l l ing Chapter 3. Methods 32 of the tank. In the first few centimeters of the tank, as the water enters the t ank boundary layer dynamics w i l l cause more m i x i n g than when the f i l l ing sponge is fully f loat ing. A n o t h e r possible reason for the densi ty difference is diffusion that occurs i n the tank over t ime wh ich w i l l increase the densi ty at the surface and decrease the density at the b o t t o m of the tank. T h e buoyancy frequency is the most impor tan t parameter (not density) a n d as long as N at the shelf break is the same i n bo th the measured and theoret ical values, the densi ty profile i n the tank is acceptable. 3.7 Long canyon vs. Short canyon A long canyon features a head that continues in land , past the shelf and slope. T h i s differs from a short canyon head, wh ich ends on the slope or shelf. A long canyon head w i l l ex tend into the shelf possibly ending i n estuaries or straits ( A l l e n , 2000). T h e canyon const ructed for this experiment must be verified to be a long canyon, as opposed to s imply a short canyon. In order to val idate this, the experiment was done under two condit ions: i n the first, the tank was fi l led n o r m a l l y such that the shelf break is 2.2 c m below the surface of the water; i n the second, the water was filled on ly to the head of the canyon. T h i s tests whether the flow through the canyon is the same i n the filled and unfil led states. If so, then the canyon can be deemed a long canyon. T h e results demonstrate that the flow around the canyon, when filled on ly to the edge of the canyon head, acts s imi l a r ly to no rma l condit ions, where the shelf break is 2.2 c m deep. T h e flow from the streak images (Figures 3.6) are interpreted i n F igu re 3.7. T h e flow along the slope enters the canyon m o u t h and turns into the canyon. A t the canyon head, the flow is contained w i t h i n the canyon walls . O n the ups t ream side of the canyon on the shelf, the flow travels s lowly i n the incident flow di rect ion. O n the downst ream side of the canyon on the shelf, the flow curves toward the shelf break showing possible upwel l ing a long the downst ream w a l l of the canyon. Chapter 3. Methods 33 3.8 Measurement Errors Several systematic errors occur due to the measurement apparatus and technique. 3.8.1 Tank Oscillation T h e part icles were found to have an osci l la t ion frequency between seven to nine seconds, w h i c h is the same frequency as the table ro ta t ion . T h i s ro ta t ion was determined to be due to the table being un-level. In conclusion, the tank needs to be re-leveled per iod ica l ly as the part icles begin to oscil late after several experiments have been carried out. Ano the r source of the tank osci l la t ion occurs when d ropp ing particles in to the tank. T h e particles are put into the tank using a smal l spoon, and as the particles drop th rough the water c o l u m n an osci l la t ion is set up (due to the tank rota t ion) . If noticeable osci l lat ions are present after inser t ing the particles, the tank is left to spin-up (wi th l id) for another 15-20 minutes. 3.8.2 Surface Wind T h e second source of error is the drift of part icles on the surface. In i t ia l ly , the par t ic les and photoflo solut ion have a veloci ty due to their input into the tank but after several minutes , the part icles slow and do not move faster t han 0.1 c m s _ 1 . However, i n the first few experiments , the surface water was s t i l l mov ing due to the a w i n d stress created as the tank rotates i n an ambient environment of non-moving air . Therefore, the particles had mot ion after their i n i t i a l inpu t into the tank (on the order of 0.1 - 0.2 c m s _ 1 ) . A l i d was placed on the tank wh ich fixed the p rob lem to some degree, but there seemed to s t i l l be some movement after leaving the l i d off of the tank for longer t han several minutes (which is required for adding the particles and runn ing the exper iment) . However, the par t ic le movement was much less t han previously (and less t han the required d r i v i n g ve loc i ty) . Chapter 3. Methods 34 3.8.3 Other Errors Other errors arise using the t r i -coloured l ight sheet due to the difficulty i n te l l ing the red, green and blue particles apart . B y changing the intensity, the colors are more v ib ran t but i t is difficult to te l l whether this is real or just a computer artifact. T h i s p rob lem w i l l be discussed i n deta i l i n section 4.2. In some cases for the dye layer experiments a dye layer was thicker t han previous layers (more diffuse). T h i s was due to slight differences i n the amount of Uran ine powder added to 1 m £ of water as wel l as inject ing the dye at a s l ight ly different i n i t i a l depth. 3.9 E x p e r i m e n t s Due to the number of experiments planned, a table showing the types of experiments for each ve loc i ty is given i n Table 3.3. O n l y one set of dye runs are performed. T h i s was done for the mid-range veloci ty of 0.6 c m s - 1 . Ve loc i ty [cm s- 1 ] 0.16 0.3 0.5 0.6 1.5 N [s- 1 ] 0 - - rgb - -1 - - rgb - -2 rgb rgb rgb dye rgb rgb white white white white white 3 rgb 3.75 rgb Table 3.3: Procedure for da ta col lect ion where rgb refers to a t r i -colored hor izon ta l l ight sheet w i t h red, green and blue colors. White represents a hor izonta l whi te l ight sheet on ly on the shelf (Tank Geomet ry I from F igure 3.3). Dye refers to a hor izon ta l layer of dye w i t h a whi te ver t ica l l ight sheet (Tank Geomet ry II from F igu re 3.3). Chapter 3. Methods 35 Slide projector Frame Video Tank Motor (a) Full rotating table geometry (i) Incident light sheet from slide projector Canyon insert (ii) (b) Geometries for the light sheet Figure 3.3: Rotating table and tank laboratory geometry, (a) Table apparatus including the tank, motor, topography, canyon insert, exterior frame and the positions of the slide projector and video camera (Tank Geometry I). The video camera and slide projector positions can be interchanged such that the camera is looking down into the center of the tank and the slide projector is attached on the outer part of the frame and shines a vertical sheet of light down into the canyon (Tank Geometry II). (b) The two positions of the light sheet showing the position of the mirror in the center of the tank, (i) Position of the light sheet in Tank Geometry I. (ii) Position of the light sheet in Tank Geometry II. Chapter 3. Methods 36 Figure 3.4: Vertical light sheet positions along the canyon used in the horizontal dye layers. Camera looks at a vertical plane at the light sheet position and records the change in height of the dye layer over time. The white lines represent the different locations of the vertical light sheet for all of the dye experiments Chapter 3. Methods 37 Figure 3.5: T a n k Dens i ty Profi le (top) showing the predicted profile as a sol id l ine and the measured profile w i t h x 's and o's. T h e x 's represent the average values f rom three conduc t iv i ty probes on the upward profile whi le the o's represent the average values from three con-duc t iv i ty probes on the downward profile. T h e buoyancy frequency i n the tank from theory (bot tom) is again shown by the sol id line and the buoyancy frequency measured from the conduc t iv i ty probes is indica ted by the x 's and o's as above. For purposes of this experiment , the buoyancy frequency at the shelf break level (6.8 cm) is required to ma tch w i t h scal ing analysis. Chapter 3. Methods 38 Figure 3.6: Particle tracks in tank with the (a) tank filled and (b) partially filled tank from 30-33 s. for U = 0.3 cm s _ 1 . Initial 1.5 s of the particle locations are denoted by light gray streaks and further particle locations are black. Shelf break depth (2.2 cm) marked with a solid contour and both x and y axes are in cm. Chapter 3. Methods Figure 3.7: Interpretat ion of part icle t racks i n tank from 30-33 s for U = 0.3 c m s 1 . Shelf and the tank edge are marked w i t h a sol id black l ine. A r r o w s are not to scale. 40 Chapter 4 Results 4.1 Results from the Horizontal: Two Dimensions T h e images from the hor izonta l are obta ined by using a hor izonta l plane of whi te l ight . These images w i l l show a qual i ta t ive descr ipt ion of the flow dynamics at the shelf break level i n two dimensions. T w o methods of cap tur ing the streaks of these particles are used. T h e first involves thresholding the image da ta such that on ly l i t part icles are found (as discussed i n A p p e n d i x B . l ) . T h e second method combines raw images (over 3 s) i n order to s tudy the effect of ve loc i ty (and strat i f icat ion) on the flow close to the head of the canyon. T h i s second method is employed i n case the first me thod does not pick up the particles closer to the canyon (as they may be s l ight ly darker due to the decrease i n l ight as i t propagates th rough the water and part icles) . Quan t i t a t ive results can also be obta ined from these images such as the ve loc i ty i n different regions of the canyon. 4.1.1 Flow away from the canyon W h e n the ro ta t ion rate of the tank is increased, the flow i n the tank flows i n the opposi te d i rec t ion to the ro ta t ion of the tank. Theoret ical ly , the ve loc i ty of this flow is the slowest at the center o f the tank and increases away from the center fol lowing u = Af2 r. However, the ve loc i ty profile does not follow this re la t ionship after 30 s (Figure 4.1). T h e is a dis t inct ive decrease i n ve loc i ty over the shelf region. T h i s decrease is due to increased effect of fr ict ion over the shelf as the dep th of the water is shal low (< 2.2 cm) (Mi r shak , 2001). Chapter 4. Results 41 - - U = (-0.0007 ± 0.0025) s~1*r +(0.35 ±0.09) cms 1 - U = A£lr ) | J ' ' 1 1 0 10 20 30 40 50 Distance away from the center of the tank [cm] Figure 4.1: Ve loc i ty away from the canyon when U = 0.5 c m s _ 1 , N = 2 s _ 1 after 30 s from the i n i t i a l change i n ro ta t ion rate w i t h two fits (solid and dashed lines). T h e blue dashed-dot ted l ine represents the theoret ical ve loc i ty assuming no fr ic t ion or topography. So l id green line represents the loca t ion of the edge of the tank and the red l ine indicates the shelf break. Ve loc i ty measurements are taken from 0.5 - 2.2 c m depth using a whi te l ight sheet. Chapter 4. Results 42 T h e flow i n the tank is fit w i t h two straight lines; the first for the shelf region and the second away from the shelf. T h e error i n the fit (Figure 4.1) is calcula ted by using a boots t rap method which re-samples the da ta 200 times to evaluate the error i n the fit. Close to the shelf break, the observed flow is close to the est imated incident alongshore ve loc i ty predicted by the scal ing and using u = AO. r. T h e flow on the shelf is constant and lower t han expected values due to b o t t o m fr ict ion. S imi la r results (bo t tom frict ion affect due to the shelf) were observed i n Perenne et a l . (2001b) w i t h their l abora tory tank. Thus , the incident flow is not of equal speed across the tank. F l o w off-shore (from the shelf break) w i l l be stronger and faster t han flow onshore (along the shelf). 4.1.2 Flow in the canyon In this section, these features are v isual ized using a hor izonta l l ight sheet (1 c m th ick) shin ing between the shelf break depth and 1 c m above. T w o t ime frames of interest are processed: 30 s and 60 s after the i n i t i a l change i n ro ta t ion . T h e change i n flow between these two chosen times is steady and constant. T h e images are combined over 2 - 6 s intervals creat ing "streak" images (Figure 4.2 and interpreta t ion of the streak images i n F igu re 4.3). A s a compar ison , these images are also shown i n A p p e n d i x C w i t h the same t ime increment (3 s) for a l l of the images. A s the ve loc i ty increases, the flow i n the canyon shows the same features but these features become more dramat ic . W h e n the flow matches the condit ions to scale to J u a n de F u c a C a n y o n (when the Rossby N u m b e r is less than 0.14), the flow is very slow and the features inside the canyon are difficult to observe i n real t ime. However, when look ing at the streak pictures, more features are noticeable. T h e lowest Rossby number flow (0.08) exhibi ts the least d ramat ic flow dynamics (Figures 4.2(a) and (b)). Af ter 30 s, the incident flow on the upstream side of the canyon is deflected into the canyon at the mouth , very close to the upstream w a l l (Figure 4.2(a)). T h e incident flow appears to separate (between flow that is deflected into the canyon along the axis and flow that is directed up Chapter 4. Results 43 onto the shelf region) just inside the canyon mou th . O n the shelf ups t ream of the canyon, several particles are seen mov ing against the incident flow and are mov ing i n the ups t ream di rec t ion at a ve loc i ty equal to the veloci ty inside the canyon. O n shelf downst ream of the canyon, part icles are mov ing i n the downst ream direct ion. After 60 s, there is an eddy at the m o u t h of the canyon, wh ich is inside the canyon wal ls (below the r i m depth) and is cyclonic i n d i rec t ion (F igure 4.2(b)). T h e inter ior flow i n the canyon (away from the eddy at the mouth) is also cyc lonic w i t h flow t ravel ing toward the head along the downstream w a l l and toward the m o u t h a long the ups t ream wa l l . W i t h flow of a Rossby number of 0.14 and after 30 s, the dynamics close to the canyon head show part icles mov ing across the head of the canyon (Figure 4.2(c)). The re is also flow i n the downst ream di rec t ion on the shelf upst ream of the canyon. F l o w on the shelf, downs t ream of the canyon, is directed toward the shelf break. Inside the canyon, flow dynamics are s imi la r (but larger i n magnitude) as when Ro = 0.08. After 60 s, the flow on the shelf, ups t ream of the canyon, is t ravel ing para l le l w i t h the shelf. O n the shelf, downst ream of the canyon, the flow is t rave l ing toward the shelf at an angle wh ich is less than at 30 s (Figure 4.3(d)). T h e eddy at the canyon m o u t h is obvious and again ro ta t ing i n the cyclonic d i rec t ion but is s l ight ly stronger i n magni tude. Inside the canyon topography, away from the mouth , there is a slow flow toward the head along the downstream side and a flow along the downstream w a l l t oward the m o u t h . T h i s cyc lonic c i rcu la t ion is the same as for Ro = 0.08 a l though larger i n magni tude. W i t h flow of a Rossby number of 0.24 and after 30 s, the dynamics close to the canyon head show particles mov ing across the head of the canyon as w i t h Ro = 0.14 (Figures 4.2(e)). In this case, particles from the upstream side of the shelf are seen t ravel ing toward the ups t ream side of the canyon and then deflected a round the canyon head. These are not upwel l ing part icles , but par t ic le or ig ina t ing from the shelf upstream of the canyon. T h e incident flow is directed into the canyon at the mou th , except i n this case, the flow exhibi ts a very dis t inct ive spl i t at the canyon m o u t h (Figure 4.3(e)). T h i s spli t occurs i n the middle of the canyon and one part of the incident flow continues Chapter 4. Results 44 at an angle to the canyon axis and then up onto the shelf. T h e other par t of the flow is di rected toward the canyon head. It then turns back toward the canyon m o u t h i n the cyc lonic d i rec t ion at the head of the canyon. There is flow i n the downst ream di rec t ion on the shelf ups t ream of the canyon w h i c h is angled s l ight ly toward the edge of the tank. F l o w on the shelf, downst ream of the canyon, is directed toward the shelf break. Af ter 60 s, the flow on the shelf, ups t ream of the canyon, is t ravel ing para l le l w i t h the shelf (Figure 4.2(f)). O n the shelf, downst ream of the canyon, the flow is t ravel ing toward the shelf at an angle wh ich is less than at 30 s. T h e cyc lonic eddy at the canyon m o u t h is set up as i n the previous cases and this is the m a x i m u m size of the eddy. T h e flow inside the canyon is f lowing toward the head on the downstream side of the canyon and toward the m o u t h on the upst ream side of the canyon. W i t h flow of a Rossby number of 0.29 and after 30 s (Figure 4.2(g)), s imi lar features are exhib i ted as i n the previous cases but they are more exaggerated. F l o w is i n the downst ream d i rec t ion on the shelf upst ream of the canyon wh ich is angled s l ight ly toward the tank edge just as when Ro = 0.24. F l o w on the shelf, downstream of the canyon, is directed toward the shelf break. Af te r the flow enters the canyon mouth , the flow splits w i t h part of the flow going toward the shelf (where i t upwells) and the other par t of the flow going toward the canyon head. Par t ic les at the canyon head t ravel t u r n toward the downstream side of the canyon and are directed out toward the shelf break along the downst ream side of the canyon. Af ter 60 s, there are not enough significant part icles on the shelf and close to the head to make any further conclusions regarding the flow on the shelf (Figure 4.3(h)). Inside the canyon, the canyon m o u t h eddy is larger t han i n previous runs and the inter ior cyclonic c i rcu la tory flow is strong, a l though lower velocities than the off-shore flow. A t 1.5 c m s _ 1 (Ro = 0.71), the flow i n and around the canyon has increased i n magni tude (Figure 4.2(i)). T h e most s t r ik ing difference between this veloci ty and others is the flow at the head of the canyon. U p w e l l i n g is occur r ing d i rec t ly through the canyon head w i t h part icles f rom inside the canyon region mov ing up onto the shelf at the head of the canyon as wel l as a long the downst ream Chapter 4. Results 45 r i m . There is flow i n the downst ream direct ion on the shelf upst ream of the canyon w h i c h is angled s l ight ly toward the tank edge just as when Ro = 0.29. F l o w on the shelf, downst ream of the canyon, is mos t ly directed i n the downst ream di rec t ion w i t h the a slight deflection t oward the shelf break depending on loca t ion on the shelf. Inside the canyon, the flow spli ts as seen i n each of the other cases and upwel l ing occurs along the entire downstream canyon r i m . After 60 s, the canyon m o u t h eddy is difficult to detect (Figure 4.2(j)) whi le the cyclonic flow pa t te rn inside the canyon ( toward the head on the downst ream w a l l and toward the m o u t h a long the ups t ream wal l ) is ve ry easy to detect. F l o w along the downst ream side of the shelf is deflected at an angle i n the general d i rec t ion toward the shelf break. T h e inflow at the canyon m o u t h is observed and t ak ing the center poin t of the canyon m o u t h at the canyon axis and m o u t h edge, the angle of the inflow does not change s ignif icant ly at this point . T h e error i n measuring this angle proved to be too large to make any significant observations of the change w i t h velocity. Fur ther analysis i n this section w i l l consider the difference i n dynamics when s t ra t i f icat ion is increased (and decreased), the vor t i c i ty of the canyon m o u t h eddy and the ve loc i ty a long the shelf and how it relates to this vor t ic i ty . A n energy balance w i l l be used to define the amount of vo r t i c i ty generated by stretching. 4.1.3 Comparison between different stratifications To observe how much of a role s trat i f icat ion plays i n the dynamics of the canyon, several experiments are conducted using stratif ications ranging between N = 0 and 3.75 s _ 1 for a constant incident ve loc i ty of 0.5 c m s _ 1 (Ro = 0.24 and Bu = 0 - 0.95). W h e n the f lu id is homogeneous (Figures 4.4(a) and (b)), the flow pa t te rn is quite different between 30 and 60 s when compared w i t h the same veloci ty w i t h N = 2 s _ 1 (Figures 4.2(e) and (f)). A n eddy, w h i c h is v is ib le at the m o u t h of the canyon and ro ta t ing i n the an t icyc lonic d i rec t ion , is Chapter 4. Results 46 F igure 4.2: Streak images of for velocities between at 30 and 60 s of a) and b) 0.15 cm s _ 1 , c) and d) 0.3 cm s _ 1 , e) and f) 0.5 cm s _ 1 , g) and h) 0.6 c m s _ 1 , and i) and j ) 1.5 cm s _ 1 . Images on the left hand side are at 30 s, and images on the r ight are at 60 s. In i t i a l par t ic le locat ions are denoted by grey streaks and further par t ic le locat ions are black. Shelf break depth (2.2 cm) marked w i t h a sol id line contour. A x e s labels are i n cm . Chapter 4. Results 47 F igure 4.3: Interpretat ion of the flow from the streak images for various velocit ies at 30 and 60 s. Shelf break and tank edge are represented by sol id black lines. A r r o w s are not to scale. Chapter 4. Results 48 half the w i d t h of the mou th , elongated and pushed further inside the canyon toward the head t han eddies (a l l cyclonic) seen i n the stratified flow. N e x t to this an t icyc lonic eddy, there is a cyc lonic eddy outside the canyon topography (Figure 4.5(a)). O n the shelf, ups t ream of the canyon, the flow is mov ing downst ream but directed at an angle toward the tank edge. O n the shelf, downst ream of the canyon, the flow is s t rongly directed toward the shelf break. Af te r 60 s, the eddy i n the canyon becomes a closed ant icyclonic eddy and another cyclonic eddy forms further downst ream of the canyon and is not contained w i t h i n the canyon topography (Figure 4.5(b)). T h i s is s ignif icantly different from the stratified case. F l o w upst ream of the canyon, on the shelf is flowing para l le l to the shelf break whi le downst ream of the canyon, the flow continues to be deflected at an angle toward the shelf break. W h e n N = 1 s _ 1 (Figures 4.4(c) and (d)), there appears to be a sma l l amount of flow upwel l ing from the canyon head as wel l as along the downstream canyon r i m . U p s t r e a m of the canyon, on the shelf, the flow is di rected i n the downst ream di rec t ion w i t h a sl ight angle toward the tank edge (much less t han when N = 0). Downs t ream of the canyon, on the shelf, the flow is di rected toward the shelf break. Af ter 60 seconds, the eddy at the m o u t h of the canyon is c lear ly vis ible and i n the same loca t ion as when N = 2 s - 1 (Figure 4.4(d)); T h e flow inside the canyon is up-canyon and has reduced i n ve loc i ty from the flow at 30 seconds. A smal l amount of flow is upwel led onto the shelf at the downst ream canyon r i m at the mouth . O n the shelf, downst ream of the canyon, the flow is directed toward the shelf break whi le upst ream of the canyon, the flow is t ravel ing i n the downstream di rec t ion . W h e n N — 3 s _ 1 and 3.75 s _ 1 (Figures 4.4(e)-(h)), the amount of upwel l ing on the downst ream canyon r i m appears to be great ly reduced when compared w i t h lower strat if icat ions at b o t h 30 and 60 seconds. Before cont inuing, i t must be noted that i n the h igh ly strat if ied cases, the thickness and intensi ty of the l ight sheet is great ly reduced. T h i s m a y be due to an increase i n the refractive index of the f luid wh ich w i l l modify the l ight sheet as i t passes th rough the water. In F igures 4.4(e)-(h)), Chapter 4. Results 49 i t was difficult for the l ight sheet to shine fully on the shelf due to this decrease i n thickness as is vis ible i n the resul t ing streak images. Despite this fact, in -canyon particles can s t i l l be s tudied and compared w i t h other stratifications. T h e part icle density on the shelf was also much lower i n these two experiments. T h e up canyon velocities are much slower at bo th t ime intervals for higher strat if icat ions. In fact, when N = 3.75 s _ 1 , the particles i n the canyon appear to be mov ing toward the m o u t h (opposite to every other case). T h i s may be an artifact of the tank osci l la t ion. However , the veloci t ies are very low at this s t ra t i f icat ion and are more sensitive to the tank osci l la t ion. Af ter 60 s, the incanyon flow shows the cyclonic c i rcu la t ion present i n a l l of the other experiments a l though s l ight ly reduced i n velocity. A n o t h e r significant difference between these images and the images for N = 2 s _ 1 and N = 1 s _ 1 is that the eddy just inside the canyon m o u t h is ro ta t ing significantly slower. T h e format ion of this eddy is also different i n that when N = 3.75 s _ 1 , the flow is di rected in to the canyon a l l the way across the m o u t h of the canyon. In previous experiments for N — 2 s - 1 , the flow enters the canyon only th rough the upst ream half of the m o u t h of the canyon. T h e format ion and dynamics of the canyon m o u t h eddy w i l l be discussed further i n the next sections. 4.1.4 Flow Separation and the Rossby Number T h e Rossby number was chosen as the scale for this experiment since i t describes the ab i l i ty for flow to follow the isobaths at the upst ream flank of the submarine canyon. It appears that i n most of the experiments, the flow observed from the streak images separates at the ups t ream m o u t h of the canyon regardless of the incident velocity. T h e flow at the lowest ve loc i ty w i t h Ro = 0.08 does follow the upstream isobath more t han the higher Rossby number flows. However , there is no dis t inct difference for the other runs. Therefore, the Rossby number m a y not be the best scal ing parameter that could be used i n this experiment. Chapter 4. Results 50 Figure 4.4: Streak images of for different stratifications at 0.5 cm s 1 between at 30 and 60 s of a) and b) N = 0 s"1, c) and d) N = 1 s _ 1 , e) and f) N = 3 a - 1 , and g) and h) N = 3.75 s"1. Images on the left hand side are at 30 s, and images on the right are at 60 s. Initial particle locations are denoted by grey streaks and further particle locations are black. Shelf break depth (2.2 cm) marked with solid contour. Chapter 4. Results 51 F igure 4.5: Interpretat ion of the flow from the streak images for various velocit ies at 30 and 60 s. Shelf break and tank edge are represented by sol id black lines. A r r o w s are not to scale. Chapter 4. Results 52 4.1.5 Vorticity observed in the Tank Description of Canyon Mouth Eddy formation After the i n i t i a l change i n ro ta t ion , when N = 2 s - 1 and U = 0.5 c m s - 1 , the incident alongshore veloci ty flows across the canyon, t u rn ing toward the canyon head and onto the shelf break along the downst ream r i m of the canyon. A s t ime progresses, this flow slows down, un t i l approx imate ly 30-35 seconds after the i n i t i a l change i n ro ta t ion rate, the flow at the m o u t h of the canyon splits between flow tha t continues up onto the shelf i n the downstream di rec t ion and a secondary flow that is being redirected inside the canyon. T h i s appears to be the i n i t i a l format ion of the canyon m o u t h eddy (Figure 4.6(a)). T h i s spli t i n the flow, to the upst ream and downst ream side of the l ine d rawn over top of the par t ic le t racks i n F igu re 4.6(a), occurs i n the midd le of the canyon. Therefore, flow that ends up along the downstream w a l l of the canyon originates from the ups t ream w a l l of canyon mou th . In the s t rongly stratif ied experiment , as ment ioned above, the vo r t i c i t y of the eddy at the canyon m o u t h is less t han i n the N = 2 s'1 case. A l s o , from the observations of the streak pictures, i t is apparent that the spli t of flow that occurs at the entrance of the canyon m o u t h does not occur at the same loca t ion i n the canyon as s trat i f icat ion increases. In fact, i t appears tha t when N = 3 s _ 1 and U = 0.5 c m s - 1 , at the canyon mouth , the spl i t of the upwel l ing flow and the flow directed toward the head occurs further downstream inside the canyon (Figure 4.6(b) w i t h the sol id green l ine) . A g a i n increasing strat i f icat ion, at N = 3.75 s _ 1 and U = 0.5 c m s - 1 , this spl i t i n the flow occurs very close to the downst ream w a l l of the canyon (Figure 4.6(c) w i t h the sol id green l ine) . T h e basic theory beh ind the flow at the canyon m o u t h and the vo r t i c i t y generated i n the canyon is a combina t ion of flow separat ion at the upst ream m o u t h and vor tex s t re tching as the flow on the shelf falls in to the canyon as defined by the Burger number . In general, when the s t rat i f icat ion is h igh (and the Burger number is large), s t re tching of water columns is more difficult as they fall into the canyon. In a h igh ly strat if ied fluid (wi th h igh Bu), Chapter 4. Results 53 Figure 4.6: C a n y o n M o u t h E d d y Forma t ion Po in t when U = 0.5 c m s - 1 , N = 2, 3 and 3.75 s _ 1 i n (a), (b) and (c). So l id green l ine represents the loca t ion of the spl i t between flow tha t is cont inuing up onto the shelf break i n the downst ream d i rec t ion a n d flow that is being redirected inside the canyon (red arrows). T h i s redi rec t ing flow is the i n i t i a l format ion of the canyon r i m eddy. T h i s figure is the combina t ion of images over 6 seconds s ta r t ing at 29 seconds after the i n i t i a l change i n ro ta t ion rate. T h e canyon shelf break dep th is h ighl ighted by the blue contour l ine. Axes are i n cm . Chapter 4. Results 54 fluid from one densi ty level w i l l be less inc l ined to move down to another higher densi ty level . For example, i f water o f densi ty p\ is on the shelf and then moves over top of the canyon, i t w i l l require energy for the part icle to drop down into the canyon where the densi ty is greater t han p\. T h i s f luid co lumn w i l l therefore ma in t a in its ver t ica l level i f the Burge r number is h igh . W h e n the water co lumn does not s tretch, there is no vor tex s t retching i n the canyon, a n d therefore there w i l l be less generation of cyclonic vor t i c i ty i n the canyon due to stretching. Conversely, i f the Burge r number is lower, a water co lumn encountering the canyon w i l l drop down generat ing cyc lonic vor t ic i ty . F l o w separat ion, as the incident alongshore flow meets the downst ream canyon w a l l , s t i l ls occurs whether the canyon is modera te ly stratified or h ighly stratified. F l o w separat ion occurs as incident flow travels d i rec t ly along the slope generating friction and as a result, the flow w i l l slow down next to the slope. M o v i n g further away from the slope, the flow w i l l be less affected by friction as the distance from the slope increases. W h e n the flow crosses the slope and enters the canyon mouth , there is no longer any fr ic t ion since the flow has detached from the slope and the v o r t i c i t y generated along the slope due to the difference i n veloci ty ini t iates cyclonic m o t i o n as i t enters the canyon. These two cases w i l l be investigated i n order to val idate each theory and determine w h i c h mech-anism dominates i n this labora tory model . Vorticity of the Canyon Mouth Eddy A n eddy is vis ible i n a l l of the experiments at the entrance of the canyon at the m o u t h and w i l l be described i n future as the canyon m o u t h eddy. T h e vor t i c i ty of this eddy can be ca lcula ted by t r ack ing part icles after the eddy forms approx imate ly 35 seconds after the i n i t i a l change i n ro ta t ion rate. Par t ic les are t racked every 0.5 seconds for 25 seconds s ta r t ing 30 seconds after the i n i t i a l change i n ro ta t ion rate and the part icle tracks are plot ted i n F igu re 4.7. F r o m each figure, the center of each eddy is approximated and several r ad i i are sketched around the center fol lowing each part icle t rack (not shown i n F igu re 4.7). Par t ic les are then t racked as Chapter 4. Results 55 they circulate a round these c i rcular paths a round the eddy. T h e t ime i t takes one par t ic le to pass th rough a par t icular angle of this pa th is calculated. T h e angular speed, u>, of the eddy is calcula ted and since w is twice the vor t ic i ty , £, then C = w / 2 . (4.1) There is a decrease i n vo r t i c i ty between the three stratif ications (Figure 4.8) and a fit is made between particles at the same radius between the three strat if ications (two fits are shown) g i v i n g an average fit of (0.27 ± 0.03) s - 2 N - C 1 - 2 0 ± 0 0 8> C _ 1 s-V5 . ( 4 - 2 ) T h e error o f the calcula ted vort ic i t ies is the s tandard dev ia t ion between the part icles. T h e systematic error was found to be less than the s tandard error and therefore disregarded. A t two separate r ad i i i n different experiments, particles are t racked fol lowing the same radius (three particles for each rad i i ) . T h e s tandard devia t ion of these vort ic i t ies (0.02 s - 1 ) is used for a l l ca lcula ted vort ic i t ies . T h e canyon m o u t h eddy does not appear to have a constant vor t ic i ty , ra ther increasing toward the center o f the eddy. T h i s m a y be due to two affects; the side w a l l f r ic t ion due to the canyon walls w i l l slow down the flow. Secondly, the depth of the canyon increases toward the center of the canyon axis, therefore increased stretching w i l l l ike ly occur. Vort i c i ty A l o n g the U p s t r e a m W a l l of the C a n y o n T h e vo r t i c i t y of the the flow along the shelf-break upst ream of the canyon is also found b y t r ack ing particles. T h e ac tua l part icle t racks for N = 1 s _ 1 (Figure 4.9(a)), N — 2 s _ 1 (F igure 4.9(b)), N = 3 s _ 1 (F igure 4.9(c)) and N = 3.75 s _ 1 (Figure 4.9(d)) a l l show dis t inc t changes i n ve loc i ty between flow against the slope w a l l and flow away from the w a l l . T h e error i n the part icle tracks is obta ined by t rack ing five particles (away from the canyon region) s tar t ing at the same loca t ion i n the tank. T h e veloc i ty is ca lcula ted , averaged and the Chapter 4. Results 56 s tandard devia t ion is calculated. T h i s was done for each s t ra t i f icat ion and the average s tandard devia t ion is 0.03 c m s _ 1 for these tracks. T h e ve loc i ty of a l l the tracks was calculated and plo t ted versus distance away from the w a l l (Figure 4.10). In general, there does not appear to be a dis t inct difference i n the re la t ionship between veloc i ty a n d distance away from the w a l l as s t ra t i f icat ion changes. Therefore, i n order to compare the effect of the vor t i c i ty generated on the ups t ream side of the canyon to the vo r t i c i t y i n the m o u t h of the canyon, a best fit function is found for a l l of the s t ra t i f icat ion cases to determine an equat ion tha t describes the veloci ty close to a wa l l . A n equat ion descr ibing the ve loc i ty on a s loping w a l l (Pedlosky, 1987) as wel l as the veloci ty i n a ro ta t ing f lu id is fitted to the ve loc i ty da t a using a non-linear least squares fit and is of the form U = t/jnterior • B o u n d a r y layer correct ion (4.3) where U is the veloci ty of the flow U = A f i r • (1 - e x p ( - z / L ) ) (4.4) and since r = R — x, where R is the radius of the tank, and x is the var iable distance away from the wa l l , thus U = An(R - x) • (1 - e x p ( - x / L ) ) (4.5) Therefore, a fit of the form U = C i (R-x)(l -exp(-x/L)) (4.6) is found where C\ is a variable that should be approximate ly equal to the change i n ro ta t ion of the tank and L is a length scale constant. T h e variables that fit the ve loc i ty curve i n F igu re 4.10 give U = 0.013 • (50 c m - i ) ( l - e x p ( - x / 0 . 4 cm)) (4.7) where the length scale constant is 0.4 cm. A n error for (4.7) is calcula ted using a boots t rap method . T h e errors are 0.001 s _ 1 and 0.2 c m for C\ and C 2 , respectively. Chapter 4. Results 57 T h e vor t i c i ty is calcula ted by differentiating (4.7) such that , . . , 0.013 • (50 c m - x) e x p ( - x / 0 . 4 cm) C = - 0.013 • (1 - exp( -a ; /0 .4 cm)) + ' V K (4.8) N o w , using (4.8), the vo r t i c i ty at any loca t ion away from the w a l l is ca lcula ted and p lo t ted i n F igu re 4.10(b). A t 0.5 c m , the vo r t i c i ty is Ci = 0 .45s" 1 , (4.9) at 0.75 c m , the vo r t i c i ty is C2 = 0 . 2 3 s - 1 , (4.10) and at 1.25 c m , the vo r t i c i ty is C3 = 0 . 0 5 s - 1 . (4.11) A s expected, the vo r t i c i ty closest to the w a l l is the greatest. However due to the fact that the veloci ty is slow very close to the wa l l , this vor t i c i ty w i l l not affect the flow inside the canyon un t i l a long t ime after the flow has been in i t ia ted . Therefore, the vo r t i c i ty between 0.5 and 2 c m away from the w a l l is of interest. For example, at 0.5 cm, the ve loc i ty is 0.5 c m s _ 1 . In 30 s, the flow w i l l have traveled approx imate ly twice the w i d t h of the canyon (15 c m i n 30 s). T h e vor t ic i t ies at 0.5 c m and 0.75 c m are larger than a l l of the vort ic i t ies observed i n the canyon m o u t h eddy. However , the most interesting aspect of this da ta is that i t does not depend on s t ra t i f icat ion whi le the canyon m o u t h eddy vor t i c i ty does. To further investigate the ve loc i ty i n the boundary layer, the boundary layer of this upst ream veloci ty profile is investigated. B o u n d a r y Layer o n the U p s t r e a m W a l l T h e exponent ia l boundary layer length scale (Figure 4.10) is 3 m m as ca lcula ted f rom (4.7). To investigate the dynamics of this boundary layer several possible theories are invest igated. Chapter 4. Results 58 T h e homogeneous E k m a n layer thickness, SE, perpendicular to the slope f rom Ped lo sky (1987) is SE = Jj^-„ (4-12) where v is the viscosi ty of water ( 1 0 ~ 6 m 2 s _ 1 ) and 6 is the slope of the cont inenta l shelf i n the tank (45° ) . T h e hor izonta l component of this layer is therefore 5E horizontal = 7 ~ (4-13) COS V For the tank, the boundary layer thickness, according to the homogeneous E k m a n theory on a slope, is 2SE = 3.8 m m wh ich is very close to the observed boundary layer length scale. T h e second me thod for f inding the boundary layer is by s imp ly scal ing the t ime dependent boundary layer equat ion du d2u , . at = "&? ( 4 - 1 4 ) such that (4-15) where U, T and L are the canyon scales. So lv ing for the lengthscale, L, gives L ~ v 7 ^ (4.16) U s i n g scales for this experiment gives L ~ \ / l 0 - 6 m 2 s - 1 3 0 s = 5 m m (4.17) wh ich is s imi lar to the scale for the homogeneous case above. T h e t h i r d poss ib i l i ty for the boundary layer format ion is an exponent ia l E k m a n layer on a slope i n a stratified f luid. T h i s can be found by model ing the hydrodynamic equations for a flow along a slope i n a stratif ied f lu id [model, S. A l l e n , personal communicat ion] . Fo r ful l details of model , see A p p e n d i x D . T h i s is ca lcula ted for bo th the shelf and slope regions i n the tank (5° and 45° respect ively) . T h e Chapter 4. Results 59 results show (Figure 4.11) that as the slope increases, the U ve loc i ty profile ( az imutha l direct ion) increases i n w i d t h whi le the V ve loc i ty profile ( in the r ad i a l direct ion) decreases q u i c k l y (F igure 4.11(b)). T h i s makes phys ica l sense since when the slope is very smal l , the ve loc i ty w i l l need to push the lower density water a long way before reaching the same depth as w i t h a 45° slope where the denser water on ly needs to be pushed a very sma l l amount up the slope before i t has moved the same depth. A s the s t rat i f icat ion increases, the U veloci ty thickness increases s l ight ly from the previous JV = 2 s _ 1 case as shown i n F igu re 4.11(a). T h e density change for the same three cases as above show complementary results (Figure 4.12). T h e E k m a n layer thickness for the 5° slope when N = 2 s _ 1 is t h i n . A s the slope increases, the density per turba t ion thickness also increases. A g a i n , as the s t ra t i f icat ion increases, the thickness of the densi ty boundary layer also increases. F i t t i n g (4.7) to the U ve loc i ty profile (Figure 4.11(a)) gives a length scale of 0.41 c m for N = 2 s _ 1 and a slope of 4 5 ° . T h i s is comparable to the observed length scale o f 0.34 c m . W h e n the s t ra t i f icat ion is increased to N = 3.75 s _ 1 , the length scale increases to 0.54 cm. In summary, a l l three cases of E k m a n layer ca lcu la t ion mentioned above give approx imate ly the same length scale as the observed results. T h e most theoret ical ly accurate me thod (stratified tank on a s loping wall) is the best me thod to use, however for ease of ca lcu la t ion , the scal ing of the boundary layer equat ion w i l l give sufficient accuracy for the boundary layer thickness. Stratification and the Relation to Stretching F r o m the observed data, there is a re la t ion between s t ra t i f icat ion and the vo r t i c i t y of the canyon m o u t h eddy (Figure 4.8). Since there appears to be no t rend between s t ra t i f ica t ion and the upst ream canyon vor t i c i ty (Figure 4.10), i t can be assumed that the change i n vo r t i c i t y i n the canyon m o u t h eddy is related to the amount o f s t retching occur r ing as s t ra t i f icat ion changes. S t re tch ing occurs i n this l abora tory experiment when water falls off the shelf and the water c o l u m n is stretched on Chapter 4. Results 60 the b o t t o m or as water enters the canyon from the slope region and is stretched on the b o t t o m as it enters the canyon topography (which is deeper). Therefore, the re la t ion between s tretching and vor t i c i ty (water co lumn height) can be described by look ing at the energy i n the water co lumn . T h i s energy balance can be s tudied by look ing at the uni form stretching of a f luid c o l u m n (wi th uni form s t re tching on bo th the top a n d bo t t om of the water column) as w e l l as s t u d y i n g the amount o f energy i n a s ink ing of a water parcel (of uniform water co lumn height) . In order to s tudy this , the incoming energy w i l l be assumed to be constant given a constant incident ve loc i ty and the incoming energy is assumed to independent of strat if icat ion. For the case of a uni formly stretched water co lumn, assume a un i fo rmly strat if ied water c o l u m n of density pi on the surface and P2 on the bo t t om where pi < P2, the to t a l change i n densi ty over the height of the water co lumn, A z , is equal to p i - P\ A/9 _ dp or (4.18) A z Az dz as shown i n F igure 4.13. T h e volume of the water co lumn is V = height • area where the height is given as 2 • h and the area is given as A. If the water co lumn is stretched by some smal l amount, e, the new height of the water co lumn is now 2h(l + e) and the new area is A / ( l + e ) as shown by the thinner c o l u m n i n F igu re 4.13. T h e change i n potent ia l energy of mov ing a parcel of f luid inside this newly stretched f lu id co lumn is as follows. T h e force due to gravi ty ( F g ) pu l l i ng on this parcel of f luid is Apg where Fg ~ (Pparcel Pbackground)g (4*19) and so lv ing (2.3) for Ap this gives = - ^ - A z g (4.20) 9 F g = -poN2(z0 - z) (4.21) where z0 is an a rb i t r a ry pos i t ion i n the f luid co lumn. Integrat ing this over the length of the stretched Chapter 4. Results 61 f luid co lumn (from the or ig ina l posi t ion) w i l l give the work done to stretch a f lu id parce l Work = - I p0N2{z0 - z)dz (4.22) So lv ing this equat ion gives W o r k = E^K (4.23) Integrat ing this work done over the entire f luid co lumn (2h) gives * P o N 2 - 2 ' 2 ARE • ° £ 2 * ( 4 2 4 ) a p £ = ^ V W ( 4 2 5 ) N o w consider a water parcel mov ing from one density level (at a reference depth of z = 0) down to depth ZQ (the s ink ing co lumn as mentioned above). T h e work required for this movement is calcula ted by integrat ing (4.22) such that W o r k = E^IA (4.26) M u l t i p l y i n g this equat ion over the length of a water co lumn (2/i) i n order to calculate the potent ia l energy i n a s ink ing water co lumn gives ARE. = PoN2zlh (4.27) T h e to ta l energy of a water co lumn that is bo th s ink ing and s t re tching (uniformly) is therefore an add i t ion of (4.25) and (4.27) g iv ing L2 2 T o t a l ARE = p0N2h(-^- + z2) (4.28) It is necessary to combine the uni formly stretched water co lumn energy w i t h the s ink ing water co lumn energy i n order to take into account the fact that when there is a s ink ing water co lumn, there must also be a r i s ing water co lumn present i n the system. T h i s t o t a l energy ca lcu la t ion is equivalent to the to ta l energy of a uniformly stretched water c o l u m n tha t includes s ink ing since the center of mass of the f luid co lumn changes for a bo t tom-only stretch. Chapter 4. Results 62 B o t h (4.25) and (4.28) show an inverse relat ionship between s t ra t i f icat ion and s t re tching such that for a constant change i n potent ia l energy, when s t ra t i f icat ion is increased (N2), the amount of s tretching is decreased by an amount defined by e 2 . T h e to t a l energy i n (4.28) provides a more comprehensive analysis of the energy associated w i t h this process. A l t h o u g h in t roduc ing s ink ing of a water c o l u m n adds a t e rm into the energy equation, the inverse re la t ionship between s t ra t i f icat ion and s tretching s t i l l holds true. Since the re la t ion between N and the vor t i c i ty of the canyon m o u t h eddy is defined by 4.2, the amount of vo r t i c i ty (C) is approximate ly propor t iona l to the the amount of s t re tching (e), wh ich is to be expected i f potent ia l vor t i c i ty was conserved. 4.1.6 Summary: Results from the Horizontal (2D) In summary, • T h e vo r t i c i ty of the canyon m o u t h eddy is p ropor t iona l to the incident ve loc i ty and inversely p ropor t iona l to s trat i f icat ion. • T h e ups t ream side w a l l vor t i c i ty does not change w i t h s t ra t i f icat ion. • St re tching vor t i c i ty is dependent on strat i f icat ion. • Therefore, s t retching vor t i c i ty is related to the vo r t i c i ty of the canyon m o u t h eddy. Chapter 4. Results 63 - 1 0 (a) 0 (b) 0 -- 2 0 - 1 5 - 1 0 - 5 0 5 - 1 0 - 5 (c) 0\ * 1 W - 2 0 - 1 5 - 1 0 - 5 0 Figure 4.7: Pa r t i c l e T r a c k i n g i n C a n y o n M o u t h E d d y for N = 2, 3 and 3.75 s _ 1 i n (a), (b) and (c), respectively. Fou r different particles are t racked for 25s s ta r t ing 35 s after the i n i t i a l change i n ro ta t ion rate. A l l particles are located at the shelf break dep th . T h e canyon loca t ion is super imposed below the part icle t racks i n order to show the loca t ion of the particles w i t h respect to the canyon. Large open circles on the t racks represent the start of the part icles. E a c h dot i n the t rack represents a 0.5s increment i n t ime . T h e x-axis is x [cm] and the y-axis is y [cm]. Chapter 4. Results 64 • r =0-0.25 cm x r =0.25-0.5 cm * r =0.5-0.75 cm < r =0.75-1 cm 0 r=1-1.25cm O r =1.25-1.5 cm . r =1.5-1.75 cm A r =1.75-2 cm r =2-2.25 cm — Fit: C = 0.30 s 0 1 1 N - 1 - 1 1 1.5 2 2.5 3 3.5 4 Buoyancy Frequency [1/s] i , , , , , , , , , i—,—,—,—,—.—,—i—.—.—i—. . .—i—.—.—i—i—.—i 0 0.5 1 1.5 Burger Number Figure 4.8: V o r t i c i t y of canyon m o u t h eddy, ( [ s - 1 ] , decreases w i t h increasing buoyancy frequency ( . /V[s - 1 ]) wh ich is ind ica ted by the fits (—). T h e different symbols represent the radius away from the center of the eddy. T h e error of the vo r t i c i t y is ± 0.02 s _ 1 and the error of the radius is ± 0.1 cm. T h e vor t i c i ty increases toward the center of the eddy. Chapter 4. Results 65 Figure 4.9: Tracks of part icles against the slope and away from the slope ups t ream of the canyon for N = ( a ) l s - \ (b) 2 s _ 1 , (c) 3 s - 1 , (d) 3.75 s " 1 . S o l i d l ine indicates the shelf break and large open circles indicate the start of the par t ic le pos i t ion . B a c k g r o u n d image is the actual t ank image wi thout water. T h e hor izonta l axis is x [cm] a n d the ve r t i ca l axis is y [cm]. Chapter 4. Results 66 0.8 V 0.6 c/j E o 0.4 o o 0.2 1 1 5 I -1-5-1,.. I I i I I IT£* 1 -I O N=1 s - 1 • N=2 S " 1 x N=3 S " 1 Q N=3.75 S " 1 1 1 - - U = (0.013 ±0.001) s" 1*(50 cm -x)(1-exp(-x/(0.4±0.2)) 0.5 0.5 (b) 1.5 2 2.5 3 Distance from Shelf Break [cm] 3.5 1 1.5 2 2.5 Distance from Shelf Break [cm] 3.5 Figure 4.10: T h e upst ream part icle veloci ty [cm s _ 1 ] i n (a) increases exponent ia l ly away from the w a l l . Resul ts are p lo t ted for various stratif ications. A l s o p lo t ted are the fit ( ) as wel l as the equat ion of the fit plus associated errors (See Sect ion 4.1.5). The re does not appear to any difference i n veloci ty profile between the different strat if ications, (b) is the associated vor t ic i ty . Chapter 4. Results 67 ,x 10 2.5 : 1.5 o CD > 0.5 7 f • if r F - a - 5° slope N=2 s"' LP - " - 45* slope N=2 s"' -e- 45° slope, N=3.75 s" 1 0.5 1 1.5 Distance away from the slope [cm] (a) U velocity profile in the Ekman layer of a stratified flow on a slope. As the slope and stratification increases, the U velocity bound-ary layer thickness increases after 30 s. ,x10 - B - 5 slope N=2 s - 4 5 ' slope N=2 s" 1 45' slope. N=3.75 s~' 0.5 1 1.5 Distance away from the slope [cm] (b) V velocity profile in the Ekman layer of a stratified flow on a slope. As slope and stratification increase, the V velocity decreases quickly after 30 s. Figure 4.11: Ve loc i ty profiles (U and V ) i n the Strat if ied E k m a n layer assuming a s loping w a l l after 30 s. T h e profiles includes a slope of 5° (squares) and 45° (crosses) for N = 2 s _ 1 and a slope of 45° for N = 3.75 s _ 1 (circles). Chapter 4. Results 68 2.5 in c CD • -0.5 - a - 5 slope N=2 s" 1 - * - 45° slope N=2 s" 1 - 6 - 45° slope, N=3.75 s ' 1 0.5 1 1.5 Distance away from the slope [cm] Figure 4.12: Dens i ty profiles i n the stratified E k m a n layer assuming a s loping w a l l after 30 s. T h e profile includes a slope of 5° (squares) and 45° (crosses) for N = 2 s _ 1 and a slope of 45° for N = 3.75 s _ 1 (circles). A s slope and s t ra t i f icat ion increase, the thickness of the densi ty per turba t ion increases great ly away from the w a l l . Chapter 4. Results 69 h ( l + e ) Az 0 Pi<P 2 - h ( l + e ) Figure 4.13: Density levels of unstretched and stretched water columns where stretching is denned by e, 2h is the height of the unstretched water column, pi and p2 are the densities at the respective levels where p\ < pi-Chapter 4. Results 70 4.2 Results from the Horizontal: Three Dimensions 4.2.1 Particle Tracking E a c h ve loc i ty and s trat i f icat ion was v isua l ized using the combina t ion of red, green and blue l ight sheets i n order to detect ver t ica l movements of the particles. T h e red l ight sheet is always on the shelf, whi le the green and blue are respectively deeper i n depth w i t h each layer hav ing a dep th range of 1 cm . T h e particles are t racked 30 s after the change i n ro ta t ion rate for between 2-3.5 s. A s seen i n the streak images, the flow features i n the canyon are ampli f ied as ve loc i ty increases. E a c h i n d i v i d u a l ve loc i ty w i l l be discussed i n detai l . W h e n the Rossby number is 0.08 (Figure 4.14), the flow inshore of the shelf break (both inside the canyon and on the shelf) is much slower than the flow offshore. B o t h blue and green part icles along the upst ream canyon w a l l are t ravel ing offshore whi le blue and green part icles a long the upstream w a l l are t ravel ing onshore. T w o blue particles are vis ible at the ups t ream corner of the canyon m o u t h t ravel ing i n the offshore di rect ion i n a c i rcular pa th . A green par t ic le , downs t ream of these blue particles, follows the same c i rcular pa th . These particles are ro ta t ing i n the canyon m o u t h eddy as vis ible from the streak images. A t the downst ream corner of the canyon mou th , a red par t ic le flows d i rec t ly downst ream whi le underneath i t , a green part icle is di rected into the canyon. A n o t h e r par t ic le ( in i t i a t ing mid-mouth) is i n i t i a l l y red and then becomes green as i t reaches the downs t ream corner of the canyon m o u t h . T h i s part icle is not directed onto the shelf. D u e to the slow movement of the part icles (and the tank osci l la t ion) , upwel l ing onto the shelf is difficult to detect. O the r errors associated w i t h these measurements w i l l be discussed i n further de ta i l at the end of this section. W h e n the Rossby number is 0.14 (Figure 4.15), the flow inside the canyon is again directed onshore along the downst ream w a l l and offshore along the ups t ream w a l l . T h e canyon m o u t h eddy is very dis t inct ive as three green particles make the entire c i rcular pa th of the eddy. Three other green particles have paths that ini t ia te at the upst ream side of the canyon, offshore, and are directed Chapter 4. Results 71 into the canyon m o u t h along the downstream wa l l . A green par t ic le is v is ib le on the downst ream corner of the m o u t h wh ich moves up (becomes red) and then decreases back down i n dep th (becomes green again) along the slope. T h i s part icle is deflected offshore at the m o u t h . A red par t ic le is vis ible t ravel ing i n ve ry close to this green/red/green par t ic le t rack and shows no offshore deflection. There is a d is t inct ive offshore flow at the upstream corner of the mou th . These part icles (most ly green) are deflected i n the upst ream and offshore directions. A s w i t h the flow of Rossby number of 0.08, the flow offshore of the shelf break is much greater than the flow inside the canyon. W h e n the Rossby number is 0.24 (Figure 4.16), cyclonic c i r cu la t ion is v is ib le i n the inter ior of the canyon (offshore along the upstream wa l l and onshore along the downst ream wal l ) . T h i s is v is ib le i n bo th green and blue particles. T h e canyon m o u t h eddy is not as apparent w i t h these part icle tracks as i n the lower Rossby number flow; however, a s trong inflow along the downst ream corner of the m o u t h is observed. T h i s flow occurs i n bo th the blue and green l ight sheets. A green part icle in i t i a t ing one- th i rd of the way across the canyon m o u t h shows upwel l ing by changing from green to red. Othe r particles (closer to the downstream corner), show upwel l ing by changing from blue to green and from green to red. Par t ic les that are just offshore of the canyon (not di rected into the canyon mouth) are deflected i n the offshore di rect ion after crossing the downs t ream corner of the canyon and show a decrease i n depth (changing from green to blue) . A par t ic le tha t is upwelled onto the shelf at the downstream corner of the m o u t h is also deflected i n the offshore d i rec t ion (but mainta ins its depth) . A part icle s tar t ing far upst ream of the canyon shows upwel l ing by changing from blue to green. W h e n the Rossby number is 0.29 (Figure 4.17), the c i rcu la t ion is v is ib le i n the inter ior of the canyon shows the same large cyclonic pat tern. T h e canyon m o u t h eddy is d is t inc t as several particles from red and green depths are fol lowing the cyclonic eddy path . A green part ic le , o r ig ina t ing from offshore and upst ream of the canyon mouth , upwells onto the shelf (changing f rom green to red). T h e s imi lar deflection i n the offshore d i rec t ion is vis ible at the downst ream corner of the m o u t h Chapter 4. Results 72 offshore of the shelf as a part icle changes from green to blue. W h e n the Rossby number is 0.71 (Figure 4.18), the canyon canyon m o u t h eddy is v is ib le w i t h bo th green and blue particles. F l o w travels onshore along the downst ream w a l l and close to the head of the canyon, a green part icle is vis ible tu rn ing toward the ups t ream di rec t ion . A l o n g the upst ream w a l l , the flow is offshore. A part icle offshore, upstream of the mou th , upwells from blue to green. Three particles are vis ible upwell ing onto the shelf along the downs t ream w a l l of the canyon. A t the downst ream corner of the mou th , m a n y particles are directed into the canyon. Some of these particles upwel l (change from blue to green and green to red). F r o m this figure, i t seems as though more part icles are directed into the canyon (and up to the head) t h a n are upwelled at the downst ream mou th . Chapter 4. Results 73 Figure 4.14: R e d - G r e e n - B l u e l ight sheet: U = 0.15 c m s - 1 , Ro = 0.08, N = 2 s _ 1 over 13 s. T h e i n i t i a l par t ic le loca t ion is denoted w i t h an open black d i a m o n d . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m and blue to 3-4 c m . T h e background image is the canyon topography i n the unfilled state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 74 -15 -10 -5 0 5 Figure 4.15: R e d - G r e e n - B l u e l ight sheet: U = 0.3 cm s _ 1 , Ro = 0.14, N = 2 s _ 1 over 13 s. T h e i n i t i a l par t ic le loca t ion is denoted w i t h an open b lack d i a m o n d . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m and blue to 3-4 c m . T h e background image is the canyon topography i n the unfilled state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 75 Figure 4.16: R e d - G r e e n - B l u e l ight sheet: U = 0.5 c m s " \ Ro = 0.24, N = 2 s " 1 over 13 s. T h e i n i t i a l par t ic le loca t ion is denoted w i t h an open black d i a m o n d . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m and blue to 3-4 c m . T h e background image is the canyon topography i n the unfilled state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 76 -15 -10 -5 0 5 Figure 4.17: Red-Green-Blue light sheet: U = 0.6 cm s _ 1 , Ro = 0.29, N = 2 s~l over 13 s. The initial particle location is denoted with an open black diamond. The red particles correspond to 1-2 cm depth, green to 2-3 cm and blue to 3-4 cm. The background image is the canyon topography in the unfilled state. The horizontal axis is x [cm] and the vertical axis is y [cm]. Chapter 4. Results 77 Figure 4.18: R e d - G r e e n - B l u e l ight sheet: U = 1.5 c m s _ 1 , Ro = 0.71, N = 2 s'1 over 13 s. T h e in i t i a l par t ic le loca t ion is denoted w i t h an open b lack d i a m o n d . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m and blue to 3-4 c m . T h e background image is the canyon topography i n the unfilled state. T h e ho r i zon ta l axis is x [cm] and the ve r t i ca l axis is y [cm]. Chapter 4. Results 78 Effect of Stratification Simi la r part icle t rack ing experiments were conducted w i t h different s trat if icat ions ranging from N =1 s _ 1 to N =3.75 s _ 1 . T h e results of the flow i n the red, green and blue l ight sheets when N =1 s - 1 are more noisy t han previous results (Figure 4.19). Pa r t i c l e colors va ry much more frequently a n d false colors are observed (part icle upwel l ing onto the shelf ac tual ly becomes green whi le on the shelf even though the shelf is on ly i l l umina ted by the red l ight sheet) w h i c h w i l l be discussed i n more de ta i l i n the next section. Therefore, on ly basic part icle dynamics w i l l be observed from this figure due to the large amount of error. A n inflow at the canyon m o u t h occurs as seen i n the streak images. Par t ic les along the upst ream canyon w a l l are mov ing offshore whi le particles along the downst ream w a l l are mov ing i n the onshore di rect ion. T h e d ispar i ty between the flow onshore and offshore of the shelf break is observed showing slower velocities on the shelf. A green part icle , o r ig ina t ing near the ups t ream w a l l near the canyon mou th , travels i n the upst ream and offshore d i rec t ion and moves further offshore t han any other particles vis ible i n the higher stratified experiments. F l o w off shore of the shelf break is deflected offshore once downstream of the canyon. T h e canyon m o u t h eddy is more difficult to detect i n this figure. W i t h increased s t ra t i f icat ion (N = 3 s _ 1 ) , the results show less noise t h a n i n the previous figure (Figure 4.20). T h e s imi lar in-canyon cyclonic c i rcu la t ion pa t te rn i n v is ib le w i t h bo th green and red particles. T h e canyon m o u t h eddy is v is ib le as particles mov ing i n the offshore d i rec t ion close to the upst ream w a l l of the canyon enter the c i rcular pa th of the eddy. U p w e l l i n g is v is ib le a long the downst ream wa l l o f the canyon as wel l as from particles upwel l ing onto the shelf i n very close p rox imi ty to the shelf break. Pa r t i c l e deflection i n the offshore d i rec t ion downst ream of the canyon is not vis ible i n this figure. W h e n N = 3.75 s _ 1 (F igure 4.21), most o f the part icles inside the canyon (away from the canyon mouth) appear to be mov ing i n the offshore d i rec t ion (even those closer to the downs t ream w a l l of Chapter 4. Results 7 9 the canyon). Closer to the canyon mouth , particles are mov ing i n a c i rcular pa th i n the loca t ion of the canyon m o u t h eddy. In the blue level, particles are mov ing off shore i n the eddy whi le closer to the downst ream wa l l , green particles are fol lowing the pa th o f the eddy m o v i n g i n the ups t ream direct ion. O n top of the blue offshore mov ing particles i n the canyon m o u t h eddy, red part icles are mov ing i n the downst ream di rec t ion v i r t u a l l y unaffected by the canyon. Chapter 4. Results 80 Figure 4.19: Red -Green -B lue l ight sheet: U = 0.5 c m s " 1 , Ro = 0.24, Bu = 0.25, N = 1 s _ 1 over 13 s. T h e i n i t i a l part icle loca t ion is denoted w i t h an open b lack d i amond . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m a n d blue to 3-4 c m . T h e background image is the canyon topography i n the unfi l led state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 81 F igure 4.20: Red -Green -B lue l ight sheet: U = 0.5 c m s _ 1 , Ro = 0.24, Bu = 0.76, N = 3 s _ 1 over 13 s. T h e i n i t i a l part icle loca t ion is denoted w i t h an open b lack d i amond . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m a n d blue to 3-4 c m . T h e background image is the canyon topography i n the unfi l led state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 82 Figure 4.21: R e d - G r e e n - B l u e l ight sheet: U = 0.5 c m s~\ Ro = 0.24, Bu = 0.95, N = 3.75 s " 1 over 5 s. T h e i n i t i a l part icle loca t ion is denoted w i t h an open b lack d i amond . T h e red part icles correspond to 1-2 c m depth, green to 2-3 c m and blue to 3-4 c m . T h e background image is the canyon topography i n the unfi l led state. T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 4. Results 83 Problems Associated with these Results A s ment ioned previously, there are large errors associated w i t h these results. T h e most significant p rob lem from the red, green and blue l ight sheet experiments, is resolving the color of the particles. In several cases, particles r ap id ly changed color (especially apparent i n F igu re 4.19). These m a y be actual changes i n depth, however, the speed at which the color change is too fast to be accounted for by the flow dynamics . Othe r indicators of the inaccurate resolut ion of the color is by look ing at the i n d i v i d u a l part icles. In some cases, the particles appear whi te w i t h slight hues of red, green or blue and subjective decisions need to be made on the true color of the part icles. T h e color contrast of the images was increased bu t this on ly gave more false colors as part icles appeared to be a combina t ion of red, green and blue. T h e par t ic le size and image resolut ion is the largest problem. T h e video camera contains a single C C D and uses a method that takes the mean of several neighboring pixels (bi l inear interpolat ion) to find the R G B values. Therefore, there is a red, green and blue value for every p ixe l , but on ly one of these values is ac tua l ly measured by the C C D . T h e other two values are in terpola ted and thus are more or less est imated using bi l inear in terpola t ion (Figure 4.22). W h e n part icles are on the scale of 1-2 pixels large, the in terpola t ion w i l l affect their f inal colour and may appear to change between any (false) colour due to this in terpola t ion as i t moves between pixels. T h i s p rob lem is apparent when smal l particles move past particles of different color or move over top of the l ight sheet reflecting on the topography. In these cases, the particles change to the color o f the background o r ne ighbour ing particles. Ano the r large p rob lem w i t h these results is the resolut ion of the red l ight sheet on the shelf. In almost a l l of the experiments, the brightness of the red sheet decreases great ly a long the shelf such that par t ic le t rack ing is very difficult. T h i s has led to an underes t imat ion of the upwel l ing on the shelf as wel l as a discrepancy i n the flow dynamics . Chapter 4. Results 84 G R G R G R B G B G G G R G / R G R B G • G B G R=(Rl+R2+R3+R4)/4 G=(GI+G2+G3+G4V4 B=B Ri-R=(Rl+R2)/2 . R? G=G B=(Bl+B2)/2 B2 Figure 4.22: C C D C o l o u r E s t i m a t i o n using bi l inear in terpola t ion. C C D is compr ised of red ( R ) , green ( G ) and blue (B) pixels . There are more G pixels and the R G B value for each p ixe l is an estimate using either d iagonal R and hor i zon ta l /ve r t i ca l G or ho r i zon ta l /ve r t i ca l R and B . M o d i f i e d from T h e Imaging Source (2002). 4.2.2 Summary: Results from the Horizontal (3D) T h e three d imensional results show that the major flow features observed from the streak images are observed w i t h these part icle t racks. A canyon m o u t h eddy is observed to affect part icles at a l l three light sheet depths (down to 4 c m depth). Upwel l ing , a l though observed near the canyon mou th , is underest imated due to inadequate l ight sheet intensi ty on the shelf. A cyc lonic c i r cu la t ion pat tern is observed i n the canyon w i t h an velocities mov ing i n the offshore d i rec t ion along the upst ream w a l l of the canyon and velocities i n the inshore d i rec t ion along the downs t ream w a l l of the canyon. A s ve loc i ty increases, ver t ica l part icle mo t ion also increases w i t h evidence from increasing numbers of particles changing colour. A s strat i f icat ion increases, ver t ica l par t ic le displacement decreases. A l t h o u g h using a red, green and blue l ight sheet is a useful way to ob ta in ve r t i ca l displacement Chapter 4. Results 85 informat ion of the flow dynamics , the uncer ta inty i n the da t a has proven to be too large to make any conclusive findings. T h e most impor tan t improvement for this exper imenta l m e t h o d is improv ing the camera resolut ion as wel l as improv ing the intensi ty and qua l i ty of the colored l ight sheets. Chapter 4. Results 86 4.3 Results from the Vertical: Two Dimensions Fluorescent dye is injected into the water at various depths, creat ing hor izon ta l layers across the tank. T h i s dye is injected at a par t icular density such that when the dye enters the tank, i t w i l l form a layer at this densi ty level . A s the experiment is r u n (at U — 0.5 c m s—1 a n d TV = 2 s—1 for a l l runs), the dye remains i n concentrat ion at the or ig ina l density level (due to the l aminar flow i n the tank, tha t is, lack of turbulent mix ing ) . Therefore, i f a density level changes dep th over t ime, the dye w i l l indica te this change b y m a k i n g a corresponding change. A ver t i ca l l ight sheet i l lumina tes the dye and provides a ver t ica l cross-section th rough the canyon wh ich gives an ind ica t ion of the i sopycnal movement over t ime. U s i n g these dye cross-sections, bo th qual i ta t ive and quant i ta t ive measurements of the i sopycnal movements can be made. 4.3.1 I m a g e A n a l y s i s : Q u a l i t a t i v e a n d Q u a n t i t a t i v e Images from the dye experiments are processed by two methods to enhance the resolut ion of the dye wh ich is discussed i n deta i l i n A p p e n d i x B . 2 . T h e processed image is an edge detected version of the or ig ina l . Therefore, instead of an entire dye layer, the edges of the dye layers are v isua l ized . Due to the l inear s t rat i f icat ion and the diffusivity of the dye as i t enters the tank, the dye layer represents a mix tu re of different densities (the dye is usual ly 0.5 c m th ick ) . A l t h o u g h the diffusion occurs between the inser t ion of the dye and then end of spin-up, the amount of diffusion occur r ing while the experiment is being r u n (over 60 s) is negligible compared w i t h other associated errors (such as convert ing the image pixels to centimeters). T h e results for a l l posi t ions A th rough E (Figure 3.4 on page 36) are shown at three stages: before the change i n ro t a t ion rate, 30 seconds after i n i t i a l change i n ro ta t ion and 60 seconds after the i n i t i a l change i n ro ta t ion . T w o different dye depths are chosen at loca t ion E i n order to capture bo th the below shelf and above shelf dye movements. T h e first experiment w i l l be referred to as E and the second exper iment at loca t ion E w i l l be referred to as E ( I I ) . Chapter 4. Results 87 T h e second image processing method looks at the progression of the dye layers i n t ime by t ak ing a single p ixe l cross-section and creat ing a t ime series of the cross section over a s ix ty second interval . T h e t ime series analysis allows for the ca lcula t ion of the change i n dep th of a dye layer over t ime. For each loca t ion ( A through E ; F igure 3.4) and for each cross-section, the change i n depth of the top, middle and bo t t om of the (normalized) dye layer is ca lcula ted by f inding the slope of these three lines. T h e top and bo t t om are defined as the locat ions a long the cross-section where the p ixe l value is s ignif icantly different from the previous one (ranges between different values for each exper iment) . T h e middle of the dye layer is defined as the loca t ion along the cross-section w i t h the m a x i m u m p ixe l value. If more than one m a x i m u m is found, an average of these locat ions is taken. T h e difference between the i n i t i a l and f inal p ixe l locat ions for each slope is then converted into centimeters (Figure 4.23 or A p p e n d i x E ) . To calculate the amount of s t re tching of a dye layer, the final separat ion between the top and bo t t om slopes are subtracted f rom the i n i t i a l separat ion of these two lines (Table 4.1). W h e n d i v i d i n g this value the i n i t i a l thickness of the dye layer, this indicates the amount s tretching (or compression i f negative) occur r ing i n the canyon i n / units (Table 4.2). U s i n g these units for stretching allows values from the l ab to be d i rec t ly compared against s t retching measured i n real canyons. Pos i t ion A A t pos i t ion A i n the canyon (Figure 3.4), the dye images show a to t a l of three layers. It should be noted that at this pos i t ion , when the l ight sheet is no longer w i t h i n the bounds of the canyon, i t is sh in ing on the cont inental slope (not the cont inental shelf). D u e to the curvature of the tank, the dye closer to the edges of the image is ac tual ly further on-shore t h a n the dye i n the center of the image (see F igu re 3.4). T h e processed image (Figure 4.24) on ly shows the upper two layers i n order to ma in t a in good resolut ion of these layers. After 60 seconds, the lower dye layer has decreased i n dep th and has become more elongated (Figure 4.24(c)). Or ig ina l ly , this layer ( in the cross-section displayed by the l ight) is bounded by the canyon walls but after 30 seconds, this layer has moved up such tha t Chapter 4. Results 88 F igure 4.23: Change i n depth [cm] of the dye from 0 s to 60 s i n the hor izon ta l dye layer where the layer is spl i t up into three components: the top ( T ) , midd le ( M ) and b o t t o m (B) of the dye layer. Ups t r eam, M i d - C a n y o n , Downs t r eam and Shelf represent the locat ions of the cross-sections th rough the images. Posi t ions A , B , C , D , a n d E represent the locat ions of the l ight sheet as shown i n F igu re 3.4. L o c a t i o n E( I I ) represents the da ta obta ined at pos i t ion E w i t h a s l ight ly shallower dye layer than the other experiments. For a table of these results, see A p p e n d i x E . No te that at a l l locat ions on the shelf, the dye is always against the topography and therefore the B changes i n depth are not significant. A l l results above have an associated measurement error of 0.05 cm. Chapter 4. Results 89 Pos i t i on Ups t r eam M i d - C a n y o n Downs t r eam Shelf A 0.01 0.01 0 0.02* B 0.15 0.1 0.05 0* C 0.37 -0.04 0.06 0.11* D 0.41 -0.02 -0.11 0.04* E 0.11* 0.13 0.19* E(I I ) -0.13 -0.34 -0.26 -0.02* Table 4.1: Difference i n c m between the distance of the top and b o t t o m of dye layer over 60 s of the t ime series. Ups t r eam, M i d - C a n y o n , Downs t ream and Shelf represent the locat ions of the cross-sections th rough the images. Posi t ions A , B , C , D , and E represent the locat ions of the l ight sheet as shown i n F igure 3.4. A l l results above have an associated measurement error of 0.07 c m . * Resul ts calculated using the difference between the top and midd le of the dye layer, not the top and b o t t o m slopes as w i t h the other cases. T h i s is required as the dye i n these two cases penetrates below the topography. *Note tha t at a l l locat ions on the shelf, the dye is always against the topography. (in the cross-section of the l ight) i t is on the slope as wel l as inside the canyon. T h e upper layer shows l i t t le change by v i sua l inspect ion except for a slight bulge at 60 seconds (Figure 4.24(c)) on the downst ream edge of the dye i n the top of the upper layer. T h e dye layer s tudied i n the t ime series at this loca t ion is the upper layer w i t h cross-sections as shown i n F i g u r e 4.25. O n the upstream side of the canyon (F igure 4.26(a)) shows a ve ry sl ight l inear decrease i n depth of the top, middle and b o t t o m layer depths (0.02 c m over 60 seconds). A t m i d -canyon (Figure 4.26(b)), a l l three layers decrease l inear ly i n depth by a s l ight ly larger amount (0.05 c m over 60 seconds). Downs t r eam i n the canyon (Figure 4.26(c)) a l l three layers decrease l inear ly i n depth (0.08 c m over 60 seconds). T h e region on the slope (Figure 4.26(d)) shows no significant change i n dye depth, w i t h sma l l l inear decreases i n a l l three layers (0.02 c m over 60 seconds). T h e change i n w i d t h of the dye layer for each cross-section is 0.01, 0.01, 0 and 0.02 ± 0.07 c m for the upstream, mid-canyon , downstream and shelf region, respectively (Table 4.1). T h i s corresponds to s tretching values below 0 . 0 2 / for each cross-section (Table 4.2). T h e values ob ta ined from the shelf cross-section do not represent t rue s tretching as the dye does not separate f rom the topography. T h i s is on ly an ind ica t ion of the change i n thickness of the dye at this loca t ion over t ime and is the Chapter 4. Results 90 P o s i t i o n Ups t r eam M i d - C a n y o n Downs t r eam A 0.01 ± 0.03 0.01 ± 0.02 0 ± 0.02 B 0.11 ± 0.01 0.07 ± 0.01 0.03 ± 0.01 C 0.21 ± 0.01 -0.02 ± 0.01 0.03 ± 0.01 D 0.49 ± 0.03 -0.02 ± 0.02 -0.09 ± 0.01 E 0.23 ± 0.01* 0.12 ± 0.01 0.45 ± 0.01* E(II) -0.14 ± 0.01 -0.29 ± 0.01 -0.21 ± 0.02 Table 4.2: St re tching and Compress ion of dye layers ( in / - u n i t s ) . U p s t r e a m , M i d - C a n y o n , D o w n -s t ream a n d Shel f represent the locat ions of the cross-sections t h rough the images. P o s i -t ions A , B, C , D , and E represent the locat ions of the l ight sheet as shown i n F igu re 3.4. * Resul ts calcula ted using the difference between the top and midd le of the dye layer, not the top and b o t t o m slopes as w i t h the other cases. T h i s is required as the dye i n these two cases penetrates below the topography. same for a l l further shelf cross-section t ime series. Chapter 4. Results 91 j 1 ; \ / / 6 4 2 0 -2 -4 - e y[cm] -8 (a) Initial Dye Position y[cm] (b) Dye after 30 seconds (c) Dye after 60 seconds Figure 4.24: D y e layer at pos i t ion A at a) Os, b) 30 s and c) 60 s after ro t a t ion change. T h e top and b o t t o m of the upper dye layer, labeled 1, is denoted by the th ick black lines. T h e middle dye layer, labeled 2, is vis ible i n its entirety (upper and lower edges of dye are not highl ighted) . T h e l ight sheet reflecting on the topography is v is ib le as the two t h i n lines enclosing the dye layers. Chapter 4. Results 92 y[cm] Figure 4.25: L o c a t i o n of four t ime series cross-sections at pos i t ion A i n the v i c i n i t y of the canyon. T h e green layers are dye layers (labeled 1,2 and 3) a n d the whi t e l ine is the l ight sheet reflecting on the t ank topography. Chapter 4. Results 93 _, i i , i 4 t 1 1 1 1 10 20 30 40 50 80 0 10 20 30 40 50 Ime [a] "™ 1*1 (c) Downstream (d) On Shelf F igure 4.26: T i m e Series of D y e at pos i t ion A over 60 s after the ro ta t ion change f rom dye layer 1. T h e top, midd le and bo t t om edges of the dye layers are found a n d p lo t t ed over top of the dye spec t rum i n red, black and blue, respectively. These lines are then replot ted below the spec t rum and a linear fit is found for each l ine and the slope of the l ine ( ± the error i n the slope) is shown to the right of this plot . T h e slope is i n uni ts of c m s " 1 . Chapter 4. Results 94 Position B T h e second experiment , w i t h the l ight sheet located at pos i t ion B (Figure 3.4) demon-strates a to ta l of three dye layers. However, i n order to ma in t a in good resolut ion for the upper two layers, the lowest layer is not vis ible i n F igure 4.27. It should be noted tha t at this pos i t ion , when the l ight sheet is no longer w i t h i n the bounds of the canyon, i t shines on the cont inenta l slope (not the cont inental shelf). In the upper dye layer, a gradual lift of this entire layer occurs over 60 seconds (Figure 4.27). A t 30 seconds, on the downstream side of the canyon, a d ip is noticeable just beyond the downst ream canyon r i m . T h i s per turba t ion is smoothed out after 60 seconds and on ly appears as a slight dev ia t ion i n the top of the dye layer at this t ime. A t 30 seconds, the lower edge of the upper dye layer t i l t s up on the upstream side of the canyon and, over 60 seconds, the entire layer has decreased i n depth from its i n i t i a l pos i t ion . T h e midd le layer (lowest v is ib le layer; F igu re 4.27) shows a slight uplift of the entire layer most not iceably on the ups t ream w a l l of the canyon after 30 seconds. F r o m the t ime series at loca t ion B , on ly the upper layer is s tudied w i t h cross-sections as shown i n F igure 4.28. In the upst ream cross-section (Figure 4.29(a)), the dye layer decreases s teadi ly i n depth over the first 30 seconds and then mainta ins a constant depth, th ickening sl ightly, for a to t a l change of 0.26 c m i n 60 seconds and a change i n thickness of 0.15 c m . A t mid-canyon (Figure 4.29(b)), the dye layer decreases l inear ly i n depth for a change of 0.46 c m i n 60 seconds for the entire w i d t h of the layer, th ickening s l ight ly less than on the upst ream side (0.1 c m i n 60s). In the downst ream cross-section (Figure 4.29(c)), the dye layer lifts l inear ly by 0.31 c m over 60 seconds. A n osc i l la t ion i n this layer is observed to have a per iod of approximate ly 8 seconds and is due to the t ank osc i l la t ion ment ioned previously. T h e dye on the slope (Figure 4.29(d)) shows very l i t t le change i n depth over 60 seconds. T h e intensi ty of the dye increases at the center of the layer (s tar t ing at 20 s). T h e amount of es t imated s tretching at this pos i t ion is 0 . 1 1 / at the ups t ream cross-section and 0 . 0 7 / at the mid-canyon cross-section (Table 4.2). N o significant s t retching occurs on the downst ream and slope regions (0 .03 / and 0, respectively). Chapter 4. Results 95 2 3 4 I ' ! N 6 7 8 \ \ j J 9 6 4 2 0 -2 -4 -6 y[cm] (a) Initial Dye Position 6 4 2 0 -2 -4 -6 y[cm] (b) Dye after 30 seconds 1 .. . -^ \ 7 '•"A \ / x J 6 4 2 0 -2 -4 -6 y[cm] (c) Dye after 60 seconds Figure 4.27: D y e layer at pos i t ion B at a) Os, b) 30 s and c) 60 s after ro ta t ion change. T h e top and b o t t o m edge of each layer are denoted by black hor izon ta l l ines. T w o layers are vis ible i n these images (labeled 1 and 2). T h e lower of the two layers does not cross the w i d t h i n the canyon i n this figure but this is an artifact of the image processing used to highl ight the upper layer of the dye. Chapter 4. Results 9G y[cm] Figure 4.28: L o c a t i o n of four t ime series cross-sections at pos i t ion B i n the v i c i n i t y of the canyon. T h e green layers are dye layers (labeled 1, 2 and 3) and the whi t e l ine is the l ight sheet reflecting on the tank topography. Chapter 4. Results 97 Slopes: +5.450-• 03 i1o-0 +4.298-03 ±36-0 +2.926-03 +2e-0 5 . 5 8 e - 0 3 +7.68e-03 +3.786-03 +26 -04 ±46-04 ±1e-04 30 40 (a) Upstream (b) Mid-canyon , • — .. « - — I * I Mf t » 10 20 30 40 SD 8 M M (c) Downstream ^ • f l f i r a i p ^ w ' ""i Slopes: +3.826-03 ±26-04 - « | +5.126-03 ±36-04 I +3.026-03 ±26-04 (d) On Shelf F igu re 4.29: T i m e Series of D y e at posi t ion B over 60 s after the ro ta t ion change of dye layer 1. T h e top, midd le and bo t t om edges of the dye layers are found a n d p lo t t ed over top of the dye spec t rum i n red, black and blue, respectively. These lines are then replot ted below the spec t rum and a linear fit is found for each l ine and the slope o f the l ine ( ± the error i n the slope) is shown to the right of this plot . T h e slope is i n uni ts of c m s _ 1 . Chapter 4. Results 98 Position C Mid-way into the canyon (position C , Figure 3.4), a single dye layer is visible. This dye begins as a horizontal layer across the canyon below the shelf break depth (Figure 4.30(a)). As time progresses, the layer tilts up on the upstream side of the canyon (Figure 4.30(b) and 4.30(c)) reaching just below the shelf break depth. After 60 seconds, the uplifted upstream side of the dye becomes like a flattened step, one quarter of the way into the canyon (Figure 4.30(c)). The bottom of this layer does not show as much of a change in depth as does the top; the layer has visibly thickened from its initial state. The upstream side (on the bottom edge of the dye) at 60 seconds shows a parabolic curvature against the wall which has decreased from the curve visible at 30 seconds. On the downstream side of the dye, the entire layer has been uplifted and is almost penetrating onto the shelf break (but not lifted as high as on the upstream side). Up to this point in the canyon, there has been a steady increase in visible stretching of the dye over the time series. The cross-sections of this time series are shown in Figure 4.31. The time series at this location (Figures 4.32(a) - 4.32(d)) on the upstream side of the canyon shows great decrease in depth of the top edge of the layer over time (Figure 4.32(a)) for a total change of 0.64 cm in 60 seconds. The bottom of this cross-section also decreases in depth by 0.27 cm over 60 seconds. The large variation in the middle dye layer depth (black line in Figure 4.32(a)) occurs due to the method used to find the middle of the layer. This is done by finding the maximum pixel value through the layer and assigning this as the middle of the dye. If there are several maximum values (of the same magnitude) an average is chosen. The mid-canyon dye cross-section (Figure 4.32(b)) again shows the same variation in the middle dye layer depth. This figure also shows a steady decrease in depth of the entire layer over time of 0.33 cm and 0.37 cm over 60 seconds for the top and bottom edges of the dye, respectively. On the downstream edge of the canyon (Figure 4.32(c)), the dye decreases in depth linearly over time. There is a slight bulge in the top layer of the dye at 53 s. The total change in depth of the top layer is 0.35 cm. The dye on the shelf (Figure 4.32(d)) begins as a very thin (visible) layer which decreases linearly in depth over 60 s. However, it should be noted that Chapter 4. Results 99 this is a very sma l l decrease (0.12 c m for the top of the layer) and that a p o r t i o n of the dye layer is ac tua l ly the l ight sheet reflecting on the shelf topography. F r o m the complete canyon cross-sections (Figure 4.32), no dye is apparent on the shelf. However, these images are created by isola t ing a part icle p ixe l value to create the black hor izonta l lines. B y choosing a lower threshold value, fainter dye w i l l be picked up and possibly show dye mov ing onto the shelf. A s mentioned i n the previous paragraph, a significant amount of s t retching occurs at this pos i t ion i n the canyon. T h e largest amount of stretching, 0 . 2 1 / over 60 seconds, occurs on the upst ream side of the canyon . O n the downstream side of the canyon, the dye stretches b y 0 . 0 3 / . A t mid-canyon , the dye appears to compress by 0 . 0 2 / over 60 seconds. Compar i sons between the amount of s tretching between three different cross-sections of the canyon (Table 4.3) show that the upstream cross-section stretches more t han s ix t imes compared w i t h the downstream cross-section. Ups t r eam M i d - C a n y o n D o w n s t r e a m Ups t r eam 1 .00±0 .18 - 0 . 1 0 ± 0 . 0 8 0 . 1 5 ± 0 . 0 9 M i d - c a n y o n - 9 . 7 9 ± 7 . 4 0 1 .00±1 .70 - 1 . 4 9 ± 0 . 5 4 Downs t r eam 6 . 5 7 ± 3 . 8 1 - 0 . 6 7 ± 0 . 2 4 1 . 0 0 ± 0 . 9 8 Table 4.3: C o m p a r i s o n between s t re tching/compress ion at Pos i t i on C . E a c h value i n the table is a ra t io of the values from Table 4.1 w i t h associated error from the slope ca lcu la t ion . Chapter 4. Results 100 F igure 4.30: D y e layer at pos i t ion C at a) 0s, b) 30 s and c) 60 s after ro ta t ion change. T h e top and b o t t o m edge of dye layer 1 is denoted by black hor izonta l l ines. Chapter 4. Results 101 y[cm] Figure 4.31: Location of four time series cross-sections at position C in the vicinity of the canyon. The green layer is a dye layer (labeled 1) and the white line is the light sheet reflecting on the tank topography. Chapter 4. Results 102 Slopes: +1.07e-02±3e-04 U{ -1.348-03 ±7e-04 +4.506-03 ±3e-04 I ' Slopes: i I . +5.50e-03 ±3e~ - 0 4 - 0 3 SO so (a) Upstream (b) Mid-canyon - 3 -iv/e-ga tie-ya r +4.826-03 ±2e-04 I 1 •MtW* 1 fa"** " ^ J V 0 1 " V +2.558-04 ±4» , . n _ . J . , 04 _. _ 05 +1.418-04 ±3e-05 10 M » 40 SO M 40 SO SO (c) Downstream (d) On Shelf F igure 4.32: T i m e Series of D y e at pos i t ion C over 60 s after the ro ta t ion change f rom dye layer 1. T h e top, midd le and bo t tom edges of the dye layers are found and p lo t t ed over top of the dye spec t rum i n red, black and blue, respectively. These lines are then replot ted below the spec t rum and a l inear fit is found for each l ine and the slope of the line ( ± the error i n the slope) is shown to the right of this plot . T h e slope is i n uni ts of c m s _ 1 . Chapter 4. Results 103 Posi t ion D Fur ther toward the head of the canyon (posi t ion D , F igu re 3.4), the dye layer (Figure 4.33) shows the same dis t inct ive upward t i l t on the upst ream side of the canyon after 30 seconds. Af ter 60 seconds, the downstream side of the dye layer has also moved up from its i n i t i a l pos i t ion and is s l ight ly below the shelf break. In this par t icular r un , there is an i n i t i a l d is turbance i n the b o t t o m of the layer wh ich , after 30 seconds, is smoothed out. T h e t ime series at pos i t ion D (wi th cross-sections shown i n F igu re 4.34), on the ups t ream side of the canyon (F igure 4.35(a)), shows a large rise of the top edge of the dye layer over the first 30 seconds wh ich flattens out over the next 30 seconds (a decrease of 0.47 c m over 60 seconds). T h e b o t t o m edge of this layer remains at approximate ly the same depth (decreasing b y 0.06 c m over 60 seconds). M i d - c a n y o n (Figure 4.35(b)) there is also a decrease i n depth of the dye layer for the first 30 seconds and a f lat tening out for the second half of the t ime series (a decrease i n dep th of 0.34 c m over 60 seconds). O n the downstream side of the canyon (Figure 4.35(c)), the dye dep th decreases l inear ly over 60 seconds for a t o t a l change of 0.20, 0.31 and 0.30 c m over 60 seconds for the top, middle and b o t t o m edge of the dye, respectively. T h e dye at this loca t ion increases i n intensi ty signif icantly from the i n i t i a l concentrat ion (from a level of 0.7 to 1 on the color scale i n F igu re 4.35(c)). O n the shelf (Figure 4.35(d)), a significant par t of this s ignal is the l ight sheet reflecting on the topography. A change does occur over t ime, meaning tha t dye is m o v i n g onto the shelf (a change of 0.07 c m over 60 seconds for the top edge of the dye s ignal) . N o significant s t re tching occurs mid-canyon (Table 4.1) whi le significant s tretching occurs on the ups t ream side of the canyon (0.49 c m over 60 seconds). Compar i sons are made between the amount of s tretching between three different cross-sections of the canyon at P o s i t i o n D (Table 4.4). A l l of the results i n this table are significant a n d show that one and a ha l f t imes more stretching occurs i n the upst ream cross-section t han i n the downst ream one. Chapter 4. Results 104 6 5 0 - 5 y[cm] - (c) Dye after 60 seconds Figure 4.33: D y e layer at pos i t ion D at a) Os, b) 30 seconds and c) 60 seconds after ro t a t ion change. T h e top and bo t t om edge of the dye layer (labeled 1) is denoted by black hor izonta l lines. Chapter 4. Results 105 Ups t r eam M i d - C a n y o n D o w n s t r e a m U p s t r e a m 1 .00±0 .14 - 0 . 0 5 ± 0 . 0 6 - 0 . 2 6 ± 0 . 0 4 M i d - c a n y o n - 1 8 . 7 5 ± 1 9 . 9 6 1 .00±2 .26 4 . 7 9 ± 6 . 5 5 D o w n s t r e a m - 3 . 9 1 ± 0 . 6 6 0 . 2 1 ± 0 . 2 9 1 . 0 0 ± 0 . 4 7 Table 4.4: C o m p a r i s o n between s t re tching/compression at P o s i t i o n D . E a c h value i n the table is a ra t io of the values from Table 4.1 w i t h associated error f rom the slope calcula t ions . 5 4 3 2 1 0 -1 -2 -3 -4 -5 y[cm] Figure 4.34: L o c a t i o n of four t ime series cross-sections at pos i t ion D i n the v i c i n i t y of the canyon. T h e green layer is the dye layer (labeled 1) and the whi te l ine is the l ight sheet reflecting on the t ank topography. Chapter 4. Results 106 Slopes: +4.71e-L_ _ +9.426-04 ± 3 e - 0 4 0 i 5.03O--03 . .5.738-03 «'<V '^VvV*'* +5.398-03 .:> o.i ± 3 e - 0 4 ± 2 8 - 0 4 (a) Upstream (b) Mid-canyon i i i i i i i i ^ ^ 40 40 l 0. I Slopes: +3.32e-i I Slopes: W| +1.128-03+le-04 +4.338-04 ± 4 e - 0 5 +5.328-04 +8e-05 (c) Downstream (d) On Shelf F igure 4.35: T i m e Series of D y e at posi t ion D over 60 s after the ro ta t ion change of dye layer 1. T h e top, midd le and bo t t om edges of the dye layers are found a n d p lo t t ed over top of the dye spec t rum i n red, black and blue, respectively. These lines are then replot ted below the spec t rum a n d a linear fit is found for each line and the slope of the l ine ( ± the error i n the slope) is shown to the right of this plot . T h e slope is i n uni t s of c m s _ 1 . Chapter 4. Results 107 Position E A t pos i t ion E (Figure 3.4), the dye is placed at two different depths i n two different experiments. In F igu re 4.36, the dye is injected 5 c m from the b o t t o m of the t ank (which w i l l be referred to as E ) and i n F i g u r e 4.37, the dye is injected 6 c m from the b o t t o m of the tank (which w i l l be referred to as E( I I ) ) . In i t ia l ly , i n bo th cases, the dye starts as a hor izon ta l layer across the canyon (Figures 4.36(a) and 4.37(a)). In F igu re 4.36(a), the dye layer is marked only by the top of the layer as the b o t t o m of the layer extends to the b o t t o m o f the canyon topography. A s t ime progresses, the b o t t o m o f the dye layer separates from the b o t t o m topography and can be dis t inguished by the dark l ine close to the b o t t o m of the canyon (Figure 4.36(c)). Af ter 30 seconds, the dye layer t i l t s up on the ups t ream side (Figure 4.36(b-c)). T h e dye on the downstream side of the canyon also decreases i n dep th but not as much as o n the upst ream side of the canyon. T h e top of the dye layer (on the downstream side) shows an ins t ab i l i t y w i t h a sma l l bulge of dye next to the canyon w a l l wh ich decreases i n depth. Af ter 30 seconds, the b o t t o m of the dye has separated from the b o t t o m of the canyon topography on the ups t ream side of the canyon. Af ter 60 seconds, the dye o n the upst ream side of the canyon has moved up as far as the shelf break and the entire upper layer across the canyon has decreased i n depth. O n the downst ream side, the ins tab i l i ty seems to have disappeared and the top layer shows a slight d ip next to the canyon w a l l . T h e b o t t o m of the dye layer has fully separated across the entire w i d t h of the canyon. T h e t ime series cross-sections at pos i t ion E are shown i n F i g u r e 4.38. T h e ups t ream cross-section (Figure 4.39(a)) shows a decrease i n the depth of the dye over 60 seconds w i t h a significant decrease s tar t ing after the first 30 seconds (an increase of 0.31, 0.2 and 0.01 c m over 60 seconds for the. top, middle and b o t t o m edge of the dye, respectively). T h e b o t t o m layer of this dye sheet does not change due to the fact tha t the entire dye layer is penetra t ing below the dep th o f the topography. Therefore, this t ime series (along w i t h others at loca t ion E ) is showing the decrease i n dep th of the dye layer and not ac tua l s tretching. In the middle of the canyon (Figure 4.39(b)), the dye s teadi ly decreases Chapter 4. Results 108 i n depth (while osci l lat ing) and the noticeable separat ion from the b o t t o m topography is vis ible i n this t ime series. T h e change i n depth o f the top of the layer is 0.44 c m over 60 seconds. O n the downstream side of the canyon (Figure 4.39(c)), the top layer of the dye s teadi ly decreases i n depth by 0.3 c m over 60 seconds. T h e b o t t o m of the dye layer does not separate from the topography. O n the shelf (Figure 4.39(d)), the i n i t i a l 20 seconds of the t ime series shows on ly the reflected l ight on the b o t t o m topography due to the l ight sheet. There appears to be a slight decrease i n dye depth at 20 seconds (dye wisp mov ing over the shelf) wh ich then increases again, slowly, by 40 seconds. It seems as though the dye at this loca t ion only reaches the shelf at approx imate ly 27 seconds when a wisp of dye has moved over the shelf. After this, the dye concentra t ion s lowly decreases (wi th no new input ) . Due to the fact that the i n i t i a l condit ions at this loca t ion have a dye layer that penetrates beyond the depth of the topography, the change i n thickness of the dye layer and the amount of s tretching occur r ing over 60 seconds is calculated by using the top and middle slopes of the dye (instead of the top and b o t t o m as previously) . T h e results (Tables 4.1 and 4.2) show tha t the top ha l f of the dye layer increases i n w i d t h by 0.11, 0.13 and 0.19 ± 0.07 c m i n 60 s for the ups t ream, mid-canyon and downst ream cross-sections, respectively. T h e largest amount o f s t re tching occurs i n the downst ream cross-section (0.45 / ) whi le the upstream cross-section is half as large (0.23 / ) . Chapter 4. Results 109 4.5-si • i , 4 3 2 1 0 -1 -2 -3 -4 y[cm] (c) Dye after 60 seconds Figure 4.36: D y e layer at pos i t ion E at a) Os, b) 30 s and c) 60 s after ro t a t ion change. D y e inserted when the water is 5 c m from the bo t tom. T h e top and b o t t o m edge of the dye layer (labeled 1) is denoted by black hor izonta l lines. Chapter 4. Results 110 (a) Initial Dye Position 0.5-1 • 1.5' 2[ N 3-3.5-4-4.5-5-0 y[cm] (b) Dye after 30 seconds 1 \ \ I I. / 0 y[cm] (c) Dye after 60 seconds Figure 4.37: D y e layer at pos i t ion E( I I ) at a) 0s, b) 30 s and c) 60 s after ro t a t ion change: 6cm from the bo t tom. T h e top and bo t t om edge of the dye layer (labeled 1) is denoted by black hor izonta l lines. Chapter 4. Results 111 y[cm] Figure 4.38: L o c a t i o n of four t ime series cross-sections at pos i t ion E i n the v i c i n i t y of the canyon. T h e green layer is the dye layer (labeled 1) and the whi te l ine is the l ight sheet reflecting on the tank topography. Chapter 4. Results 112 40 SO 80 Slopes: 03±4e-04 04 ±5e-05 40 ID ~_ i i 'i r <f,<". l „ SO*" • W • •• r—— Slopes: 4-7.360-09 i2e--04 +6.686-03 +36-04 +5 260-03 ±2e-04 30 40 50 C49 (a) Upstream (b) Mid-canyon 0 10 20 SO 40 50 ec Brow Slopes: -2.91e-03+66-04 -8.40e-05 ±2e-04 -2.26e-04 ±1e-04 (c) Downstream (d) On Shelf Figure 4.39: T i m e Series of D y e at pos i t ion E over 60 s after the ro ta t ion change from dye layer 1. T h e top , midd le and bo t tom edges of the dye layers are found and p lo t t ed over top of the dye spec t rum i n red, black and blue, respectively. These lines are then replot ted below the spec t rum and a l inear fit is found for each l ine and the slope of the l ine ( ± the error i n the slope) is shown to the right of this p lot . T h e slope is i n uni ts of c m s " 1 . Chapter 4. Results 113 Position E(II) T h e dye layer at pos i t ion E( I I ) (Figure 4.37) demonstrates the i n i t i a l cond i t ion of the dye where i t ful ly covers the shelf break dep th a n d penetrates be low the shelf break in to the canyon. A t 30 s, the top of the dye layer shows a slight bulge upward on the downs t ream side of the canyon (Figure 4.37(b)). N e x t to the side walls of the canyon, the b o t t o m of the layer shows an upward t i l t of the dye on bo th the upstream and downst ream side of the dye. Af te r 60 s, the b o t t o m of the dye has flattened out and no longer shows the large t i l t up on the ups t ream and downst ream sides (Figure 4.37(c)). T h e b o t t o m of the dye has also decreased s l ight ly i n depth on the downst ream side inside the canyon. A t the top of the dye layer, the bulge on the downs t ream side has decreased i n size but is s t i l l v is ible and corresponds w i t h the decrease i n depth of the b o t t o m of the layer. T h e t ime series cross-sections for E( I I ) are shown i n F igu re 4.40. T h e ups t ream t ime series (Figure 4.41(a)) shows a sma l l l inear decrease i n the middle of the dye layer (0.09 c m over 60 seconds). In the center of the canyon, the top edge of the dye increases l inear ly i n dep th over t ime (0.26 c m over 60 seconds for the top edge of the dye (Figure 4.41(b))) whi le the b o t t o m edge of the dye decreases i n depth (by 0.08 c m over 60 seconds). O n the downst ream side of the canyon (Figure 4.41(c)), the midd le of the dye layer increases i n depth over t ime (0.29 c m over 60 seconds). O n the shelf (Figure 4.41(d)), the dye compresses and increases l inear ly i n depth (0.08 c m over 60 seconds). T h e remarkable event of compression occur r ing mid-canyon is 0 . 2 9 / over 60 seconds (Table 4.2). T h i s is the first major compression observation. T h e upst ream and downst ream b o t h have lower compression values (0 .14 / and 0 . 2 1 / , respectively). Compar i sons are made between the amount of s tretching between the four different cross-sections o f the canyon at P o s i t i o n E ( I I ) (Table 4.5). T h e mid-canyon cross-section compresses two a n d a ha l f and four t imes more than the upst ream and downstream cross-sections. Chapter 4. Results 114 Ups t r eam M i d - C a n y o n D o w n s t r e a m U p s t r e a m 1 . 0 0 ± 0 . 3 3 2 . 5 5 ± 0 . 5 7 1 . 9 6 ± 0 . 5 2 M i d - c a n y o n 0 . 3 9 ± 0 . 0 9 1 .00±0 .12 0 . 7 7 ± 0 . 1 2 Downs t r eam 0 . 5 1 ± 0 . 1 3 1 . 3 0 ± 0 . 2 1 1 . 0 0 ± 0 . 2 0 Table 4.5: C o m p a r i s o n between s t re tching/compress ion at P o s i t i o n E ( I I ) . E a c h value i n the table is a ra t io of values from Table 4.1 w i t h associated error from the slope ca lcu la t ion . 4.3.2 Summary: Results from the Vertical (2D) F r o m qual i ta t ive and quant i ta t ive analysis of the hor izonta l dye layers, several observations can be made. T h e dye layers (below the shelf break depth) show a d is t inc t uplift o n the ups t ream side o f the canyon wh ich corresponds to observational data . T h e t ime series analysis shows tha t the greatest amount of s tretching occurs on the upstream side of the canyon from Pos i t ions C - E (Figure 3.4) on the scale of 0.2 - 0 . 5 / over 60 s (Figure 4.42). T h i s agrees w i t h results f rom Perenne et a l . (2001b) wh ich indicate s tretching of 5 m m from their experiment. T h e compar i son between locat ions (Tables 4.3 - 4.5) demonstrate that the difference i n s tretching between the ups t ream loca t ion and the other locat ions varies from 5 - 1 2 times as much as the other locations. F r o m conservat ion of poten t ia l vor t ic i ty , this large amount of s tretching at the upstream loca t ion of the canyon w i l l induce a cyclonic vor t ic i ty . Chapter 4. Results 115 5 4 3 2 1 0 -1 -2 -3 -4 -5 y[cm] Figure 4.40: L o c a t i o n of four t ime series cross-sections at pos i t ion E ( I I ) i n the v i c i n i t y of the canyon. T h e green layer is the dye layer (labeled 1) and the whi te line is the l ight sheet reflecting on the tank topography. Chapter 4. Results 116 1.5 Slopes: , -9.25e-04 ± 2 8 - 0 4 z +1.526-03 ± 2 e - 0 4 f +1.278-03+7e-04 5 2.5 a as - -•• - ,„! „ • „ , , ' „ "UMwil' y ^ , i y , ( .HM^H , , ^ „ h- - „ i Slopes: -4.306-03 ± 2 8 - 0 4 -2.366-03 ± 3 e - 0 4 +1.308-03 +26-04 (a) Upstream (b) Mid-canyon • V " v1' * Slopes: -2.968-03 ± 2 e - 0 4 9 o - Q 3 ± 1 0 ~ Q 4 7 e - 0 3 ± 1 e - 0 4 1e-03 ± 7 8 - 0 5 (c) Downstream (d) On Shelf Figure 4.41: T i m e Series of D y e at pos i t ion E(I I ) over 60 s after the ro t a t ion change f rom dye layer 1. T h e top, midd le and b o t t o m edges of the dye layers are found a n d p lo t ted over top of the dye spec t rum i n red, black and blue, respectively. These lines are t hen replot ted below the spec t rum and a linear fit is found for each l ine and the slope of the l ine ( ± the error i n the slope) is shown to the right of this p lot . T h e slope is i n uni t s of c m s " 1 . Chapter 4. Results 117 I Greatest amount of stretching Figure 4.42: S u m m a r y of dye t ime series data: P l a n view of the canyon showing the greatest amount of s t retching occur r ing on the upstream side of the canyon close to the m o u t h . T h e grey shaded region is the continental shelf. Chapter 4. Results 118 4.4 Steady State W h e n the ro ta t ion rate of the tank is increased to drive the incident veloci ty , f r ic t ion slows the flow down. T h e resul t ing ve loc i ty i n the tank is transient. Therefore, to s imulate a steady current, the ve loc i ty is main ta ined by cont inuing to increase the rate of ro ta t ion of the t ank at a new rate of change, AO,?/At. 4.4.1 Creating a steady state Several exper imenta l t r ia ls were conducted i n order to f ind a new rate of change ( A ^ / A i ) over a long per iod of t ime to ma in t a in a flow veloci ty at the shelf break of 0.015 c m s _ 1 . T h i s was carr ied out by using part icles as flow trackers. T h e rate of change required i n order to m a i n t a i n the desired veloci ty is achieved by increasing the ro ta t ion of the tank from / = 1.5 s _ 1 to / = 0.1 s _ 1 over 1000 seconds (27.3 s after the i n i t i a l change i n ro ta t ion rate from / = 1.4875 s _ 1 ) . Dye is used as the v i sua l iza t ion technique due to the ease of flow v i sua l i za t ion and the ab i l i ty to place the dye at any depth and locat ion. T w o different geometries of the dye syringe placements are used as discussed i n Chap te r 3. T h e l ight sheet is posi t ioned such tha t the hor izon ta l sheet is between 0 -2.2 c m (ie: shallower than the shelf break) for ful l coverage of the shelf break region. 4.4.2 Dye upstream of the canyon Syringes are placed d i rec t ly on the shelf at different locat ions across the shelf ups t ream of the canyon. T h e results (Figure 4.43) show that as the flow travels across the shelf i n the downst ream direct ion, i t follows various paths depending on its i n i t i a l loca t ion on the shelf. T h e dye closest to the w a l l (denoted by 1 i n F igu re 4.43) flows i n the downst ream di rec t ion u n t i l i t reaches the canyon where i t bends toward the canyon head. T h e dye is vis ible un t i l about three quarters of the way across the canyon when i t disappears from view (Figure 4.43(b)). B y phys ica l ly observing the dye i n the labora tory du r ing the experiment , the dye appears to sink down below the canyon r i m . Af te r 400 Chapter 4. Results 119 Original 0 5 10 15 20 25 time = 75.0 s Original 0 5 10 15 20 25 time = 200.0 s c • I "J* w 5 10 15 20 25 5 10 15 20 25 Original 10 15 time = 400.0 s Figure 4.43: Steady State images (Or ig ina l and Enhanced) w i t h dye s ta r t ing ups t ream of the canyon. Four syringes (denoted by the X ' s and associated numbers 1 - 4 ) are placed on the shelf. Images are 75 s, 200 s and 400 s after i n i t i a l change i n ro t a t ion rate. In the enhanced images, red, yellow and blue indicate h igh , lower and zero dye concentrat ions, respectively. T h e l ight sheet is reflected on the canyon topography w h i c h appears as l ight blue to yel low. Chapter 4. Results 120 seconds, the dye from this syringe is no longer being released and no l ine of dye is evident at this locat ion. A t this loca t ion , a large amount of dye is visible i n the b o t t o m bounda ry layer on bo th sides of the injected dye l ine. T h e E k m a n layer flow accounts for the dye o n the on-shore side of the dye, but the dye on the off-shore side of the dye is unexpected. T h i s is due to the osc i l la t ion i n the tank. A s dye is released from syringe 1, the osc i l la t ion causes the dye to be pushed i n the offshore d i rec t ion (as vis ible i n F igu re 4.43(a)). A s the dye propagates toward the canyon, this i n i t i a l bulge of dye that is further offshore t han the outf lowing dye from syringe 1 travels as a t h i n sheet. Some of this dye is then advected onshore i n the bo t t om E k m a n layer. There are two possible reasons for the dye mov ing to a deeper depth. T h e first is tha t w i t h the addi t ion of the uranine salts the density of the water increases sl ightly. T h e second is the d i rec t ion of the m o u t h of the needle. T h e needles have slanted mouths wh ich face any possible d i rec t ion and the needle on this syringe may have been po in t ing downslope which , when the dye is released, w o u l d send the dye i n the downslope d i rec t ion m i x i n g w i t h denser water. F r o m non- ro ta t ing t ank tests, the most dominant mechanism for determining the loca t ion of the dye is the d i rec t ion of the m o u t h of the needle. W h e n the needle m o u t h is po in t ing d i rec t ly upward (or downward) , the dye tends to radiate away from the m o u t h of the needle equal ly i n b o t h direct ions. Conversely, when pointed left (or r ight) , the dye radiates away from the needle i n the d i rec t ion w h i c h the needle m o u t h is po in t ing (to the left or r ight ) . T h e next syringe (2) does not start releasing dye un t i l jus t before 400 seconds after the i n i t i a l change i n ro ta t ion rate had elapsed. N o dye is vis ible i n the images i n F igu re 4.43 at this loca t ion . T h e next l ine of dye (3) flows i n the downstream direct ion un t i l i t reaches the canyon r i m where i t bends toward the canyon head (Figure 4.43(b)). T h i s dye, unl ike tha t at (1), remains i n the l ight sheet and bends back out toward the canyon m o u t h once i t reaches three-quarters of the way cross the canyon. Af te r crossing this point , the dye bends offshore and moves onto the shelf. Once on the shelf, the dye bends more s t rongly toward the shelf break. Af ter 400 seconds, the amount of Chapter 4. Results 121 dye released from this syringe is great ly reduced (compared w i t h tha t from pos i t ion (4)). T h e dye released f rom posi t ions (3) and (4) do not cross paths, bu t m a i n t a i n their o w n (s imilar) p a t h across the canyon. T h e dye d i rec t ly next to the shelf break (4) follows the same downst ream d i rec t ion as the other dye lines. A sma l l amount of dye is observed fal l ing off of the shelf (upstream of the canyon) down the slope wh ich is most l ike ly due to the needle m o u t h po in t ing downslope (as ment ioned above). T h i s dye falls down to at least 6 c m depth. T h i s dye l ine (on the shelf) is the first to reach the canyon. W h e n i t reaches the canyon r i m , the dye turns toward the head and once three-quarters of the way across the canyon, the dye bends back toward the m o u t h . T h e dye tha t falls off the shelf break and down onto the slope has now been carr ied downst ream as a t h i n sheet a long the slope. A s i t crosses the canyon mouth , i t remains as a t h i n sheet and at approx imate ly 1 c m before the downst ream edge of the canyon, this sheet turns up toward the canyon head fo rming an eddy vis ible i n F igures 4.43(b) and 4.43(c). T h e eddy is cyclonic and is vis ible as a t h i n sheet wel l below the shelf break depth (visible greater t han 2 c m below the shelf break depth) . T h e eddy remains enclosed inside the canyon m o u t h and is flattened on the edge facing the middle of the t ank by the flow that is crossing the canyon mou th . O n the downst ream side o f the shelf, dye is present o n the shelf. T h i s dye is located between the shelf break and approximate ly half way up the downstream canyon r i m . T h e dye from pos i t ion (2) is the source of the dye closest to the head of the canyon. T h i s dye is located closer to the shelf break t han from its o r ig ina l pos i t ion on the shelf (the flow has been deflected i n the offshore d i rec t ion on the shelf). D y e from posit ions (3) and (4) do not cross w i t h dye f rom pos i t ion (2) and thus, dye or ig ina t ing f rom pos i t ion (2) is at the shallowest depth on the downs t ream side of the canyon whi le dye from posit ions (3) and (4) are located close to the shelf break. Chapter 4. Results 122 Dye at the canyon axis A steady state experiment is conducted w i t h the syringes of dye centered i n the canyon axis w i t h three syringes 0.5 c m below the canyon r i m depth (Figure 4.44). D u e to the slope o f the shelf, these syringes are at s l ight ly different depths w i t h syringe 3 being the deepest and syringe 1 being the shallowest. T h e results show a dis t inct per turba t ion of the flow due to the submarine canyon. After 75 seconds (Figure 4.44(a)), the dye at pos i t ion (1) has flowed into the canyon and turned toward the canyon head. Conversely, the dye at pos i t ion (3) i n i t i a l l y turns toward the head o f the canyon and then, approx imate ly 1 c m before reaching the downst ream canyon r i m , the flow turns back toward the canyon m o u t h and up onto the shelf. F r o m the i n i t i a l syringe pos i t ion , the dye has moved 1.4 c m closer toward the shelf break. T h i s corresponds to an increase i n dep th of the canyon r i m of 0.25 c m . Therefore, the dye has decreased i n dep th b y at least 0.25 c m since the i n i t i a l dye depth was 0.5 c m below the canyon r i m depth. It is not obvious from the first 75 seconds where the dye from syringe (2) has moved. After 200 seconds, the dye at pos i t ion (3) has main ta ined the same flow pa t te rn whi le the dye at pos i t ion (1) has spli t in to two parts. T h e first part has cont inued up toward the head of the canyon as a tongue that is hugging the downstream canyon wa l l . Af ter 200 seconds, the dye has reached the canyon head and turns back down toward the m o u t h a long the ups t ream canyon w a l l . T h e second part of this dye turns toward the m o u t h just after its release from the syringe a n d moves up onto the shelf. Af ter 400 seconds, the dye at the canyon head has complete ly tu rned at the head of the canyon and is mov ing toward the canyon m o u t h along the upst ream wa l l . N o dye is v is ib le upwel l ing onto the shelf near the canyon head. A large section of dye is now upwel l ing onto the shelf close to the m o u t h (wid th of approx imate ly 4 cm) as a band or ig ina t ing from a l l three syringes. D y e at pos i t ion (2) does not show any visible movement i n the captured images. T h i s is possibly due to the dye not being released from the syringe proper ly or tha t the dye moved to an un l i t section Chapter 4. Results 123 or h idden part of the canyon. However, from observations made i n the lab i n this exper imenta l run , a very long t h i n sheet is created and spins cy lon ica l ly keeping w i t h i n the topography of the canyon. T h r e e - D i m e n s i o n a l F low Feature One dis t inct feature vis ible i n bo th upst ream and midcanyon axis dye locat ions is the three-dimensional flow at the canyon mouth . T h i s feature is located at the downs t ream canyon w a l l near the m o u t h (Figure 4.45). There is a dis t inct ive separat ion between the shelf dep th flow and flow inside the canyon below the shelf. T h i s difference is due, i n part , to the canyon m o u t h eddy. T h e flow i n the eddy prevents any upwel l ing d i rec t ly on the downs t ream corner o f the canyon and forces incident flow at this point in to the canyon where i t can the upwel l onto the shelf or r emain i n c i rcu la t ion i n the canyon m o u t h eddy. 4.4.3 Summary: Steady State Therefore, from the steady state experiments, upwell ing occurs cont inuously i n the l abora to ry long canyon. U p w e l l i n g (from 0.5 c m below the canyon r im) occurs on the downst ream r i m of the canyon close to the m o u t h i n a 4 c m section. A cyclonic eddy is vis ible t r apped inside the canyon m o u t h and cyclonic c i rcu la t ion is v is ib le i n the interior of the canyon up to the canyon head. Three-d imens iona l flow is observed at the downstream corner of the canyon m o u t h where flow tha t is jus t inside the canyon m o u t h is directed into the canyon v i a the canyon m o u t h eddy where i t remains i n c i rcu la t ion i n the eddy or upwells onto the shelf. Chapter 4. Results 124 5 10 15 20 25 time = 75.0 s -14 -12 -10 -8 -6 -4 -2 0 2 Original time = 400.0 s Figure 4.44: Steady State images (Or ig ina l and Enhanced) w i t h dye s ta r t ing mid -canyon 0.5 c m below the canyon r i m . Three syringes (denoted b y the X ' s a n d associated numbers 1 - 3) are used. Images are 75 s, 200 s and 400 s after i n i t i a l change i n ro ta t ion . In the enhanced images, red, yel low and blue indicate h igh , lower and zero dye concentrat ions, respectively. T h e l ight sheet is reflected o n the canyon topography w h i c h appears as l ight blue to yel low. Chapter 4. Results 125 17 18 19 20 21 22 23 24 25 x [cm] Figure 4.45: Enlargement of Steady State with dye starting upstream of canyon at 200 seconds. Three-dimensional flow features are shown with black (2.6 - 2.0 cm) and white (2.6 -5 cm) arrows. Red, yellow and blue indicate high, lower and zero dye concentrations, respectively. The light sheet is reflected on the canyon topography which appears as light blue to yellow. This is a magnification of Figure 4.43(b) 126 Chapter 5 Discussion 5.1 Summary of Results T h i s is the first experiment to m y knowledge to s tudy the flow dynamics i n a l abora to ry mode l of a long canyon. Several different techniques are used i n order to ob ta in a comprehensive set of results inc lud ing the use of particles and dye. A summary of the results is i t emized below: • F l o w i n the canyon is s imi lar between different velocities; an increase i n ve loc i ty increases the magni tude of the dominant features (Section 4.1.2) • T h e incident ve loc i ty on the shelf is ha l f as large as the incident ve loc i ty offshore (Section 4.1.1). • A cyclonic eddy forms at the canyon mouth , increasing i n vo r t i c i t y as incident ve loc i ty increases and decreasing i n vo r t i c i ty as s t rat i f icat ion increases (Section 4.1.5). • Side w a l l vo r t i c i ty generated against the slope is large enough to account for the increase i n vo r t i c i t y of the canyon m o u t h eddy w i t h increasing incident ve loc i ty (Sect ion 4.1.5). • V o r t e x s t re tching/compress ion, wh ich is dependent on s t rat i f icat ion, explains the reduct ion i n vo r t i c i ty of the canyon m o u t h eddy w i t h increasing s t ra t i f icat ion (Sect ion 4.1.5). • T h e greatest amount of s tretching below the canyon r i m depth occurs close to the ups t ream w a l l of the canyon, inside the m o u t h (Section 4.3.1). Chapter 5. Discussion 127 • U p w e l l i n g onto the shelf occurs along the downstream w a l l at low Ro, increasing and cont inuing toward the canyon head at h igh Ro (Section 4.1.2). • W h e n forced as a steady state, upwell ing occurs continuously, and an eddy (visible wel l below the shelf break depth) circulates cyc lonica l ly at the canyon m o u t h (Sect ion 4.4.2). • Onshore of the canyon mou th , a slow cyclonic c i rcu la t ion occurs inside the canyon. F l o w travels toward the head of the canyon on the downstream w a l l and offshore a long the ups t ream w a l l (Section 4.1.2). These results w i l l be compared w i t h other canyon projects to draw conclusions about the flow dynamics i n long canyons. 5.1.1 Comparison of horizontal dye layers with real data Due to the scarci ty of cross-sectional da ta from long canyons, da ta f rom A s t o r i a canyon (a short canyon w i t h Rossby number of 0.42; Hickey (1997)) is compared w i t h the ve r t i ca l dye cross-sections from the present l abora to ry work (recal l ing tha t these results have a R o s s b y number of 0.24). Isopy-cnals below the shelf break depth compare wel l w i t h those from i n s i tu short canyon results as wel l as s tretching values from the upstream side of the canyon. A cross-section from the m o u t h of A s t o r i a canyon (just pr ior to m a x i m u m upwell ing) shows a t i l t i n g up of the isotherms at the shelf break dep th f rom the ups t ream side to the downs t ream side ( 6 . 5 ° C and 7 ° C contours i n F igure 5.1), w i t h a change i n depth of approx imate ly 50 m (from the ups t ream to downst ream side). Be low these isotherms, the 6 ° C and 5 .75° C contours (Figure 5.1) t i l t i n the opposite d i rec t ion from the contours above. T h e 6 ° C contour makes a 70 m change i n depth across the canyon m o u t h . H i c k e y (1997) compares a long shore w i n d d a t a w i t h measured currents inside the canyon and finds a significant correla t ion between the two. F r o m the corre la t ion , there is a 1.25 day lag between the w i n d forcing and the upwell ing signal . Chapter 5. Discussion 128 N S , I I I I I I I L _ J I I 1 1 I , -10.0-Figure 5.1: Cross-sect ion from m o u t h of temperature contours ( ° C ) across A s t o r i a canyon from H i c k e y (1997) jus t pr ior to a m a x i m u m upwel l ing event. T h e x-ax is is f rom N o r t h to Sou th across the canyon (denoted w i t h N and S) . (Reproduced w i t h permiss ion from the author) . A cross-section further toward the head of A s t o r i a canyon (at m a x i m u m upwell ing) shows a s imi lar t i l t i ng up of the isotherms at the shelf break depth from the ups t ream side to the downst ream side ( 6 . 5 ° C and 7 ° C contours i n F igure 5.2), w i t h a change i n depth of approx imate ly 30 m (from the upst ream to downst ream side). Be low these isotherms, the 6 ° C contour is t i l t i n g i n the opposite d i rec t ion w i t h a change i n depth of approximate ly 100 m . A l t h o u g h this cross-section is closer to the canyon head, i t occurs at the t ime of m a x i m u m upwel l ing and w i l l be useful to compare w i t h the t ime of m a x i m u m upwell ing from the labora tory results (at 30 s). C o m p a r i n g Figures 5.1 and 5.2 w i t h results from the long canyon exper iment (Figure 4.33(b), for example) , the 6 . 0 ° C contour corresponds w i t h this downward t i l t i n g dye layer. T h e distance tha t the top of this dye layer changes over 30 seconds is approximate ly 0.55 c m i n the t ank or approx imate ly a 55 m change i n the ocean scale. T h i s is measured by ca lcula t ing the difference i n depth of the dye layer at the up and downst ream sides at 30 s. T h e t ime difference between the beginning of the Chapter 5. Discussion 129 F igure 5.2: Cross-sect ion from mid-canyon of temperature ( ° C ) contours across A s t o r i a canyon from Hickey (1997) du r ing the m a x i m u m of an upwel l ing event. T h e x-axis is from N o r t h to South across the canyon (denoted w i t h N and S). (Reproduced w i t h permiss ion from the author) . forcing and this measurement is approximate ly equivalent to 3.5 days. T h e l abora to ry value is very s imi lar to tha t observed from F igure 5.1. However, the value from the l abora to ry results is on ly half the depth change across the canyon as measured i n F igu re 5.2. F i n d i n g a dye experiment tha t corresponds w i t h the upward t i l t i n g i so therm ( 7 ° C contour) is more difficult. In most experiments, the dye is below the shelf break depth . T h e dye at pos i t ion E(II) is bo th below and above the shelf break depth which makes i t difficult to ma tch w i t h an upward t i l t i ng i sotherm (due to the diffusion of the dye over several density levels). Therefore, f inding s imi lar features i n cross-sectional isopycnals at depths below the shelf break between the short canyon (field data) and long canyon ( labora tory data) is possible despite the smaller Rossby number of the long canyon compared w i t h that of the short canyon. T h e features i n the short canyon appear to be much larger i n magni tude and despite the non-advect ive nature of the forced flow i n the long canyon and the consequently low Rossby number, features are s imi la r i n magni tude to the short canyon, where advect ion dominates. Chapter 5. Discussion 130 Hickey (1997) also looked at the amount of s tretching vor t i c i ty i n A s t o r i a canyon by ca lcu la t ing the change i n thickness of a par t icular i sopycnal (or isotherm) d iv ided by the ups t ream thickness of the i sopycnal (or isotherm). Close to the mouth , the results from A s t o r i a canyon near to the upstream w a l l of the canyon are posit ive, ranging from 0 to 6 / , w i t h higher values closer to the shelf break depth (Figure 5.3). Closer to the head, the results near the ups t ream w a l l of the canyon are also posi t ive below the shelf break, ranging from 0 to 4 / . There is also a sma l l region of negative vor t i c i ty (-0.5/) located at the shelf break depth (Figure 5.4). T h e results from the l abora tory experiments (Table 4.2 and F igure 5.5) show that s tretching increases a long the ups t ream w a l l of the canyon as the measurement loca t ion moves closer to the canyon head (from A to D ) . There is a smaller amount of s t retching mid-canyon as wel l as along the downst ream canyon w a l l (except for at loca t ion D ) . Compress ion occurs at l oca t ion E ( I I ) w i t h the largest amount occur r ing mid-canyon. A l l of the s t retching vort ic i t ies f rom the l abora to ry are below 1 / and the l abora tory model corresponds to results from H i c k e y (1997) between 250 m and 180 m along the upst ream w a l l and below 180 m along the downst ream w a l l (F igure 5.3). D u r i n g the height of upwel l ing, s t re tching values f rom the l ab correspond w i t h those f rom A s t o r i a canyon between 165 m and 210 m on the upstream side of the canyon and between 130 and 160 m on the downstream side of the canyon. T h e s tretching vort ic i t ies along the upst ream side of the canyon below the shelf break are posi t ive as found i n H i c k e y (1997) and i t seems that the results from the lab at 30 s agree wel l w i t h the cross-section just pr ior to m a x i m u m upwell ing. 5.1.2 Deepest depth of upwelling T h e theoret ical depth of deepest upwell ing ( A l l e n and Hickey , 2004a) for advect ion dr iven upwel l ing i n a short canyon s l ight ly underestimates the results obta ined from the labora tory . A l l e n (2004b) describes an equat ion for ca lcula t ing the deepest depth of upwel l ing, Z, i n a canyon where Z is the Chapter 5. Discussion 131 F igure 5.3: Cross-sect ion at m o u t h of stretching vor t i c i ty across A s t o r i a canyon (Hickey , 1997) jus t pr ior to a m a x i m u m upwell ing event. The y-axis is dep th [m] a n d the x-axis is from N o r t h - S o u t h across the canyon (from left to r ight) . (Reproduced w i t h permiss ion from the author) . F igure 5.4: Cross-sect ion at m o u t h of s tretching vor t i c i ty across A s t o r i a canyon (Hickey , 1997) dur-ing the m a x i m u m of an upwell ing event. The y-axis is dep th [m] a n d the x-axis is from N o r t h - S o u t h across the canyon (from left to r ight) . (Reproduced w i t h permiss ion from the author) . Chapter 5. Discussion 132 0 .5r Upstream Midcanyon Downstream Cross-section Location Figure 5.5: Stre tching across labora tory canyon from hor izonta l dye layers. A - E ( I I ) represent the five different locat ions along the canyon indica ted i n F igu re 3.4. Chapter 5. Discussion 133 depth below the depth of the canyon head. T h i s value is denned, for low Rossby number , by where Lc is the length of the canyon and R is the radius of curvature of the ups t ream flank of the canyon. Fo r the dye layer cross-section experiments w i t h U = 0.5 c m s _ 1 , Lc = 16.5 c m , R = 1.4 c m and N = 2 s _ 1 , gives Z = 1.46 cm. A d d i n g the depth at the canyon head (0.8 cm) , gives the deepest depth of upwel l ing for this canyon of 2.3 c m which is jus t below the shelf break depth . It appears tha t when look ing at the cross-sections at Pos i t ions C , D and E (Figures 4.32, 4.33 and 4.36) that water below 2.6 c m does not upwell on the shelf whi le water above 2.6 c m does upwell onto the shelf. Therefore, the calculated depth of deepest upwel l ing is s imi la r to the observed deepest depth of upwel l ing (2.3 c m compared w i t h 2.6 cm) qual i ta t ively . N o t on ly do the canyons differ i n forcing mechanism and length, but assumptions were made i n the scal ing argument i n A l l e n and H ickey (2004a) such that the incoming flow is un i form along the canyon. T h i s is not the case i n the l abora tory canyon as the incident ve loc i ty has an inherent shear. 5.1.3 Effect of Canyon Width T h e canyon w i d t h can be non-dimensional ized by d i v i d i n g the average w i d t h b y the in ternal defor-ma t ion radius, a (Cushman-Ro i s in , 1994) where such that a non-dimensional w i d t h can be calcula ted for each s t ra t i f icat ion (Table 5.1). N u m e r i c a l results, w i t h va ry ing canyon w i d t h ( H y u n a n d K l i n c k , 2004), can be compared w i t h results from these labora tory experiments w i t h va ry ing stratifications showing b o t h s imi lar i t ies and differences between a numer ica l mode l and this physical model . A l t h o u g h the w i d t h of the numer ica l mode l canyon changes between 8-60 k m , the length is constant at 20 k m . T h e Rossby number for a l l of the cases from H y u n and K l i n c k (2004) is 0.8 where where the speed of slope jet is 0.2 m s " 1 , / is (5.1) Chapter 5. Discussion 134 1 0 - 4 s _ 1 and R is 2.5 k m along the shelf break isobath at 150 m ( H y u n , personal communica t ion) . F l o a t trajectories from the numer ica l model ing results (Figure 5.6) show tha t upwel l ing occurs near the canyon head (downstream corner) and that as the canyon w i d t h increases, the t o t a l number of floats crossing the shelf break increases. A s w i d t h increases, the flow separat ion point on the downst ream w a l l of the canyon moves closer toward the head of the canyon. Ro (lab) N [s" 1] a [cm] W / a Desc r ip t ion Case 0.24 1 1.5 4.0 W i d e / W i d e s t 6 0.24 2 2.9 2.0 W i d e r 4 0.24 3 4.4 1.3 Intermediate 3 0.24 3.75 5.5 1.1 Nar rower 2 Table 5.1: Non-d imens iona l w i d t h for l abora tory experiments w i t h associated descr ip t ion and case as from H y u n and K l i n c k (2004). A l l numer ica l cases from H y u n and K l i n c k (2004) have a Rossby number of 0.8. T h e l abora to ry results for the widest canyon (compar ing F igu re 4.5(c) to Case 6 from F igure 5.6) shows a comparable upwel l ing pat tern close to the head of the canyon w i t h a large number of particles upwel l ing onto the shelf from the head. In the phys ica l model , the flow separat ion point is not as close to the head as i n the numerica l case. In fact, the flow separat ion point i n the l abora tory results d i d not appear to move significantly w i t h any veloci ty or s t ra t i f icat ion changes (except for the homogeneous fluid). T h e labora tory results for the narrower canyon (compar ing F igu re 4.5(g) to Case 2 from F igure 5.6) has the same cyclonic c i rcu la t ion inside of the canyon a l though i t shows no significant upwel l ing at the canyon head. However , i t should be noted that the l ight sheet i n this l abora to ry case was not fully on the shelf, and upwel l ing is s l ight ly underest imated. T h e l abora to ry results show a dis t inct offshore flow on the upst ream side of the canyon, not present i n the float t racks. T h e point of flow separat ion (between flow enter ing canyon a n d flow t ravel ing downstream) is at the m o u t h of the canyon on the downst ream w a l l i n bo th the l abora tory and numer ica l results. Chapter 5. Discussion 135 5.1.4 Comparison with Previous Results (3D) from a Short Laboratory-Canyon A l l e n et a l . (2003) s tudied the upwell ing i n a short canyon wh ich had an j'initial — 0.4 s _ 1 and increased to / = 0.52 s _ 1 over 27.3 s to drive a 1.2 c m s _ 1 flow across the canyon. These results are compared w i t h results from the long canyon to show how upwel l ing and flow dynamics change between long and short canyons. T h e results from the short canyon (Figure 5.7) show that near surface flow is not s t rongly affected by the canyon and as the flow gets deeper into the water co lumn, i t becomes more s t rongly affected. I n the deepest layers of the canyon, there is a very faint cyclonic m o t i o n at the m o u t h of the canyon w i t h a s tagnat ion point vis ible at the downstream edge of the canyon near the m o u t h wh ich is also seen i n lab work for the same short canyon by Hewet t (1998). In the upper layers, there is upwel l ing a l l along the downstream r i m of the canyon (al though part icles do not make significant depth changes). A s imi lar exper iment is carr ied out for the long canyon and the results (Figure 5.8) show greater upwell ing (wi th significant depth change) over a larger area on the downs t ream side of the canyon when compared w i t h the short canyon results. These dep th changes (colour changes) occur at the m o u t h (up and downst ream side), along the downstream r i m , and near the canyon head. For the long canyon, the upwell ing flux at 30 s is calcula ted using F igu re 5.8 where the length of the upwel l ing region is taken from the first upwel l ing part icle on the shelf close to the m o u t h up to the last upwel l ing par t ic le on the shelf close to the head. T h e distance between these particles is 11.4 cm. Since the angle of the topography on the shelf is 5 ° , the area th rough wh ich upwel l ing occurs is assumed to be a t r iangle. T h e area of the t r iangle is 6.04 c m 2 . T h e speed of the particles th rough the midd le o f the upwel l ing region is 0.9 c m s _ 1 . T h e flux is therefore $ = AA • U = 5.4 c m 3 s _ 1 (5.3) Chapter 5. Discussion 136 For the short canyon experiment , the equat ion for mass flux onto the shelf from M i r s h a k and A l l e n (2005) (2.13) gives $ = 0.43 • 2.2 c m • ( 1 . 6 ) 2 / 3 • ( 1 . 2 ) - 1 • (0.52 s " 1 ) " 1 • (1.2 c m s " 1 ) 2 (5.4) using da ta from A l l e n et a l . (2003) where 0.43 is the drag coefficient, 2.2 c m is the shelf break depth, 1.6 is the Rossby number, 1.2 is a Burger number, 0.52 s _ 1 is the Cor io l i s parameter and 1.2 c m s _ 1 is the velocity. T h e upwel l ing flux from the short canyon is $ = 3.0 c m 3 s _ 1 . (5.5) T h e upwel l ing flux i n the long canyon is jus t under twice that of the short canyon. T h e length of the short canyon is 8 c m whi le the length of the long canyon is 16.5 cm. F r o m A l l e n and Hickey (2004a), the amount of upwell ing flux from the short canyon onto the shelf is p ropor t iona l to the square root of the length of the canyon. In the case of the short canyon from A l l e n et a l . (2003), * = l . l c m V 1 - (5.6) 1 cm1'* However, for the long canyon we find ^ ^ L S c m V 1 - ^ (5.7) 1 c m 1 ' ^ Therefore, the flux w i l l be underest imated using the theory from the short canyon i m p l y i n g tha t the dynamics i n the long canyon are different. 5.1.5 Flow upstream of the canyon A l l e n (2000) discusses the use of singular points i n cases where flow is l i m i t e d b y the topography (such as at the canyon head which is very shallow) and that flow becomes s t rongly non-linear i n smal l regions a long the canyon topography. One such singular poin t is at the canyon head. T h e effect of this s ingular point may t ravel down the upst ream w a l l of the canyon (on the shelf) s lowing Chapter 5. Discussion 137 flow on the upst ream side of the canyon (very close to the canyon) causing flow to poss ib ly fal l off the shelf break. T h i s may prove to be an explanat ion of the reduct ion i n ve loc i ty a long the shelf. T h e ve loc i ty of this flow is lower than the ve loc i ty further away from the canyon (Figure 5.9). A ve loc i ty measurement approx imate ly 9 c m away from the edge of the t ank is much larger t h a n the other measurements and is b ias ing the resul t ing slope. C a l c u l a t i n g the slope wi thou t this da ta point gives a mean veloc i ty of approximate ly 0.2 c m s - 1 . T h i s par t ic le m a y be ve ry close to the surface and m a y exp la in the increased velocity. However, using a l l of the data , the fit to these points gives a ve loc i ty profile wh ich is jus t s l ight ly lower t han the ve loc i ty of the part icles away from the canyon at 30 s. T h e results show tha t the flow does slow down upst ream of the canyon and leads to the inference that this s ingular point theory may be, i n part , responsible for the decrease i n flow as wel l as reduct ion i n flow due to fr ic t ion (as found i n M i r s h a k (2001)). Chapter 5. Discussion 138 F igure 5.6: F l o a t t racks for va ry ing canyon w i d t h ( H y u n and K l i n c k , 2004) showing narrower, i n -termediate, wider and widest canyons (comparable to l abora to ry experiments i n F igures 4.5(g), 4.5(e), 4.5(e) and 4.5(c), respectively) for flow w i t h a Rossby number of 0.8. T h e number on the upper r ight i n each plot is the case number a n d below tha t denotes the number of particles (out of 90) that upwel l onto the shelf (150 m) . (Reproduced w i t h permiss ion from the author) . Chapter 5. Discussion 139 F igure 5.7: Resul ts from A l l e n et a l . (2003): Strat i f ied Case. T h e red layer is between 1.2-2.2 c m , green is between 2.2 - 3.2 c m as i l lumina ted by the l ight sheet depth . T h e contours are i n c m increasing w i t h depth and the axes are the t ank frame i n c m . T h e t racks are marked w i t h open diamonds and the last pos i t ion of the t rack is marked by an open square. (Reproduced w i t h permission from the author) . Chapter 5. Discussion 140 F igure 5.8: L o n g canyon results for compar ison to experiment f rom A l l e n et a l . (2003). T h e red layer is between 1-2.2 cm, green is between 2.2 - 3.2 c m and blue is between 3.2 a n d 4.2 c m . T h e hor izon ta l axis is x [cm] and the ver t ica l axis is y [cm]. Chapter 5. Discussion 141 Figure 5.9: Velocity on the shelf upstream of the canyon for U = 0.5 cm s _ 1 and N = 2 s _ 1 after 30 s are plotted with x's. Data from Figure 4.1 are plotted with dots as well for comparison. The velocity calculated at 9 cm away from the tank edge may be biasing the results of the fit giving a slightly higher velocity fit. Particles are tracked between 0 - 7 cm away from the upstream canyon rim on the shelf. The particle depths range between 0.5 -2.2 cm. Chapter 5. Discussion 142 5.1.6 Physics behind the flow in the canyon F r o m the l abora tory results, there appears to be two separate stages of the flow evolu t ion i n the tank. T h e first is an i n i t i a l stage and the second is a quasi-steady stage (recal l ing that the flow is actual ly transient i n bo th cases). T h e force balance i n the tank when the flow is in i t i a ted is between the Cor io l i s force and the differential centrifugal t e r m as described i n Sect ion 2.2.2. T h e incident ve loc i ty i n the t ank is s l ight ly different t han expected. T h e ve loc i ty i n the tank does not follow u = u> • r, but decreases a long the shelf. T h e onshore force balance has an added fr ic t ion t e rm wh ich is significant. T h e i n i t i a l stage (Figure 5.10), when t > 30 s and t < 40 s (equivalent to 3.5 - 4.8 days after the i n i t i a l forcing) features the incident ve loc i ty ac t ing l ike a je t a long the slope. T h i s flow enters the canyon at the m o u t h below the shelf break and turns into the canyon. T h e isopycnals respond i n accordance w i t h the the rmal w i n d balance. W h e n this inflow reaches the downst ream w a l l of the canyon, one of three things happen; the flow either upwells onto the shelf, continues t oward the canyon head or turns complete ly out of the canyon. Reca l l i ng the force balance i n the tank defined by (2.12), when the flow reaches the downstream wa l l , the alongshore flow (ug) is const r ic ted due to the topography. Therefore the centrifugal force dominates d r i v i n g the flow toward the head of the canyon. A t the head of the canyon, flow is very slow and begins a slow cyc lonic c i r cu la t ion inside the canyon. A s incident ve loc i ty increases, the amount of upwel l ing increases. A counter flow is observed inside the canyon along the upstream w a l l wh ich is t ravel ing i n the offshore d i rec t ion . T h i s is due to f luid columns being stretched upon entering the canyon (either from offshore or by fal l ing off the shelf) generating cyclonic vor t i c i ty wh ich drives the flow i n the offshore d i rec t ion . A flow stagnat ion point is observed close to the downstream canyon mou th . T h i s point does not move w i t h increased ve loc i ty or s t ra t i f icat ion i n these experiments cont rary to the results of H y u n and K l i n c k (2004). F l o w wel l above the shelf break depth is unaffected by the canyon. In the quasi-steady stage of the flow (Figure 5.11) when t > 60 s (equivalent to 7 days after the Chapter 5. Discussion 143 in i t i a l forcing), the flow inside the canyon slows dramat ica l ly . A slow cyc lonic m o t i o n is observed inside the canyon t ravel ing along the downstream w a l l t oward the head and then i n the offshore di rect ion a long the upst ream wa l l . A cyclonic eddy is vis ible at the canyon m o u t h and this on-shore/offshore ve loc i ty inside the canyon m o u t h is comparable to the across-shelf ve loc i ty from a wider canyon (Figure 5.12) as wel l as the eddy observed at the canyon m o u t h of a short canyon i n Perenne et a l . (2001b). T h e depth of the canyon m o u t h eddy goes we l l below the measurement levels (4 c m or equivalent to 400 m i n the oceanic scale). T h i s eddy is formed due to a combina t ion of the inherent shear i n the flow, the side w a l l boundary layer and the s t re tching f luid columns as they enter the canyon. T h e same offshore flow along the upst ream w a l l is observed i n this case as is vis ible i n the first case. F l o w wel l above the shelf break depth is unaffected by the canyon. Rossby N u m b e r A s mentioned i n Chap te r 4, the Rossby number used for this l abora to ry exper iment as one of the p r i m a r y scal ing parameters m a y not have been the most suitable choice as the flow shows separat ion i n most runs regardless of veloci ty or s trat i f icat ion. T h i s scale was used as i t was the p r i m a r y scal ing parameter used i n most short canyon studies. In order to p roper ly characterize the flow a new scale needs to be der ived for the flow. Forc ing mechanisms of different stages of the flow T h e two dis t inct stages of the flow may be influenced by several different factors. E a c h different poss ib i l i ty w i l l be discussed and results w i l l show whether or not these are possible factors affecting the flow. Change in Incident velocity T h e two dis t inct stages of the flow m a y be influenced by changes i n the incident ve loc i ty off the shelf break. I n order to access th is difference, the ve loc i ty off the shelf break was calcula ted for U = 0.5 c m s _ 1 at 30 s and again at 60 s. B y t r ack ing five particles Chapter 5. Discussion 144 i n each case, a mean veloc i ty was calculated of 0.563 and 0.561 c m s _ 1 for flow at 30 s and 60 s, respectively. T h e difference between the two velocit ies (0.002 c m s _ 1 ) is we l l below the error i n the part icle t rack ing and ca lcu la t ion ( ± 0.06 c m s _ 1 ) . Therefore, the ve loc i ty off the shelf does not change significantly between the two stages. Change in shelf velocity There is another forcing mechanism that m a y be causing the change i n flow dynamics i n the canyon between the two different stages. T h i s possible forcing mechanism is the fast spin-up of flow over the shelf. Since the flow on the shelf is a lready flowing at a slower ve loc i ty than the offshore flow, the shelf flow w i l l spin-up much faster than flow offshore. T h i s spin-up w i l l reduce the ve loc i ty on the shelf as wel l as flow inside the canyon. In order to test this hypothesis, flow far away from the canyon, on the shelf, at 60 s is compared w i t h flow away from the canyon, on the shelf, at 30 s (as i n F igu re 4.1). T h e veloci ty after 60 s on the shelf shows a decrease from the shelf break toward the edge of the tank (Figure 5.13). T h e form of this decrease is expected since the depths are shallowest at the tank edge and flow w i l l spin-up the fastest at this point . However, this decrease is not large enough to account for such a large (quali tat ive) change i n the i n the flow dynamics . Acceleration vs. Steady state For the first 27.3 s i n the experiment , the tank is accelerating. After this t ime, the ro ta t ion rate of the tank is constant. T h e fluid, however, is s t i l l adjust ing to this change after 30 s and may be exh ib i t ing the t ime dependent terms associated w i t h the accelerat ion appl ied to the f luid i n order to drive the incident flow. T h e difference between the two stages described above may be a result of the first stage being taken d i rec t ly after the accelerat ion of the flow (and m a y s t i l l be exh ib i t ing t ime dependent terms) whi le the second stage is more representative of the steady state i n the canyon. T h e second steady stage of the flow agrees w i t h results observed when the ro ta t ion rate of the tank was increased constant ly (after the i n i t i a l 27.3 s increase) over 1000 s to create a steady state. Chapter 5. Discussion 145 T h e difference between the two flows is the amount of upwel l ing. In the case where the ro ta t ion rate of the tank remains constant after 27.3 s, upwel l ing is reduced signif icant ly after 60 s. In the dye r u n where the ro ta t ion rate of the tank increased constantly, upwel l ing occur red cont inuous ly at the m o u t h of the canyon. W a v e P r o p a g a t i o n A n o t h e r poss ibi l i ty for the difference between the flows is the propagat ion of waves i n the opposite d i rec t ion to the flow. A s discussed i n A l l e n (2000), the waves propagated from the downst ream side of the canyon. A s these waves follow the canyon r i m topography, they reduce the amount of upwel l ing onto the shelf, on the downst ream r i m of the canyon. U p s t r e a m of the canyon, these waves cause the flow to t u r n i n the offshore d i rec t ion, thereby reducing upwel l ing (downstream) as wel l as water co lumn stretching (upstream). Evidence from the labora tory results has shown that after 60 s, upwel l ing at the downst ream m o u t h of the canyon is reduced compared w i t h the flow at 30 s. Af te r 60 s, water c o l u m n stretching is an impor tan t mechanism as shown by the decrease i n canyon m o u t h eddy v o r t i c i t y w i t h s t ra t i f icat ion. D i r ec t l y upst ream of the canyon, the veloci ty at 30 s and 60 s (Figures 5.9 and 5.14) is slower t han the ve loc i ty away from the canyon. A significant change i n flow d i rec t ion ( in the offshore d i rec t ion or opposite to the incident flow) is not observed upst ream of the canyon. Therefore, a significant reduct ion i n s tretching is not evident from these results a l though the flow di rec t ly ups t ream of the canyon seems to be reduced and upwel l ing decreases after 60 s. These reductions may be due, i n part, to wave propagat ion. T i l t e d I s o p y c n a l s W h e n the ro ta t ion rate of the tank is increased from Q to 1^ 2, the surface of the fluid i n the tank raises at the edges of the tank causing a subsequent t i l t of the isopycnals . T h e surface (and isopycnal) t i l t as wel l as the ro ta t ion of the tank results i n a force balance between the Cor io l i s and centrifugal force due to the ro ta t ion change as i l lus t ra ted i n F igu re 2.3. Af te r 27.3 s, the ro ta t ion rate becomes constant once again after reaching Q.2- T h i s w i l l reduce the differential Chapter 5. Discussion 146 centrifugal force ac t ing toward the edge of the tank, and, i n effect, cease upl i f t ing the isopycnals . T h e Cor io l i s Force on the relative induced flow w i l l be left and acts toward the center of the tank reducing the flow upcanyon. F r o m the dye layer t ime series results, the t ime series da ta from Pos i t ions D , F i g u r e 3.4, shows a d is t inct change i n the dye layer after the new ro ta t ion rate is reached. In the ups t ream and mid-canyon cross-sections, the dye decreases l inear ly i n depth over the first 30 s and then remains at a constant depth for the next 30 s (Figures 4.35(a) and 4.35(b)). O n the downs t ream side of the canyon, the middle of dye layer l inear ly decreases i n dep th over the first 30 s and then remains at a (mostly) constant depth for the remaining t ime series (Figure 4.35(c)). A t pos i t ion C from F igure 3.4, s l ight ly different results are observed. In the ups t ream t ime series (Figure 4.32(a)), the dye makes a gradual l inear decrease i n depth for the first 30 s after wh ich the dye seems to make a large decrease i n depth (35 s) and then remains at a constant depth. T h e mid-canyon a n d downst ream t ime series bo th follow the same change as the ups t ream t ime series a l though the large decrease i n depth occurs at s l ight ly later t imes (40 s and 50 s for the mid-canyon and downst ream t ime series, respectively). Therefore, t i l t ed isopycnals due to the increasing ro ta t ion rate have an effect on the flow after the new ro ta t ion rate has been reached. T h e t ime series results at pos i t ion D show tha t after 30 s, the dye layers r emain at a constant depth. T h i s m a y be a result of a back-pressure t e rm w h i c h reduces the i sopycnal uplift . If this is the case, this w i l l reduce the entire flow i n the canyon, thus reducing the upwel l ing i n the long canyon. U n l i k e some of the phys ica l processes discussed above, the effect due to the t i l t i ng of the isopy-cnals w i l l have an effect i n bo th long and short canyon labora tory experiments . In previous short canyon experiments, upwel l ing may be reduced due to this adjustment of the isopycnals after the forcing is complete. P rev ious experiments as discussed i n Hewet t (1998), A l l e n et a l . (2003) and M i r s h a k and A l l e n (2005) may a l l be affected by the same phys ica l mechanism w h i c h is reducing Chapter 5. Discussion 147 the flow i n this canyon. Chapter 5. Discussion 148 Upwelling at canyon head' • • • from below rim depth Figure 5.10: Initial stage of the laboratory flow. Near surface flow is unaffected by the canyon. Upwelling occurs at the head of the canyon and along the downstream rim. Flow travels in the offshore direction below the shelf break depth along the upstream wall of the canyon. Flow separation occurs at the canyon mouth between flow entering the canyon and flow traveling toward the head. The deep layer (4 cm) demonstrates inflow at the canyon mouth. The shelf break depth is 2.2 cm. Chapter 5. Discussion 149 F igure 5.11: Secondary quasi-steady stage of the labora tory flow. Near surface flow is unaffected b y the canyon. A smal l amount of upwell ing occurs close to the canyon m o u t h . F l o w travels i n the offshore d i rec t ion below the shelf break depth a long the ups t ream w a l l of the canyon. T h e canyon m o u t h eddy affected flow between 2.2 - 4 c m depth. S low cyclonic c i r cu la t ion occurs inside the canyon away f rom the m o u t h . T h e shelf break depth is 2.2 c m . Chapter 5. Discussion 150 F igure 5.12: H o r i z o n t a l ve loc i ty from a cross-section toward the head inside the m o u t h from H y u n and K l i n c k (2004) for a wider canyon for flow w i t h a R o s s b y number of 0.8. So l id and dot ted contours are onshore and offshore, respectively. (Reproduced w i t h permiss ion f rom the author) . Chapter 5. Discussion 151 0.8r 0.7-0.6r E 0.5r > CD 3 0.3 r CO CL 0.21-o o u Shelf Break 0.1 M Edge of Tank — U = (-0.0007 ± 0.0024) s"N + (0.35 ± 0.09) cm s _ 1 - U = (-0.0047 ± 0.0055) S~ 1V+ (-0.0006 ± 0.2255) cms o 40 10 20 30 wDistance away from the center of the tank [cm] 50 Figure 5.13: V e l o c i t y away from the canyon when U = 0.5 c m s - 1 , N — 2 s _ 1 after 60 s from the i n i t i a l change i n ro ta t ion rate and t racked for 20 s denoted w i t h x 's . S imi l a r measurements taken after 30 s are denoted w i t h the so l id dots and the fit of these being the sol id black l ine. So l id green l ine represents the loca t ion of the edge of the tank and the red l ine indicates the shelf break. Ve loc i ty measurements are taken from 0.5 - 2.2 c m depth using a whi te l ight sheet. Chapter 5. Discussion 152 0.8 0.7 0.6 E 0.5 o. jj 0.4 > CD ^ 0.3 •c CO 0. 0.2 0.1 1 Shelf Break Edge of Tank U = 0.0015 s" 1*r +0.26 c m s " 1 -X X X x x . x ft • X i — X • - X X x x 1 1 1 30 25 20 15 10 Distance away from tank edge [cm] Figure 5.14: Ve loc i ty upst ream of the canyon when U = 0.5 c m s - 1 , N = 2 s _ 1 after 60 s from the i n i t i a l change i n ro ta t ion rate are denoted w i t h dots. C o m p a r i n g w i t h results from F i g -ure 5.9 at 30 s (denoted w i t h x ' s ) , the ve loc i ty after 60 s is the same order of magni tude as the ve loc i ty upst ream of the canyon measured at 30 s. V e l o c i t y measurements are taken from 0.5 - 2.2 c m depth using a whi te l ight sheet. Chapter 5. Discussion 153 5.2 Laboratory Results 5.2.1 Consistency of Results T h e incident ve loc i ty spat ia l s tructure is inconsistent between the l abora to ry and the ocean wh ich may have a profound effect on the results and conclusions. In order to replicate flow i n the ocean, the flow on the shelf should be the same speed as the flow offshore. T h i s m a y be achieved by changing the depth of the water. A s the depth increases, b o t t o m fr ict ion w i l l take longer to slow the flow down. A n o t h e r poss ib i l i ty is to r u n the tank i n the steady state in 'o rde r to remove any transients i n the veloci ty field (even i f the spat ia l s tructure of the ve loc i ty field is sheared). A n o t h e r issue regarding the tank ve loc i ty is that the s tudy involves the transient effect of the flow. Af ter the i n i t i a l 27.3 s, the f luid i n the tank is s lowly sp inning up, once again, and therefore the veloci ty decreases over t ime. A steady state experiment was carr ied out and proves to be a useful var ia t ion of the experiment . A s w i t h M i r s h a k (2001), the l abora tory results were contamina ted w i t h a per iodic osc i l la t ion which at low incident velocities great ly affects the flow v i sua l iza t ion . T h e osc i l l a t ion is due to the insert ion of the particles as wel l as, to a lesser degree, due to a misa l ignment of the t ank to the axis of ro ta t ion . W h e n the particles are inserted into the water, the effect of d ropp ing sma l l spoonfuls of the s lur ry mix tu re (Photof lo/par t ic les) causes a dis turbance i n the t ank w h i c h is ampli f ied by the ro ta t ion of the tank. Osci l la t ions caused by inser t ing part icles into the t ank can be reduced by al lowing the tank to spin-up for another 15-20 minutes. T h e par t ic le density throughout the images is inconsistent and i n order for an entire representa-t ion of the flow, the particles need to be dispersed evenly throughout the shelf/slope region. There is, perhaps, an underes t imat ion or under-representation of the flow close to the canyon head, and regions close to the tank wa l l . However, difficulty arises since the image qua l i t y decreases w i t h increased part icle density as the l ight sheet is obscured before i t reaches the canyon region w i t h Chapter 5. Discussion 154 increased part icle density. T h e da ta from the part icle t r ack ing also contains a lot of scatter and for a more accurate analysis of the flow, part icle image ve loc imetry techniques m a y reduce the size of the errors. D y e is useful as an imag ing too l as i t can be placed at any loca t ion required for measurement. P rob lems arise when using dye as the densi ty of the water increases s l igh t ly when add ing the U r a n i n e powder. A useful experiment wou ld be to place a syringe just below the r i m depth at the head of the canyon to visual ize the flow at this loca t ion (due to the possible under-representat ion by the part icles) . 5.2.2 Image Quality and Resolution T h e image qua l i ty from the video camera (720 X 480) is average but w i t h more sophis t icated cameras can be improved wh ich w i l l reduce the error i n the par t ic le t r ack ing results. T h e most serious prob lem w i t h the image qua l i ty is the resolut ion of colour and is discussed i n deta i l i n Sect ion 4.2. W h e n s t ra t i f icat ion increases, the index of refraction increases and the l ight sheet thickness decreases when i t reaches the shelf. A s tandard thickness of the l ight sheet needs to be main ta ined regardless of s t rat i f icat ion. 5.3 Future Work T h e l abora tory work that may improve and a id i n the unders tanding of these results is the compre-hensive s tudy of the flow at the canyon head. T h i s wou ld involved p lac ing dye just below the canyon r i m depth at the head and s tudy ing the evolut ion, especial ly i n the h i g h l y s trat i f ied cases where the upwel l ing is underest imated i n this labora tory experiment. A further s tudy of the ve loc i ty profiles close to the canyon r i m on the shelf w i l l provide further unders tanding of the effect of s ingular points postulated i n A l l e n (2000). T h i s l abora to ry experiment deals w i t h the most basic flow dynamics i n the J u a n de F u c a C a n y o n Chapter 5. Discussion 155 assuming previous scales used i n other submarine canyon studies. However , the Rossby number scal ing using the radius of curvature for the length scale proved to be insufficient for character iz ing the flow. A better representation of the flow may be found by w i t h further s tudy of this da t a set. Other phys ica l considerations about the J u a n de F u c a C a n y o n is tha t the flow i n and around this canyon is affected by several different mechanisms such as estuarine inpu t and tides (Foreman and T h o m s o n , 1997; Fo reman et a l . , 2000). A d d i n g these two phys ica l mechanisms to the l abora to ry experiments w i l l help i n the unders tanding of how these mechanisms suppress or enhance upwel l ing as wel l as the generation of vor t i c i ty i n the canyon. T h e dominant flow field used i n this experiment is to m i m i c summer condi t ions off the coast of Vancouver Is land. H o w w i l l this be changed when the flow is reversed? W i l l the canyon m o u t h eddy s t i l l form and how w i l l i t compare i n size and vor t i c i ty? These are a l l questions tha t can be answered w i t h changes to the labora tory set-up and w i l l further the knowledge and unders tanding of J u a n de F u c a C a n y o n and long canyons i n general. 156 Chapter 6 Conclusions T h e l abora to ry experiment of a long canyon provided useful in format ion on the flow dynamics i n a long canyon i n the ocean. T h e deepest depth of upwell ing, when Ro = 0.24, is 2.6 c m wh ich corresponds to 260 m i n the real ocean. T h e deep canyon vor t i c i ty (> 4 c m w h i c h corresponds to 400 m i n the real ocean) is s imi lar to the vor t i c i ty of the eddy observed at the shelf break depth and increases w i t h increasing incident flow ve loc i ty and decreases w i t h increas ing s t ra t i f icat ion. T h e greatest area of upwel l ing at velocities match ing that of J u a n de F u c a C a n y o n is close to the m o u t h along the downst ream r i m of the canyon. T h e size of this region increases as incident ve loc i ty increases. A t a Rossby number of 1.5, upwel l ing is observed along the entire downs t ream r i m as wel l as over the canyon head. L o n g canyons were shown to provide greater upwel l ing flux t h a n short canyons w i t h s imi lar Rossby numbers. T h e canyon m o u t h eddy is apparent approx imate ly 7-8 iner t ia l periods after the forcing is in i t i a ted and is found just inside the m o u t h of the canyon. T w o dis t inct stages of the flow are observed. T h e i n i t i a l stage features increased upwel l ing along the downst ream r i m and s t re tching along the upst ream side o f the canyon. T h e second stage of the flow features a cyclonic canyon m o u t h eddy along w i t h complementary cyc lonic flow inside the canyon. U p w e l l i n g decreases dur ing this second stage. T h e two dis t inc t flow features exh ib i ted i n the tank may be due to several physical processes. T h e two major factors inf luencing the flow are the t ime dependent terms i n the flow after 30 s (equivalent to 3.5 days) due to the adjustment w i t h i n the canyon. T h e second phys ica l process occurs after the ro ta t ion rate of the t ank has increased is constant. T h e isopycnals reduce their t i l t causing a back pressure t e r m w h i c h reduces the flow i n Chapter 6. Conclusions 157 the canyon (and any subsequent upwell ing). T h e incident ve loc i ty i n the tank was found to have an inherent shear w h i c h m a y be increas ing the s ignal of flow into the canyon at the m o u t h (and the vor t i c i ty of the canyon m o u t h eddy due to flow separation). However, due to the change i n vo r t i c i ty of the eddy w i t h s t ra t i f icat ion, s tretching has proved to be an impor tan t mechanism for vo r t i c i ty generation i n long canyons. F l o w separat ion is observed i n a l l exper imenta l runs and the Rossby number does not adequately characterize this flow. A new better scale needs to be derived i n order to p roper ly scale the flow i n a long submarine canyon. Fur the r s tudy a n d improvements i n the methodology w i l l enhance further work of these l abora -to ry canyons w i t h special emphasis on d r i v i n g a steady state flow. 158 References A l l e n , S. E . (2000). O n subiner t ia l flow i n submarine canyons: Effect of geometry. Journal of Geophysical Research 105(Cl), 1285-1297. A l l e n , S. E . (2004b). Rest r ic t ions on deep flow across the shelf-break and the role of submarine canyons i n faci l i ta t ing such flow. Surveys in Geophysics 25, 221-247. A l l e n , S. E . , M . S. D i n n i m a n , J . M . K l i n c k , D . D . Gorby , A . J . Hewet t , and B . M . H i c k e y (2003). 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Journal of Fluid Mechan-ics 20(3), 383-399. Wolf , A . V . , M . G . B r o w n , and P . G . Prent iss (1978). CRC Handbook of Chemistry and Physics (59 ed.). 163 Appendix A Equations Describing Canyon Shape T h e canyon used i n the lab experiment is designed to resemble J u a n de F u c a C a n y o n and is composed of an add i t ion of three hyperbol ic tangent functions, one for each section of the canyon (as ind ica ted by open boxes i n F igu re 3.2). A.1 Canyon Depth T h e depth along the canyon axis is denned by ^center — ifhead ~\~ kraid—canyon ~\~ ^ m o u t h ) * C2 C3 (A.1) where h-head = tank h m i d c a n y o n — t anh h m o u t h = t anh y - Lss ~y-Ws Sm9 y-La C l (A.2) (A.3) (A.4) where y is the loca t ion i n the tank, c-i is a constant to increase the entire scale ( in the ver t ical) of the depth function (120), c 3 is a ver t ica l constant to move the canyon to the correct s ta r t ing depth at the coast (480.5 m) , Lss is the length of the slope at the head of the canyon (18.6 k m ) , Sss defines Appendix A. Equations Describing Canyon Shape 164 the slope at the canyon head (5000 m) , Ws is the hor izonta l length of the shelf break (68.6 k m ) , Sms defines the angle of the slope i n the middle of the canyon (10 k m ) , Ci is a constant to scale the length of the midd le canyon depth (2.5), Las is the length of the slope at the m o u t h of the canyon (35 k m ) , and Sas defines the angle of the slope at the canyon m o u t h (10 k m ) , T h e center depth of the canyon is a smooth function (Figure A . 1 ) . - i 1 r \ i i i i 1 1 '— 0 10 20 30 40 50 60 70 distance starting from canyon head [km] Figure A . 1 : C a n y o n center depth function i n the field scale. A.2 Canyon Width T h e canyon w i d t h varies depending on locat ion. A w a y from the canyon, the w i d t h is set to equal one such that i t w i l l not have any affect on the geometry of the topography. Offshore of the shelf break, the w i d t h is given by \y-(ws-wlby Width = W - Wcl + r i • W, lb (A.5) for y>Ws Appendix A. Equations Describing Canyon Shape 165 where W is the mean w i d t h of the canyon (12 k m ) , Wc\ is a constant (4 k m ) , r i is a constant (300 m) and Wu, is the w i d t h of the canyon at m i d canyon (12.8 k m ) . F r o m the head of the canyon to the canyon entrance at the mouth , the w i d t h is f W-Wc2 + r2 Width = y-(W.-L+Wlc) y 1/4 c 4 (1 m)V4 (A.6) for y < W s + Wic where W c 2 is a constant (5 k m ) , r2 is a constant (100 m) , L is the length of the canyon (57 k m ) , W i c is the w i d t h of the slope at the canyon m o u t h (13 km) and C 4 is a constant (14.5 m ) . A.3 Canyon Function T h e canyon w i d t h is combined w i t h the depth and the exponent ia l form of the val ley shape of the canyon such that h — haway from canyon 4* [^center haU}ay from canyon] ^Xp( ^^y^) (A.7) A w a y from a l l canyon topography, the region takes the shape of h = d c + ( A ^ ) y ( A . 8 ) where dc is the depth of the cont inental shelf at the coast (50 m) and ds is the dep th of the shelf break (180 m) . T h e final version of the canyon topography is as shown i n F igu re 3.2. % This i s a matlab s c r i p t that generates the long canyon '/, used i n the laboratory experiment '/. LIST OF C0NSTANTS-'/, Dimensions of g r i d nx=400; ny=400; nz=8; '/, Nominal depth of model (m) Appendix A. Equations Describing Canyon Shape 166 Hd=900; % Length of canyon (m) L=57e3; '/, Width of canyon (m) W=12e3; '/. depth of she l f at coast (m) dc = 50; depth of shelfbreak (m) ds = 180; '/„ width of shelfbreak (m) Ws=68.6e3; '/, width of slope (m) Wl=33e3; '/, width of slope at three d i f f e r e n t regions of canyon (m) Wla=22e3; Wlb=12.8e3; Wlc=13e3; '/, length of canyon axis : shoresect ion (m) Lss = 18.6e3; '/, length of canyon axis : abyssa lsect ion (m) Las = 35e3; '/, smoothness of slope of canyon axis : shoresect ion (m) Sss = 5e3; '/, smoothness of slope of canyon axis : midsect ion (m) Sms = 10e3; '/, smoothness of slope of canyon axis : abyssa lsect ion (m) Sas = 10e5; '/, Hor izonta l r e s o l u t i o n (m) dx=5e3/4; '/, Rotat ion rate (1/s) f=le-4; '/, S t r a t i f i c a t i o n (1/s) N=7.5e-3; '/, Grav i ty g=9.8i; */. E . O . S . alpha=2.e-4; '/, constants: '/. r a t i o of depth of canyon middle sec t ion depth of she l f slope c l = 2.5; 7, constants for s e t t i n g depth to correct l o c a t i o n c2 = 120; c3 = 480.5; c4 = 14.5; '/, width constant '/o width constants wcl = 4e3; wc2 = 5e3; r l = 0.3e3; */. width r a t i o Appendix A. Equations Describing Canyon Shape 167 r2 = 0.1e3; t width r a t i o I CALCULATIONS Tz=N~2/(g*alpha); dz=Hd/nz; x=(l:nx)*dx;x=x-mean(x); y=(l:ny)*dx;y=y; z=-dz/2:-dz:-Hd; [Y,X]=meshgrid(y,x); % DEPTH OF CANYON '/, depth away from the canyon fo r j=l:ny i f y(j)>Ws+Wla; ha(j)=Hd; '/, depth of the abyssal region e l s e i f y(j)>Ws; ha(j)=ds+(Hd-ds)*(y(j)-Ws)/Wla; '/, depth of the slope e l s e i f y(j)<Ws; ha(j)=dc+(ds-dc)*y(j)/Ws; depth of the continental shelf end; end; '/, depth along the canyon axis he = -(tanh((y-Lss)/Sss)+tanh((y-Ws)/Sms)*cl+tanh((y-Las)/Sas))*c2-c3; '/, depth away from slope/shelf region but along axis for k=75:400; hc(k)=-Hd; end; % WIDTH OF CANYON k=l; f o r j=l:ny '/, away from the canyon: set == 1 such that nothing happens i f y(j)>Ws+Wla; Wp(j)=l; '/, beyond the shelf break depth e l s e i f y(j)>Ws; Wp(j)= W-wcl + rl*(y(j)-(Ws-Wlb))/(Wlb); '/, from the entrance of the canyon toward the head e l s e i f y(j)<Ws+Wlc; Wp(j)= (W-wc2 + r2*(y(j)-(Ws-L+Wlc))/Wlc)*y(j)*.25/c4; end; end; '/. CANYON SHAPE (WIDTH and DEPTH) for i=l:nx fo r j=l:ny h ( i , j ) = ha(j)+ ( - h c ( j ) - h a ( j ) ) * e x p ( - x ( i ) * x ( i ) * x ( i ) * x ( i ) / ( W p ( j ) - 4 ) ) ; i f y(j)<Ws-L; h(i,j)=dc+(ds-dc)*y(j)/Ws; end; end; end; h=-h; Appendix A. Equations Describing Canyon Shape 168 [cs .hf ig] =contour(h/100,10); ax is ( [0 85 160 230]); axis equal c l a b e l ( c s , h f i g , ' m a n u a l ' ) % add the scale ( in cm) of the canyon onto the f igure x lab=ge t (gca , 'x t i ck ' ) ; y l a b = g e t ( g c a , ' y t i c k ' ) ; xconv = 16.1/(55.517-13.145); xax = ([0:10:80])*xconv + 1.40354; yax = ( [160:10:230]-200)*6.5/16; set (gca , ' x t i c k l a b e l ' , s tr2num(sprintf ('/ /,2.3g \ n ' ,xax))) set (gca, ' y t i c k l a b e l ' ,str2num(sprintf ( ' ° / ,2 .2g \ n ' ,yax))) 169 Appendix B Image Processing techniques B.l White light sheet images T h e images from the whi te hor izonta l l ight sheet are processed by choosing a t ime in te rva l (ranging between 1.5 - 6 s), and i n d i v i d u a l images are then taken from this range and processed. F i r s t , a background image is subtracted from the or ig ina l to remove non-moving part icles and the effect of the l ight sheet reflecting on the topography. T h e n , the image intensi ty is adjusted to highl ight the l i t part icles and the da ta is then normal ized . For a set i n i t i a l t ime (ranging between 1 - 3 s), the posit ions i n the image wh ich are colored (having color intensities greater tha t 0.2) are set to equal 0.5. T h i s marks the i n i t i a l posit ions of the particles w i t h gray. Af ter this i n i t i a l t ime interval , the posit ions i n the image wh ich are colored (having color intensities greater t h a n 0.2) are set to 1. T h i s marks the latter particles w i t h black. These images (ranging between 1.5 - 6 s) are then combined to produce an image w i t h par t ic le streaks and the i n i t i a l posit ions of the streaks denoted w i t h gray. T h e scale of the image is then added and an out l ine of the shelf break dep th is added to the image. B.2 Dye images O n l y the green value from the dye images is used since the dye, itself, is green. T h e images are rota ted such tha t the image plane is oriented w i t h the upst ream side of the canyon on the left hand side of the image and that the hor izonta l axis is level . A n upper and lower threshold is chosen for each dye r u n i n order to isolate the upper and lower bounds of the dye layer. T h e images are then adjusted to this threshold denot ing the top and b o t t o m layer of the dye w i t h a black l ine. T h e resul t ing images show the progression of the top and bo t t om of the dye layer over t ime. Appendix C Streak imag Appendix C. Streak images 171 F igure C . 1 : Streak images of for velocities between at 30 and 60 s of a) a n d b) 0.15 c m s _ 1 , c) and d) 0.3 cm s - 1 , e) and f) 0.5 c m s " 1 , g) and h) 0.6 cm s _ 1 , and i) a n d j ) 1.5 cm s - 1 over a 3 s in terval . Images on the left hand side are at 30 s, and images o n the r ight are at 60 s. In i t i a l par t ic le locations are denoted by grey streaks and further par t ic le locat ions are black. Shelf break depth (2.2 cm) marked w i t h a so l id l ine contour . A x e s labels are i n cm . Appendix D 172 Boundary layer model T h e fol lowing p rogram is F O R T R A N code developed for runn ing a bounda ry layer mode l follow-ing the h y d r o d y n a m i c equations for a flow along a slope i n a strat if ied f luid (S. A l l e n , personal communica t ion) . Resul ts are shown i n Figures 4.11 and 4.12 E K M A N . F : : p rog ram ekman p a r a m e t e r (nvp=100) r e a l * 8 u ( n v p ) , v ( n v p ) , r h o ( n v p ) r e a l * 8 u n ( n v p ) , v n ( n v p ) , r h o n ( n v p ) p a r a m e t e r ( f = 1 . 5 , A = l e - 6 , d z = 0 . 0 2 / n v p , g = 9 . 8 , e s p = 5 * 3 . 1 4 1 6 / 1 8 0 > , rho0=1000 ,eN=2,d t=0 .01 ,ugmax=0 .012) c s e t - u p do k = l , n v p u ( k ) = 0 . v ( k ) = 0 . r h o ( k ) = 0 . enddo u ( l ) = 0 . do i t = l , 3 0 0 0 t = t + d t i f ( t . I t . 2 3 . 7 ) t h e n ug = u g m a x / 2 3 . 7 * t f o r c e = u g m a x / 2 3 . 7 e l s e Appendix D. Boundary layer model 173 ug = ugmax force = 0. endif un( l ) = 0 .0 vn( l ) = 0 .0 rhon( l ) = 0 . 0 do k=2 ,nvp- l un(k) = u(k)+dt*(f*C0S(SIN(esp))*v(k)+A*(u(k+l)-2*u(k)+u(k-D) > /(dz*dz)+force) vn(k) = v(k)+dt*(-f*COS(SIN(esp))*u(k)+f*COS(SIN(esp))*ug-g*SIN(esp)*rho(k) > /rhoO+A*(v(k+l)-2*v(k)+v(k-l)) / (dz*dz)) rhon(k) = rhon(k)+dt*(SIN(esp)*rhoO*eN*eN/g)*v(k) enddo un(nvp) = un(nvp-l) vn(nvp) = vn(nvp-l ) rhon(nvp) = rhon(nvp-l) do k=l,nvp u(k) = un(k) v(k) = vn(k) rho(k) = rhon(k) i f ( i t / 2 0 0 . e q . i t * 0 . 0 1 ) write (*,*) t , ( k - l ) * d z , u ( k ) , v ( k ) , r h o ( k ) enddo i f ( i t / 2 0 0 . e q . i t * 0 . 0 1 ) write (*,*) enddo 0PEN(2 ,FILE='u .da t ' ) do i = l , 1 0 0 write (2 ,*) u ( i ) enddo c lose (2) 0 P E N ( 2 , F I L E = ' v . d a t ' ) do i = l , 1 0 0 write (2 ,* ) v ( i ) enddo c lose (2) Appendix D. Boundary layer model 174 OPEN(2,FILE='rho.dat') do i=l ,100 write (2,*) rho ( i ) enddo close(2) OPEN(2,FILE='force.dat ' ) do i=l ,100 write (2,*) force enddo close(2) end Appendix E Dye Depth Data U p s t r e a m M i d - C a n y o n Downs t ream Shelf T M B T ' M B T M B T M B A 0.04 0.02 0.03 0.05 0.05 0.04 0.04 0.08 0.04 0.01 0.02 0 B 0.33 0.26 0.18 0.33 0.46 0.23 0.23 0.31 0.18 0 0.03 0 C 0.64 -0.08* 0.27 0.33 -0.14* 0.37 0.35 -0.11* 0.29 0.12 0.02 0.01 D 0.47 0.28 0.06 0.30 0.34 0.32 0.20 0.31 0.30 0.07 0.03 0.03 E 0.31 0.20 0.01 0.44 0.40 0.32 0.30 0.11 0.01 -0.17+ -0.01+ -0.01+ E( I I ) -0.06 0.09 0.08 -0.26 -0.14 0.08 -0.18 -0.29 0.08 -0.08 -0.08 -0.06 Tab le E . l : Change i n depth [cm] of the dye from 0 s to 60 s i n the hor izonta l dye layer where the layer is spl i t up into three components: the top ( T ) , midd le ( M ) and b o t t o m (B) of the dye layer. Ups t r eam, M i d - C a n y o n , Downs t ream and Shelf represent the locat ions of the cross-sections th rough the images. Pos i t ions A , B , C , D , and E represent the locations of the l ight sheet as shown i n F i g u r e 3.4. L o c a t i o n E( I I ) represents the da ta obta ined at pos i t ion E w i t h a s l ight ly shallower dye layer than the other experiments . * Resul ts tha t are s t rongly biased toward lower values close to the end of the t ime series, + Resul ts that are inconclusive due to the large amount of scatter. No te tha t at a l l locations on the shelf, the dye is always against the topography and therefore the B changes i n depth are not significant. A l l results above have an associated measurement error of 0.05 c m . 

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