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Measurements of the velocity field in the Fraser River plume 1977

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MEASUREMENTS OF THE VELOCITY FIELD IN THE FRASER RIVER PLUME RUTH ELEANOR CORDES B-Sc. Dalhousie U n i v e r s i t y , 1973 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE THE FACULTY OF GRADUATE STUDIES IN THE DEPARTMENT OF PHYSICS AND THE INSTITUTE OF OCEANOGRAPHY We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1977 (^) Ruth Eleanor Cordis, 1977 i n In presenting th is thes is in p a r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l ica t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my wri t ten permission. Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 i ABSTRACT A program of Lagrangian v e l o c i t y measurements was c a r r i e d out i n the Fraser River plume, at the mouth of the main (south) arm of that r i v e r . The data were c o l l e c t e d over three days of equatorial t i d e s and three days of t r o p i c t i d e s during the early part of freshet (May 28-31 and June h-6, 197*0 • Mini-Fix p o s i t i o n i n g was used to hand-record positions of the drogues. The data were keypunched and checked f o r e r r o r s , and smoothed po s i t i o n s and v e l o c i t i e s were i n t e r p o l a t e d between the observed points. The experimental data give a more d e t a i l e d d e s c r i p t i o n of the s p a t i a l and temporal v a r i a t i o n s of flow i n the plume than was previously a v a i l a b l e . Tides were found to be the dominant factor c o n t r o l l i n g the flow. The v e l o c i t y f i e l d s measured on s i m i l a r stages of the t i d e were compared and contrasted, noting the e f f e c t s of winds and C o r i o l i s f o r c e . Composite v e l o c i t y f i e l d s were prepared by averaging the data from s i m i l a r t i d a l phases. Plots of v e l o c i t y components as a function of distance were prepared to correspond to most of the composite v e l o c i t y f i e l d s ; these provided an alternate way of looking at the r e s u l t s . Examination of the h o r i z o n t a l divergence y i e l d e d estimates of the entrainment v e l o c i t y consistent with those of other i n v e s t i g a t o r s . i i TABLE OF CONTENTS Page ABSTRACT i LIST OF FIGURES i i i ACKNOWLEDGEMENT v i i CHAPTER 1 INTRODUCTION 1 CHAPTER 2 THE EXPERIMENT 12 CHAPTER 3 THE DATA ANALYSIS AND METHOD OF PRESENTATION 25 CHAPTER h RESULTS 36 CHAPTER 5 SUMMARY AND CONCLUSIONS 127 LIST OF REFERENCES . 136 i i i LIST OF FIGURES Page Figure 1 .1 Map of the S t r a i t of Georgia 2 1 .2 Discharge from the Fraser River, 1974 k 1 .3 Map of the area . near the mouth of the Fraser River 5 1 .k Graphs of t i d e height at Tsawwassen 7 2 .1 Map of the southern S t r a i t with the Mini-Fix g r i d 13 2 .2 Schematic diagram of a . drogue 17 2 .3 Sample l o g sheet - observer's copy 19 2 .4 Sample l o g sheet - co n t r o l copy 21 2 .5 Sample hand pl o t of f l o a t paths 22 h. .1 Tide height and wind v e l o c i t y f o r Week 1 38 k, .2 Path l i n e s , Set 2 ho U. 3 Path l i n e s , Set 6 kl h. .1+ V e l o c i t y f i e l d s , Sets 2 and 6, near lower low t i d e h2 k. • 5 Composite v e l o c i t y f i e l d , Sets 2 and 6, time sampling h5 h. .6 Composite v e l o c i t y f i e l d , Sets 2 and 6, distance samplini s hi h. • 7 Path l i n e s , Set 4 h9 h. .8 Path l i n e s , Set 4 50 k. 9 V e l o c i t y f i e l d , Set h, on small f l o o d t i d e 51 h. ,10 V e l o c i t y f i e l d , Set k, near lower high t i d e 53 h. 11 V e l o c i t y f i e l d , Set 1+, on small ebb t i d e 54 k. 12 Path l i n e s , Set 7 55 It. 13 Path l i n e s , Set 7 57 k. Ik V e l o c i t y f i e l d , Set 7, on small f l o o d t i d e 58 k. 15 V e l o c i t y f i e l d , Set 7, near lower high t i d e 59 i v LIST OF FIGURES (continued) Page Figure 4.l6 V e l o c i t y f i e l d , Set 7, small f l o o d and high t i d e , 6 l distance sampled 4.17 V e l o c i t y f i e l d , Set 7, small f l o o d and high t i d e , , 62 time sampled 4.18 V e l o c i t y f i e l d , Set 7, small ebb t i d e 63 4.19 Path l i n e s , Set 1 65 4.20 V e l o c i t y f i e l d , Set 1, small ebb t i d e 66 4.21 Composite v e l o c i t y f i e l d , Sets 4 and 7» small f l o o d 67 t i d e 4.22 Composite v e l o c i t y f i e l d , Sets 1, 4 and 7, small ebb 69 t i d e 4.23 Path l i n e s , Set 5 70 4.24 V e l o c i t y f i e l d s , Set 5, before and a f t e r higher high 71 t i d e 4.25 Path l i n e s , Set 8 73 4.26 V e l o c i t y f i e l d , Set 8, before higher high t i d e 74 4.27 V e l o c i t y f i e l d , Set 8, a f t e r higher high t i d e 76 4.28 Path l i n e s , Set 3 77 4.29 V e l o c i t y f i e l d , Set 3, a f t e r higher high t i d e 79 4.30 Composite v e l o c i t y f i e l d , Sets 5 and 8, before 80 higher high t i d e 4.31 Composite v e l o c i t y f i e l d , Sets 5 and 8, a f t e r 8 l higher high t i d e 4.32 Tide height and wind v e l o c i t y f o r Week 2 82 4.33 Path l i n e s , Set 12 84 4.34 V e l o c i t y f i e l d s , Set 12, s t a r t of large ebb 85 4.35 Path l i n e s , Set 16 87 V LIST OF FIGURES (continued) Page Figure 4.36 V e l o c i t y f i e l d s , Set l6, s t a r t of large ebb 88 4.37 Composite v e l o c i t y f i e l d , Sets 12 and l6, s t a r t 89 of large'ebb 4.38 Path l i n e s , Sets l6 and 17 90 4.39 V e l o c i t y f i e l d , Sets l6 and 17, end of large ebb 92 4.40 Path l i n e s , Sets 13 and 9 94 4.41 V e l o c i t y f i e l d s , Sets 13 and 9, end of large ebb 95 4.42 Composite v e l o c i t y f i e l d , Sets 9, 13, 16 and 17, 97 end of large ebb 4.43 Path l i n e s , Sets 10 and l4 98 4.44 V e l o c i t y f i e l d s , Sets 10 and 14,. s t a r t of large f l o o d 99 4.45 Path l i n e s and v e l o c i t y f i e l d , Set 18, star t of 100 large f l o o d 4.46 Composite v e l o c i t y f i e l d , Sets 10, 14 and 18, s t a r t 102 of large f l o o d 4.47 Path l i n e s , Sets 11 and 15 103 4.48 V e l o c i t y f i e l d s , Sets 11 and 15, end of large f l o o d 105 4.49 V e l o c i t y versus distance p l o t s , Sets 2 and 6 108 4.50 V e l o c i t y versus distance p l o t s , Sets 4 and 7 110 4.51 V e l o c i t y versus distance p l o t s , Sets 1, 4 and 7 111 4.52 V e l o c i t y versus distance p l o t s , Sets 12 and 16 113 4.53 V e l o c i t y versus distance p l o t s , Sets 9, 13, 16 and 17 115 4.54 V e l o c i t y versus distance p l o t s , Sets 10, l4 and 18 ll6 4.55 Current meter data from 1967 120 4.56 Sample c a l c u l a t i o n of Keulegan's constant 125 v i LIST OF FIGURES (continued) Page Figure 5.1 Composite v e l o c i t y f i e l d s f o r small floods and 128 ebbs, Week 1 5.2 Composite v e l o c i t y f i e l d s f o r large floods and 130 ebbs, Week 1 5.3 Composite v e l o c i t y f i e l d s f o r large ebbs and 132 floods, Week 2 v i i ACKNOWLEDGEMENT The study of the Fraser River plume was d i r e c t e d by Dr. S. Pond of the I n s t i t u t e of Oceanography, U.B.C., and Dr. P. B. Crean of the Marine Sciences Directorate of the Department of the Environment, but i t could not have been c a r r i e d out without the assistance of the many graduate students and s t a f f members of IOUBC and s t a f f members of MSD who volunteered to act as observers. They a l l deserve many thanks for t h e i r contributions to the success of the project. Thanks are also extended to MSD f o r providing the Eichardson, the two A r c t i c launches, and crews f o r these three v e s s e l s , as w e l l as f o r chartering the Swift Invader f o r our use. The loan of the Caligus and crew from the Nanaimo laboratory of the F i s h e r i e s Research Board was arranged through the generous cooperation of Dr. J. S i b e r t . We also wish to thank the Canadian Hydrographic Service, MSD, which provided, i n s t a l l e d and maintained the Mini-Fix system. Funding for the experiment was provided by a contract from the Department of the Environment. I was supported by a postgraduate scholarship from the National Research Council and from a DoE grant. This acknowledgement would not be complete without s p e c i a l mention of those, who, as w e l l as working hard on the experiment, helped me struggle through the task of t h e s i s w r i t i n g . I am very g r a t e f u l to J. R. Buckley who provided me with a great deal of assistance i n carrying out the data a n a l y s i s . F i n a l l y , I wish to thank my supervisor, Dr. S. Pond, whose patience, encouragement and guidance were of great value to me during the preparation of t h i s t h e s i s . 1 CHAPTER 1 INTRODUCTION The S t r a i t of Georgia, shown i n Figure 1.1, i s a large water- way between Vancouver Island and the mainland of B r i t i s h Columbia. I t i s connected with the P a c i f i c Ocean to the south by passages through the Gulf Islands and San Juan Islands t o the S t r a i t of Juan de Fuca, and to the north by channels among the northern i s l a n d s . I t trends northwest- southeast, with a length of about 220 km, and an average width of 33 km (Waldichuk, 1957). The water i n the S t r a i t i s a mixture of s a l t water from the P a c i f i c and fresh water supplied by runoff and p r e c i p i t a t i o n . The l e s s dense fresh water forms a d i s t i n c t surface l a y e r over the whole S t r a i t i n summer and i t s s t a b i l i t y i s increased by heating due to sol a r r a d i a t i o n . Turbulent mixing caused by strong t i d a l currents i n the narrow entrance passages combines the fresh water with the deeper s a l t water. This water i s c a r r i e d i n t o the S t r a i t , forming the denser lower la y e r . In winter, the reduced supply of fresh water, cooling of the surface waters, and mixing by strong winds break down the surface l a y e r and create a much more homogeneous water column i n the S t r a i t ( T u l l y and Dodimead, 1957). Most of the fresh water comes from the Fraser River, the drain - age basin of which covers a large p o r t i o n of the i n t e r i o r of southern B r i t i s h Columbia. T u l l y and Dodimead (1957) c a l c u l a t e that i t supplies 80 to 85% of the fresh water flowing i n t o the S t r a i t , the re s t flowing from.small r i v e r s into the f j o r d - l i k e i n l e t s which'open into the S t r a i t . Outflow from the Fraser River varies greatly throughout the year, since a Figure 1.1 Map of the Strait of Georgia, showing it s connections to the Pacific Ocean to the north and south. The scale is approximately 1: 200000Q 3 a l a r g e p o r t i o n of the p r e c i p i t a t i o n i n i t s - drainage b a s i n f a l l s as snow i n the w i n t e r . The r i v e r c a r r i e s i t s l a r g e s t volume of water during the l a t e s p r i n g and e a r l y summer f r e s h e t , when m e l t i n g snow r a i s e s the r i v e r l e v e l , o c c a s i o n a l l y causing f l o o d i n g . There may a l s o be a secondary maximum i n the discharge i n autumn i f heavy r a i n s occur before the temperatures drop enough t o t u r n the p r e c i p i t a t i o n over most of the drainage b a s i n t o snow. The Fraser R i v e r discharge as measured at Hope f o r the year 1974 i s shown i n Figure 1.2. The t r i b u t a r i e s which enter the Fraser below Hope increase the volume by about 35% (Waldichuk, 1957). S i l t c a r r i e d by the r i v e r has b u i l t up a l a r g e d e l t a and exten- s i v e shallow banks. The f l a t , a rable l a n d of the d e l t a and the g e n t l e slopes nearby have become the s i t e of B r i t i s h Columbia's most densely populated area, Vancouver and i t s suburbs. Figure 1.3 shows the area of the r i v e r mouth, where the r i v e r d i v i d e s i n t o smaller channels as i t flows through the d e l t a . The South Arm c a r r i e s the l a r g e s t p o r t i o n of the outflow. The r i v e r ' s channel across the- banks has been found t o s h i f t over the years. To mark i t s l o c a t i o n and make n a v i g a t i o n s a f e r f o r l a r g e ships u s i n g the r i v e r the Steveston J e t t y was b u i l t i n the e a r l y 1950s. I t c o n s t r a i n s the r i v e r water from spreading t o the north u n t i l i t reaches the edge of the banks. The momentum of the f r e s h water causes i t t o remain as a j e t or plume when i t flows i n t o the S t r a i t , although there i s some spreading t o the south. The s i l t y f r e s h water of the plume forms an e a s i l y recognized surface l a y e r , o v e r r i d i n g the denser, c l e a r e r S t r a i t water. At some phases of the t i d e , the s a l t water Figure 1.2 Fraser River discharge f o r 1974, measured at Hope. During the experiment (May 28 - June 6), discharge was about 60% of the maximum attained on June 21. 5 Figure 1.3 Map of the area near the mouth of the Fraser River. The dotted l i n e s i n d i c a t e the extent of the shallow banks of the delta. The scale i s 1:250000. . 6 intrudes into the r i v e r under the fresh water, forming a s o - c a l l e d s a l t wedge. As the plume spreads over the s a l t water i n the S t r a i t , the surface l a y e r "becomes thinner. Entrainment and/or mixing of s a l t water occurs, making the surface l a y e r l e s s and l e s s well defined. Once the fresh water of the r i v e r plume has entered the S t r a i t i t i s subject to a l l the forces a f f e c t i n g the c i r c u l a t i o n there. Of primary importance are the t i d e and the wind. Tides i n the S t r a i t of Georgia are of the semidiurnal mixed v a r i e t y and are strongly d e c l i n a t i o n a l . They pass through t r o p i c and equatorial sequences ( T u l l y and Dodimead, 1957). Figure l.k shows t y p i c a l t i d e curves of the two types. The t i d a l range i s greater during the t r o p i c t i d e s , when there i s one large and one small t i d e each day. The l a r g e s t t i d a l ranges occur near the s o l s t i c e s , while the smallest ranges are observed at the times of the equinoxes. The t i d e s i n the S t r a i t are driven by those i n the P a c i f i c , with water flooding and ebbing through the channels at both the north and south ends. T i d a l f l u c t u a t i o n s at the mouth of the Fraser are driven from the southern channels, so the water moves northwest on the flo o d t i d e and southeast on the ebb. It has been observed that the currents associated with the flooding t i d e are stronger on the east side of the S t r a i t , while those of the ebb dominate on the west side. The net e f f e c t i s a counter-clockwise gyre i n the r e s i d u a l current. This hypothesis i s supported by T u l l y and Dodimead, (1957) who noted that the s t a b i l i t y of the surface l a y e r decreased with distance north from the r i v e r mouth along the east side of the S t r a i t , and continued to diminish to the south along the west side. The C o r i o l i s T Figure l.U Tide height at Tsawassen, during a. a period of e q u a t o r i a l t i d e s and b. a period of t r o p i c t i d e s . 8 force, which causes moving water to veer to'the r i g h t of i t s o r i g i n a l path i n the northern hemisphere may be responsible for t h i s i n e q u a l i t y i n the flow. Wind stress acts on the surface of the water and imparts momentum to i t . The e f f e c t of t h i s force decreases with depth. When there i s a surface layer of l e s s dense water defined by a f a i r l y sharp i n t e r f a c e , the wind stress influence w i l i be confined almost completely to the upper layer and can have quite a pronounced e f f e c t i f t h i s l a y e r i s shallow. The p r e v a i l i n g winds over the S t r a i t of Georgia are from the northwest and southeast - along the axis of the S t r a i t - but there are often l o c a l v a r i a t i o n s . A counterclockwise gyre i s often observed i n the southern S t r a i t . Since the wind stress on the water surface i s proportional to the square of the wind v e l o c i t y , strong winds have a much lar g e r e f f e c t on the v e l o c i t y of the surface water than weaker winds do. Ekman (1905) developed a t h e o r e t i c a l model of a steady wind act i n g on a homogeneous r o t a t i n g ocean. In h i s Ekman s p i r a l , the surface water moves U50 to the r i g h t of the wind d i r e c t i o n , and the v e l o c i t y of deeper water decreases i n magnitude and continues to rotate i n d i r e c t i o n . In a s i t u a t i o n l i k e the S t r a i t of Georgia the l i m i t e d fetch of the wind, i t s v a r i a b i l i t y , and the presence of a well defined surface l a y e r probably prevent the c l a s s i c a l s p i r a l from occurring; instead, one might expect the wind-driven water to move i n a d i r e c t i o n close to that of the wind, and much, of the wind influence to be confined to the surface l a y e r . Wind mixing helps to make the layer homogeneous, so the i n t e r f a c e becomes sharper and the layer more stable. 9 As the main source of fresh water for the surface l a y e r of the S t r a i t of Georgia, the Fraser River a f f e c t s the b i o l o g i c a l p r o d u c t i v i t y of the whole S t r a i t . With increased use of the r i v e r and the S t r a i t f o r both i n d u s t r i a l and r e c r e a t i o n a l purposes, bet t e r knowledge of the c i r - c u l a t i o n can help i n making decisions about such things as e f f l u e n t d i s p o s a l . For example, p o l l u t a n t s i n the r i v e r entering the S t r a i t on a strong ebb t i d e might be mostly flushed from the S t r a i t , while those entering on the flood could be pushed to the north and remain i n the S t r a i t much longer. In an attempt to understand the c i r c u l a t i o n and properties of the S t r a i t , many sets of measurements have been made. The e a r l i e s t oceanographic work i n the S t r a i t of Georgia was done by members of the Nanaimo Laboratory of the F i s h e r i e s Research Board of Canada, who began by studying aspects o f i t s b i o l o g i c a l oceanography (e.g., Fraser and Cameron, 19l6). To better understand the d i s t r i b u t i o n of f l o r a and fauna, they began to measure the p h y s i c a l properties of the water and observed some of the e f f e c t s on p r o d u c t i v i t y of the nu t r i e n t - r i c h mixed surface l a y e r generated by the Fraser. The f i r s t study of the surface c i r c u l a t i o n was made i n 1926-31, with the release of a serie s of l i n e s of d r i f t b o t t l e s . These data were examined by Waldichuk (1958), and show the basic gyral c i r c u l a t i o n , but also i n d i c a t e that large v a r i a t i o n s may occur because of the influence o f wind and t i d e . T u l l y and Dodimead (1957) analyzed data c o l l e c t e d by Carter and T u l l y i n 1931-32. They occupied a serie s of b o t t l e stations covering the S t r a i t and i t s approaches during d i f f e r e n t seasons of the year, c o l l e c t i n g data at each over a f u l l t i d a l cycle i n order to assess both d a i l y and seasonal v a r i a t i o n s . 10 Hutchinson and Lucas (l93l) summarized their work on the physical oceanography of the S t ra i t , and related plankton productivity to the physical properties. They were part icularly concerned with the Fraser River as a source of fresh water and nutrients which the plume entrains from below. More recently, studies have been directed toward an under- standing of the processes governing the c irculat ion. Newer instruments (e.g. recording current meters) and use of computers for data reduction have increased the scope of possible projects, but the complexities of the Strait s t i l l make i t d i f f i cu l t to obtain detai l in sampling. One problem which generated a great deal of study was the selection of a site for a sewerage outfa l l to serve the greater Vancouver area. Before choosing the Iona Island site near the North Arm of the Fraser River, extensive oceanographic work, supplemented by aeria l photography, was carried out in the waters near Vancouver. The photographs have been analyzed in an attempt to study the motion of the Fraser River plume (Tabata, 1972). When the sewage disposal f a c i l i t y at Iona Island was to be expanded, further study was done, involving drogue tracking, current prof i l ing with a meter, and tracking of suspended dye tracers (Tabata et al. , 1-971). In 1966 and 19&7 drogue tracking was done in the Fraser River plume, chiefly off the (main) South Arm (Giovando and Tabata, 1970). Since only one vessel was available i t was impossible to obtain a syn- optic picture of the plume. They were able to gain some knowledge of the water movement at various stages of the t ide , and to estimate the 11 e f f e c t s of the wind on the surface flow. Some current meter data was also taken i n the Fraser plume area i n 1967 a n ( l subsequent years (e.g. Tabata et al.,1910). In order to obtain more d e t a i l e d information about the move- ment of the Fraser River plume, an experiment was c a r r i e d out i n 1974 by members of the I n s t i t u t e of Oceanography, U n i v e r s i t y of B r i t i s h Columbia, (lOUBC), and the Marine Sciences Directorate (now Ocean and Aquatic A f f a i r s ) , Department of the Environment. The r i v e r has i t s greatest influence on the S t r a i t during freshet i n l a t e spring and e a r l y summer, which i s also the time much of the b i o l o g i c a l growth occurs. The experiment was thus scheduled for two 3-day periods during the beginning of freshet, i n c l u d i n g one period of equatorial t i d e s (May 28- 31) and one of t r o p i c t i d e s (June 4-6)(Fig. 1.4). The t i d e s were of near maximum range since the time selected was near the summer s o l s t i c e . Surface drogues were used to make quantitative measurements of the flow i n the plume, i n order to determine the e f f e c t s of the t i d e s , winds and other forces on the flow. As w e l l as the drogue-following work, some water property data were c o l l e c t e d with an Inter-Ocean CSTD, and a e r i a l photographs of the plume were taken. The remaining chapters of t h i s t h e s i s describe the c o l l e c t i o n , a n a l y s i s , and i n t e r p r e t a t i o n of these data. I t i s hoped that the existence of such d e t a i l e d data on an important aspect of the S t r a i t ' s c i r c u l a t i o n w i l l a i d i n planning future use of the waters. It should also be of assistance to those who are attempting to simulate aspects of the c i r c u l a t i o n by means of numerical modelling. 12 CHAPTER 2 THE EXPERIMENT In studying the water movement i n the Fraser River plume, we chose to use the Lagrangian method of t r a c k i n g f r e e - f l o a t i n g drogues. A c o l l e c t i o n of drogues which had been used by the IOUBC group working on surface c i r c u l a t i o n was a v a i l a b l e so the f i r s t major de c i s i o n to be made was how to track t h e i r p o s i t i o n s . The e a r l i e r experiments (Buckley and Pond, 1976) had used radar f o r t h i s purpose, and each f l o a t had a radar r e f l e c t o r attached to i t . By frequently photographing the radar screen and a watch, quite a large number of drogues (20 to Uo) could be tracked at once. This procedure gives a f a i r l y d e t a i l e d d e s c r i p t i o n of the flow, but since the radar set used cannot detect the drogues beyond a range of three n a u t i c a l miles, i t i s only f e a s i b l e f o r work i n r e l a t i v e l y small enclosed areas. Because of the diverging flow i n the Fraser plume area a l a r g e r range was necessary. We had to look for a system which was r e a d i l y a v a i l a b l e and would give the desired coverage. The system chosen was "Mini-Fix", which was generously loaned to us and i n s t a l l e d by the Canadian Hydrographic Service (CHS) of the Marine Sciences Directorate i n V i c t o r i a . The Mini-Fix system consists of three synchronized transmitters which produce two i n t e r s e c t i n g interference patterns. As i l l u s t r a t e d i n Figure 2.1, these form a hyperbolic g r i d which the receivers use as a coordinate system when i n d i c a t i n g t h e i r p o s i t i o n s . The receivers must be set at a known p o s i t i o n , but as they are moved they count nodal l i n e s to keep track of t h e i r current l o c a t i o n . P o s i t i o n i s displayed as 'lanes' Slave One Ik and hundredths for each of the coordinates, "Pattern 1" and "Pattern 2". The p r e c i s i o n of p o s i t i o n i n g i s ±5 f t . Based on the observed d r i f t of a f i x e d receiver at Steveston, the v a r i a t i o n over several days i s ±50 f t . and i s mainly d i u r n a l . Correction for t h i s d r i f t can be made by monitoring the p o s i t i o n displayed by a f i x e d r e c e i v e r , but was unnecessary i n t h i s experiment since the r e s u l t s are based on differences between p o s i t i o n s observed within a short time of each other. Each of the vessels used i n the operation was equipped with a r e c e i v e r , from which p o s i t i o n coordinates were recorded when a f i x was taken on a drogue. Occasionally a receiver would temporarily lose lock and a f t e r regaining s t a b i l i t y would show the wrong lane number. This lane skipping could be missed i f the observers were busy with other tasks. To watch f o r possible occurrences the vessels checked t h e i r p o s i t i o n s whenever i t was convenient against known references such as the navigation buoys or with each other. I f a lane skip had occurred i t was noted so that the data could be corrected a.nd the r e c e i v e r was reset to show the proper p o s i t i o n . It i s a c r e d i t to the members of the CHS e l e c t r o n i c s group who i n s t a l l e d and maintained the system that i t functioned so w e l l . I t had not previously been used at night and they were a f r a i d that increased sky wave transmission might cause problems then. While there was more noise than during the day, with rapid o s c i l l a t i o n s of two to f i v e hun- dredths of a lane occurring at times, lane skips occurred no more frequently. Another cause for concern was the proximity of the Van- couver International A i r p o r t to the Fraser plume area. Planes have 15 been known to cause lane skips, but we had l i t t l e trouble from that source. In a l l , l e s s than ten instances of lane skipping were detected during the whole experiment. Five boats were used to do the f l o a t t r a c k i n g . The Canadian Hydrographic Service k i n d l y lent us the Richardson, a 65 f t . survey v e s s e l , and two A r t i e launches, as well as supplying crews to operate them. The loan of the Cdligus and crew from the F i s h e r i e s Research Board B i o l o g i c a l Station i n Nanaimo was arranged by Dr. J . Si b e r t . An aluminum-hulled j e t boat, Swift Invader, of Vancouver was chartered by the Marine Sciences D i r e c t o r a t e , V i c t o r i a . I t and Caligus each had two crews and worked two s h i f t s . During the f i r s t week of the experiment we attempted to work around the clock i n two 12-hour s h i f t s . Caligus, Swift Invader, and the two launches worked the day s h i f t , while Richardson was anchored near Sand Heads at the end of the Steveston Je t t y and was used as the con t r o l centre. At night Richardson worked with Caligus and Swift Invader. To obtain better coverage of the large t i d e s which occurred during the days of the second week, the night s h i f t was dropped i n favour of morning and afternoon.shifts f o r vessels with two crews and staggered s h i f t s f o r the others. Float t r a c k i n g was done from about 6 a.m. to 9 p.m. each day. An experiment such as t h i s could not be expected to proceed without some problems. One of the launches ran aground when returning from V i c t o r i a a f t e r the weekend and was out of service f o r most of the second week. Swift Invader developed engine trouble and Richardson had e l e c t r i c a l problems, but these did not take too long to r e p a i r . On one 16 occasion during each week operations had to be stopped because of high winds. However, a much more extensive data set than any obtained previously was c o l l e c t e d . The drogues used i n the experiment were of the window-blind v a r i e t y , i n which the drag element i s a heavy p l a s t i c " s a i l " which can be r o l l e d up l i k e a window b l i n d f o r easier handling and compact storage. Figure 2.2 i s a schematic diagram of a drogue showing i t s structure and dimensions. Vachon (197*0 t e s t e d drogues of various shapes and found the window-blind drogue to have the highest drag c o e f f i c i e n t of the group. I t remains e s s e n t i a l l y perpendicular to the d i r e c t i o n of flow, o s c i l l a t i n g only i n s i t u a t i o n s with high r e l a t i v e v e l o c i t y . He noted that i n a v e r t i c a l v e l o c i t y shear the bottom of the drogue must be s u f f i c i e n t l y weighted to keep i t from r i s i n g up and e f f e c t i v e l y reducing the drag area. The shear i n the surface l a y e r forming the Fraser River plume was apparently quite pronounced, since the drogues sometimes had t i l t s of 15 degrees or so from the v e r t i c a l despite the weighting of each s a i l with an i r o n r e i n f o r c i n g rod. When there i s a v e l o c i t y shear the drogue moves at an "average" v e l o c i t y and i s t i l t e d at a small angle to the v e r t i c a l . Buckley (1977) who used the same drogues i n an e a r l i e r experiment has derived equations for the behaviour of a s a i l i n a v e r t i c a l shear by balancing the forces and torques acting on i t . Solving these equations for simple v e l o c i t y p r o f i l e s with a l l the shear i n the top two meters shows that , f or small t i l t angles, the drogue speed i s no more than 10% greater than the c a l - culated average speed for the p r o f i l e . In a l i n e a r v e l o c i t y p r o f i l e i n 17 7F Radar Reflector Snap Hook and Ring Wood 2"x2" Poly we ave Sa i l Flashing Light 2 m Aluminum Top Pole Col lar Float . C o l l a r Aluminum Bottom Pol-e '2 m Snap Hook and R i n g ^ £ - 3 m x I Re in forc ing R o d : jj Figure 2.2 Design of the surface drogues used i n t h i s experiment (after Buckley and Pond, 1976.) 18 which the speed decreases from 70 cm/s at the surface to zero at a depth of two meters, a drogue would he t i l t e d at an angle of l6°. I t s speed would be k% l a r g e r than the average water speed. Shear e f f e c t s thus seem to be small enough to be neglected. The procedure f o r taking a p o s i t i o n f i x on a f l o a t was deter- mined by the nature of the Mini-Fix system. Each boat was equipped with a receiver which indicated i t s p o s i t i o n . When the boat came up beside a f l o a t , attempting to be a standard distance away from i t , the p o s i t i o n was recorded on s p e c i a l l y prepared l o g sheets l i k e the one shown i n Figure 2.3. An Accutron watch was used for timing. Since the hundredths of lanes and seconds were changing quickly, they were recorded f i r s t , with hours, minutes and lanes being f i l l e d afterward. Occasionally, a lane number changed "between recording of the hundredths and the whole number. I f the observer d i d not notice t h i s change and correct f or i t , the recorded p o s i t i o n was i n error by one lane. This and other errors such as times out by f i v e minutes and lane skips made i t necessary to check the data c a r e f u l l y during processing. The data an a l y s i s , however, was much simpler than that for a radar p o s i t i o n i n g experiment, since the data were already i n d i g i t a l form, ready for key- punching. The long and tedious job of d i g i t i z i n g p o s i t i o n s and times from pi c t u r e s of the radar screen was eliminated. Each boat was i n charge of tracking three to s i x f l o a t s at a time. Ideal coverage involved taking a f i x on each one at l e a s t once every 20 minutes; i f p o s s i b l e , two f i x e s were taken a few minutes apart to give a measure, of i t s v e l o c i t y . To aid i n r e l o c a t i n g the f l o a t s INSTITUTE of O C E A N O G R A P H Y UNIVERSITY of BRITIS H C O L U M B I A 19 t-ld TIME s 10 1 i l l '2 i 1 3 r 1 ~b 3 1 0 o J *> 3 S 1 c 7. o ) u ft ] 5" / 0 r 1 5 r 0 Iv U 0 / D 7 •4n \ *f / ••;•!? 1 / b . i . :r 1 5 1 1 l i b 1 H } 1 r D f it I '1 3, 0 1 f n '0 1 4 / ) t; o j i b ! >U b <•> 1 ) l y s j 1 .! r ? i. "1 I A 7 I 5 "2 j •r ' • / 0 i ] b 1 ~> 0 I 5 ) 4 FLOAT NO. 12 is U2: I N 1ft 12. I P R 2 ^ 0 ) Ui 0 / I? PAT. 1 17 / 1 ) j 0 1 OJO 1 Ut-? ifio H';- »•>j- /is 1 ? I-'.' > . 1 ) Ail / vi 1 v.O / 4 3 •' \o I:? H I K '; L 5 in 1 si f / ^ :M": —t— r I R OPERATOR PAT. 2 22 — 1 — Qs0 IP /~ / ^ ?!- '-i — • ""jo i a ! o| o 0 1 P i ! : ? ^ i i —i ' < f\ \ >*, 7\?V ft ^ V 2?. 7 ?! 1 & a / S ' c ' i * > 7'',' .'J;' j >iv ii V.l* A, ,1 /' I ). 7i^p~ I 0 C B 3 1 n ' I t CS 1 3! ? 3 1 1 | i X p I J. -\ -\ 7 1. i 3. i !'-: 13 i i •3 L U 2 J -i - i ^ j J i \ I s " 7 K Figure 2.3 Copy of a log sheet recorded on the f i r s t day of the experiment by observers on the Swift Invader. Time i s recorded i n hours, minutes and seconds. The position coordinates are i n "lanes" and hundredths. I0CB stands for " i n " , "out", "check", "boat". The data were keypunched d i r e c t l y from log sheets l i k e t h i s one, 20 the observers made p l o t s of t h e i r positions'on chart overlays p r i n t e d with the Mini-Fix g r i d . In the diverging flow, f l o a t s o c c a s i o n a l l y were l o s t f o r an hour or more, but only one escaped completely. I t was l o s t one night i n high winds and rough water, but was found washed ashore on Mayne Island. To coordinate the e f f o r t s of the i n d i v i d u a l boats, a c o n t r o l centre was established on the Richardson. From time to time, the observers radioed i n t h e i r recorded f l o a t p o s i t i o n s which were copied onto l o g sheets, as i n Figure 2.h. Master p l o t s of a l l the f l o a t tracks were kept, and the people looking a f t e r c o n t r o l used them i n deciding when f l o a t s should be put i n , taken out, or have t h e i r custody t r a n s - ferred to a d i f f e r e n t vessel." Figure 2.5 i s t y p i c a l of these p l o t s . The usual plan o f a c t i o n was to have a l i n e of about f i v e f l o a t s l a i d across the r i v e r near Sand Heads perpendicular to the Steveston J e t t y . As t h i s l i n e moved outward and spread apart i n the diverging flow, gaps might be f i l l e d i n with more f l o a t s . When these f l o a t s were some distance out a second l i n e would be l a i d behind them and tracked s i m i l a r l y . When the f i r s t l i n e of f l o a t s was taken from the water, the boats would go back to the r i v e r mouth to put i n a t h i r d l i n e behind the second. Of course, things d i d not always run so smoothly as t h i s d e s c r i p t i o n may imply. There were times when the coverage was not as complete as we had hoped and gaps often occurred near s h i f t change times. In an attempt to l e a r n about the thickness of the surface l a y e r and the sharpness of the i n t e r f a c e , some water property measurements 21 INSTITUTE o f O C E A N O G R A P H Y UNIVERSITY of BRITISH C O L U M B I A DATE TIME 5 10 FLOAT NO. l 2 1 Z 5 1 4 i 4 7 1 3 o s '+ H Y 1 3 o t> 5 •A H •7 •b 3 4 5 M 6 3 3 8 4 5 '1 1 I 3 1 ?! 5 S \ 8 ! l 3 *> 0 t 1 3 "b 6 I r 1 I 3 s 2 0 1 % 3 1 5 5 1 3 5 0 I o l o u .2 1 B 8 I s ) (?, I 5 l 4 s I 1 , 3 M 2 •\ 1 1 3 1 4 5 H 2 1 S t 2 •o a & ) 5 o 9 3 \ H o 1 0 r> 'I M , 3 5 "=) S i z_ o 1 4 o H 0 •> 0 ! Hi 0 1 c 1 9 MM 1 s 4 5 1 1 1 t "7 o \ •3 4 0 °i M 1 <l 5 i L l 1 b 0 I ' i 5 3 1 b '» I H 4 i 3 2 2 s _4_ 4 JL 7 3 0 c i 3 3 I 7 < y \ 3 4 & 3 5 1 4 i i 3 5 0 5 PAT. 1 17 1 0 1 i 5 I 4 | 2 s 7 1 4 P 5 / , 1 5J7 1 . k 1 (ii / l h ! 4 :o i / S : 8 I 3 T Tic 1 3 1 \ k ' 3 sis i S ; ? V i s b sjw i Sj2> »j3j$ ^ 7 I 3J3 8!| ."Is •2. >U l ! & 1 \!S 5|7 i 4 712- l q I 7J3 I 3 M all 1 3 1 S'o \ !<-il i \ ; H|o 1 7)2. 1 \3\S 1 O 1 S l | j J 5 2 5 OPERATOR A i . PAT. 2 •2 r; 2 "7 i 5 I s z ° \ 2. I io 11' 7 1 i i ; i r i h 2- i • i f It 1 •z 1 jo 5 ?]•-/ 1 7 ij o j3 1 i k h 7.0 2- o j l 2 1 Is Z.z s; 3 7 : o n!3 2Jo'l M7 2 jo! 1 2_i (? Z\o\c 1 h h i h h cia- » I 0 C B 1 •\ 1 1 1 4 1 1 1 1 3 1 5 1 3 1 -> 1 1 1 3 3 1 2 1 2- 1 2 1 Lf 1 1 1 3 1 i s l f! 1 H 1 H \ 1 1 1 \ 1 1 1 1 1 1 NO. IN 2 8 if •7\ 13 i t ill M l Lilj H i ••1 COMMENTS Figure 2.4 Copy of a log sheet recorded on the f i r s t day of the experi- ment at the control centre on the Richardson. Included i n the data are some of the f i x e s from the log sheet i n Figure 2.3, which were radioed i n by the observers on the Swift Invader (boat 3).' Figure 2.5 Sample preliminary plot of the float tracks in Set 2, plotted on the Mini-Fix grid. The i n i t i a l posit ion of each float is c i r c l ed , the f inal one is in a box, and the time when each f ix was taken is noted. Grid lines are ten lanes apart. The Steveston Jetty i s in the upper right corner and the banks are marked by dotted l ines . The scale is 1:50000. 23 were taken. The instrument used was an Interocean CSTD (Conductivity, S a l i n i t y , Temperature, Depth recorder) belonging to Mr. A. Ages of Marine Sciences. He worked from a launch near the r i v e r mouth during the day s h i f t s of the f i r s t week, using the CSTD as he tracked a t r i a n g l e of drogues. The data were hand-recorded from the d i g i t a l display. During the nights of the f i r s t week and the days of the second week, i t was operated by Dr. P.B. Crean from the Richardson, which was equipped with a chart recorder. Due to the many problems encountered with both the CSTD and the chart recorder, the a v a i l a b l e data are l i m i t e d . The instrument's range was 0 to 100 m, so the depth accuracy was poor near the surface. The depth readout d i d not agree with estimates of the cable out for about the top f i v e meters, so accurate depths could not be assigned to measurements i n t h i s i n t e r e s t i n g zone. Better data would have been obtained i f a CSTD with a 0 to 30 m range had been a v a i l a b l e . Problems developed with the c i r c u i t r y and wires i n the cable broke, d i s r u p t i n g the measurement of temperature and c a l c u l a t i o n of s a l i n i t y . I t may be poss i b l e to extract some information from the CSTD data, but because of i t s poor q u a l i t y , i t has not been used i n t h i s t h e s i s . Unfortunately, the time spent by the observers i n t r y i n g to r e p a i r the instrument reduced t h e i r a v a i l a b i l i t y f o r t r a c k i n g f l o a t s . A e r i a l photography of the plume was done by Dr. J . Gower, on contract to the Marine Sciences Directorate. Working from a chartered plane, he flew over the plume on several occasions during the experiment taking p a i r s of pi c t u r e s with a normal and a 'fish-eye' lens. The pictures give some information on the extent of the plume, but l i t t l e on movement within i t . Sheets of cardboard which we hoped would be 2k v i s i b l e from the a i r were placed i n the water so t h e i r motion could b followed. Unfortunately, the contrast was poor and the cardboard doe not show up i n the photographs. 25 CHAPTER 3 THE DATA ANALYSIS AND METHOD OF PRESENTATION 3.1 E r r o r checking and i n t e r p o l a t i o n As mentioned i n Chapter 2, one of the advantages of using the Mini-Fix system f or f l o a t t r a c k i n g i s that the data are recorded i n d i g i t a l form, and can be keypunched d i r e c t l y from the log sheets. Two copies of the data were recorded, the f i r s t by the observers on the vessels taking the f i x e s , and the second by those at the co n t r o l centre to whom the observers radioed t h e i r data. Sample log sheets from these two copies were shown i n Figure 2.3 and Figure 2.h. Each l i n e contains the date, time, f l o a t number, and Mini-Fix p o s i t i o n coordinates, as well as information on whether the f l o a t was being put into the water, taken out, or merely checked, a number to ind i c a t e which boat took the p o s i t i o n f i x , and a running t o t a l of how many f l o a t s were i n the water. Both copies of the data were keypunched from photocopies of the o r i g i n a l l o g sheets. Since the data were recorded i n p e n c i l , some of the photo- copies were f a i n t and not e a s i l y l e g i b l e . Errors from t h i s source had to be corrected as we l l as those due to mistakes i n logging the data. In a search f o r such e r r o r s , the two copies of the data were cross-checked to locate discrepancies between them. The keypunched cards f o r each copy of each day's and night's observations were stored i n a separate f i l e on U.B.C.'s IBM 370 computer. In each f i l e , the l i n e s of data were sorted i n order of increasing f l o a t number and, for each group of l i n e s having the same f l o a t number, i n order of increasing time. The points making up each f l o a t track were then i n sequence. 26 Each p a i r of f i l e s was compared l i n e by l i n e , and whenever a discrepancy was found, an error message was printed. Reference was made to the o r i g i n a l l o g sheets to determine the correct values before the f i l e s were amended. At t h i s stage of the a n a l y s i s , an attempt was made to locate errors caused by lane skipping. A study of the records of the Mini-Fix checks made by the various vessels on known po s i t i o n s or with other boats ind i c a t e d the time i n t e r v a l s i n which skips had occurred. In order to determine the actual time of each lane skip, the p l o t of the f l o a t tracks i n question were examined. On a plo t such as P'igure 2.5, a change of one lane (100 to 150 m)is d i f f i c u l t to detect. Only changes of several lanes could be seen r e a d i l y , so further c o r r e c t i o n of lane skips had to be made l a t e r i n the a n a l y s i s . Before any u s e f u l information could be obtained from the data, the p o s i t i o n s had to be transformed from the hyperbolic Mini-Fix coordinates to a rectangular system. The Marine Sciences Directorate i n V i c t o r i a provided a computer program which would c a l c u l a t e them i n Universal Transverse Mercator (UTM) coordinates. The o r i g i n of the UTM coordinates i n the zone which includes the S t r a i t of Georgia i s at l a t i t u d e 0°, longitude 123°, but i t seemed appropriate to the data to tr a n s l a t e the o r i g i n of my coordinates to Sand Heads, making the numbers a more manageable s i z e . Over a small area the UTM coordinates are e s s e n t i a l l y rectangular, but t h e i r north-south/east-west o r i e n t a t i o n was not p a r t i c u l a r l y s u i t a b l e . A counterclockwise r o t a t i o n of 31° was done to produce a system with axes p a r a l l e l and perpendicular to the 27 Steveston J e t t y . To make the data more.easily compatible with computer programs written by J.R. Buckley, p o s i t i o n coordinates were converted from the UTM units of meters to B r i t i s h n a u t i c a l miles ( l B r i t i s h naut. mi. = 1853 m). The observed data points were now i n a workable coordinate system, but were s t i l l unevenly d i s t r i b u t e d i n time and space. Most f l o a t tracks comprised about ten p o i n t s , though some had as few as two or as many as twenty-eight. In order to obtain anything more than rough estimates of v e l o c i t i e s i n the plume, i t was desirable to f i t a smooth curve through the points making up each path l i n e . The components of v e l o c i t y at points along the curves could be found by taking the d e r i v a t i v e s of the smoothed p o s i t i o n components with respect to time. The i n t e r p o l a t i o n of x and y coordinates was done with a cubic spl i n e routine described by Madderom (1974). It makes use of a method given by Reinsch (1971). The method allows the s p e c i f i c a t i o n of an error i n each ordinate, so that the f i t t e d curve need not pass exactly through the given points. The f i t t e d curve i s c o n t r o l l e d by a para- meter which sets a l i m i t on the normalized sum of the squares of the differences between the given values and the f i t t e d ones. Subject to t h i s constraint the curvature of the f i t t e d curve i s also minimized, that i s , the smoothest possible curve i s f i t t e d , which s a t i s f i e s the imposed l e a s t square error l i m i t . The error s p e c i f i e d for each p o s i t i o n coordinate was ±0.01 naut. mi. (l8.5 m) , which had to allow f o r i n - accuracies i n recording time, as well as p o s i t i o n , since the routine 28 assumes the abscissae to be exact. The d e s c r i p t i o n of the routine suggested that the parameter c o n t r o l l i n g t o t a l normalized error should be i n the range N-(2N) 2 to N+(2N) 2, where N i s the number of observed points. A f t e r some experimentation, i t was decided that a reasonable value for the parameter f o r my data was N-(2N) 2. This value, i n com- bin a t i o n with the allowed error on each point of ±0.01 naut. mi., r e s u l t e d i n f a i r l y smooth curves which s t i l l cont reasonable amount of d e t a i l . A f t e r f i t t i n g , the curves were sampled at one minute i n t e r v a l s to obtain the i n t e r p o l a t e d data set. For the two tracks which had only two data points and thus could not be handled by the cubic s p l i n e routine, a s t r a i g h t l i n e was f i t t e d through the p o s i t i o n s . Sampling was also done at one minute i n t e r v a l s along these f l o a t tracks. The data were now i n a form which allowed more r e l i a b l e detection of errors since the components of v e l o c i t y and a c c e l e r a t i o n , the f i r s t and second derivatives of p o s i t i o n , were a v a i l a b l e . A cubic spline routine operates by f i t t i n g a cubic polynomial between each p a i r of points and matching f i r s t and second d e r i v a t i v e s at these points. The f i t t e d curves of p o s i t i o n vs time were thus very smooth, while the v e l o c i t y curves showed more v a r i a b i l i t y . The a c c e l e r a t i o n components were made up of s t r a i g h t l i n e segments. While the slopes of these l i n e s changed at the observed data points, the changes were us u a l l y not too extreme. I f a sharp change di d occur, i t often s i g n a l l e d an error i n the data. To make use of t h i s i n d i c a t o r , graphs of the i n t e r p o l a t e d components of p o s i t i o n , v e l o c i t y and a c c e l e r a t i o n as a function of time 2 9 were made f o r each f l o a t track. The p l o t t i n g was done on a 6-track analog brush chart recorder, using the d i g i t a l to analog converter of the IOUBC PDP-12 computer system. When a suspicious a c c e l e r a t i o n spike was found, reference was made to the o r i g i n a l l o g sheets. The Pattern 1 and Pattern 2 coordinates were hand-plotted as a function of time, to see i f a change of one lane or an i n t e g r a l number of minutes would lead to a smoother f l o a t track. Such changes were necessary because of recording e r r o r s , as w e l l as lane skips. With corrections made, the curve f i t t i n g and p l o t t i n g were redone. I f , as sometimes happened, the change had made the s i t u a t i o n worse, the data were re-examined. The point i n question might be discarded i f no simple c o r r e c t i o n could be found. One segment of the data which required much co r r e c t i o n was a four-hour period on June 5 when the data c o l l e c t e d by Launch 1 (Set 13, Floats 7 to 10 i n Figure 4.40a) contained several lane skips as well as recording e r r o r s . Occasionally the f i r s t observed p o s i t i o n of a f l o a t track was discarded. This was done i f the p o s i t i o n f i x had j u s t been a rough one, taken quickly as a l i n e of f l o a t s were being put i n the water, and i f a more accurate f i x had been taken soon afterward (usually within f i v e minutes). Since d i f f e r e n t vessels usually took t h e i r p o s i t i o n f i x e s at s l i g h t l y d i f f e r e n t distances from the f l o a t s , an unusually large error might occur i f two ships took f i x e s on the same f l o a t within a few minutes. In t h i s case one of the f i x e s would be discarded. 30 A f t e r several passes through the data, the points i n doubt had been e i t h e r corrected or discarded, leaving r e l a t i v e l y smooth f l o a t tracks. While a few of the " e r r o r s " may a c t u a l l y have been r e a l f l u c t - uations i n the flow, the sampling i n t h i s experiment was s u f f i c i e n t l y sparse that study of such phenomena was not f e a s i b l e . Instead, the analysis i s d i r e c t e d toward showing the large scale features of the flow pattern i n the plume. 3.2 Supplementary data: wind and t i d e It i s generally accepted that surface flow i n a s i t u a t i o n l i k e the Fraser River plume i s influenced by the l o c a l winds and t i d e s . In order to understand the observed water motion, i t was thus necessary to obtain data on the winds and t i d e s which occurred during the experiment. Although a few measurements of wind speed were recorded by Launch 1 and Caligus, a comprehensive program of wind v e l o c i t y measure- ment was not included i n the experiment. To obtain such information, the C l i m a t o l o g i c a l Information Section of the Vancouver A i r p o r t Weather O f f i c e , Atmospheric Environment Service was contacted.. There was no sing l e source which gave complete coverage of the area during the time periods i n question, so data from several stations were used to compile a composite table of wind speed and d i r e c t i o n as functions of time. The data were taken from the lighthouse reports from Sand Heads (eight readings d a i l y ) and Tsawwassen (three readings d a i l y ) , from a recording anemometer at Tsawwassen (hourly averages of wind speed and d i r e c t i o n were measured, but t h i s anemometer d i d not function properly f or part of the time), and from the routine hourly observations at the Vancouver A i r p o r t . The r e s u l t i n g composites of hourly v i n d v e l o c i t i e s are found in- Chapter 4 (Figure 4.1 and Figure 4.32). Information on the times and heights of t i d a l extremes i s found i n the Canadian Tide and Current Tables published by the Canadian Hydrographic Service. The smooth curves of t i d a l height vs time shown i n Figure 1.4 were generated from the t i d a l constants for Tsawwassen by Mr. P. Richards, a computer analyst working for Dr. P.B. Crean of MSD. 3.3 Computer generation of a "movie" of the r e s u l t s While the f l o a t tracks do contain much information about the plume's flow pattern, i n t e r p r e t a t i o n of a p l o t such as Figure 2.5 i s d i f f i c u l t . The wind and t i d e conditions may change considerably during the time involved, e f f e c t i n g changes i n the flow. To a i d i n understanding the observations, a "movie" showing the motions of the f l o a t s was displayed on the CRT screen which i s part of the IOUBC PDP-12 system, using programs developed by Mr. J.R. Buckley. Each frame of the movie shows dots representing several successive i n t e r p o l a t e d p o s i t i o n s of each f l o a t , displayed against an o u t l i n e map of the area. Since the points for each f l o a t represent pos i t i o n s at one minute i n t e r v a l s , the length of the "worm" thus created i s proportional to i t s v e l o c i t y . Each successive frame represents a time one minute l a t e r , so a new point i s added to each f l o a t track and the oldest point i s dropped. Disp l a y i n g these frames i n rapid succession showed changes i n v e l o c i t y as well as i n p o s i t i o n . 32 To make the movie more informative, the time corresponding to each frame was written on the screen, and wind v e l o c i t y and t i d e height were a.dded. The components of the wind vector were obtained by r e s o l v i n g the previously described composite hourly winds in t o north/south and east/west components and i n t e r p o l a t i n g them to values at one minute i n t e r v a l s , using a cubic sp l i n e routine. A t i d e curve was displayed, on which a moving marker in d i c a t e d the t i d e height appropriate to each frame. The area shown i n the movie was a t h i r t y kilometer square centred just south of Sand Heads. The o u t l i n e of the land areas was d i g i t i z e d from a map produced by the Geological Survey of Canada, which uses the UTM p r o j e c t i o n . The edge of the underwater banks was d i g i t i z e d from a Canadian Hydrographic Service chart of the area, i n Mercator p r o j e c t i o n . -The s l i g h t d i f f e r e n c e i n these two projections i s apparent i n the r i v e r channel, where the Steveston J e t t y on one side was from the UTM map and the banks on the other side were from the Mercator chart. The gap between them on the movie map i s narrower than i t should be. 3.h Grouping of the data and methods of presentation A f t e r viewing the movie several times, i t became apparent that the flow i n the plume was af f e c t e d p r i m a r i l y by the t i d e . To f a c i l i t a t e study of the data with regard to t i d a l phase, they were re - organized to group together the tracks of f l o a t s which had been i n s t a l l e d as a l i n e across the r i v e r mouth a.nd those which were added to the l i n e as i t moved out i n the plume. One or more of these l i n e s of f l o a t s 33 which occurred on each stage of the t i d e were considered to form a "set". The analysis then involved comparisons of sets which occurred on corresponding phases of the t i d e on d i f f e r e n t days. To allow a more l e i s u r e l y examination of the data than the movie would allow, computer programs were written to produce p l o t s on the UBC Computing Centre's Calcomp p l o t t e r . (When I moved from Vancouver to H a l i f a x , the programs were adapted f o r use on the Dalhousie U n i v e r s i t y CDC 6400 system.) F i r s t , path l i n e s f o r each l i n e of f l o a t s were p l o t t e d . (These pl o t s are shown i n the r e s u l t s , f o r example, i n Figure 4.2.) It was decided that s u f f i c i e n t d e t a i l would be retained i f only one point every f i v e minutes were p l o t t e d along each f l o a t track, instead of using the complete i n t e r p o l a t e d data set. The points corresponding to even hours and h a l f hours were marked with s p e c i a l symbols to i n d i c a t the r e l a t i v e speeds of the f l o a t s . The f l o a t s i n each set were assigned consecutive numbers, repla c i n g the numbers a c t u a l l y w r i t t e n on the f l o a t to avoid confusion on the part of the reader i n cases where a f l o a t was removed from the water and r e - i n s t a l l e d i n a d i f f e r e n t part of the plume Where a f l o a t was b r i e f l y removed for repa i r s and returned to a nearby p o s i t i o n , the two f l o a t tracks might be numbered 21a and 21b, as i n Figure 4.12b. While the data coverage was simply not complete enough to allow a general transformation to Eulerian v e l o c i t i e s from Lagrangian ones, i t was considered u s e f u l to display v e l o c i t y f i e l d s f o r the various sets of data. Each v e l o c i t y f i e l d covers a time period of 34 several hours, so the v e l o c i t i e s displayed i n d i f f e r e n t parts of the plume were not measured simultaneously. To generate a v e l o c i t y f i e l d such as Figure 4.9, the area was divided i n t o h a l f - m i l e squares by a g r i d of l i n e s p a r a l l e l and perpendicular to the Steveston J e t t y . The v e l o c i t y vector p l o t t e d at the centre of each square represents the average v e l o c i t y of a l l the drogues i n the s p e c i f i e d time i n t e r v a l which f e l l within that square. The computer printout l i s t e d the component averages, t h e i r standard deviations and the number of points used for each square. In composite v e l o c i t y f i e l d s such as Figure 4.5, data c o l l e c t e d on d i f f e r e n t days at s i m i l a r stages of the t i d e have been averaged- A l l the data points from the various sets f a l l i n g within each g r i d square were averaged i n forming the composites, rather than ju s t averaging the vectors found for each of the sets. Some thought was given to what type of sampling of the one- minute i n t e r p o l a t e d data would give a meaningful average v e l o c i t y f i e l d . One possible sampling method was taking one point every f i v e minutes, as was done i n p l o t t i n g the path l i n e s . The other method considered was to take points spaced at 0.1 mile i n t e r v a l s along the f l o a t t r a c k s . The method chosen for most of the p l o t s was the l a t t e r . The reasoning behind the choice i s discussed i n Chapter 4 with reference to Figures 4.5 and 4.6, and to Figures 4.l6 and 4.17. Much of the discussion and i n t e r p r e t a t i o n of the data i n Chapter 4 i s based on the p l o t s of path l i n e s and v e l o c i t y f i e l d s pre- sented i n Figures 4.2 to 4.31 and 4.33 to 4.48. The sets are compared and contrasted with respect to the changing e f f e c t s of t i d e and wind on the flow which they portray. For each phase of the t i d e f o r which there 35 i s s u f f i c i e n t coverage, a composite v e l o c i t y f i e l d has been generated. The flow patterns observed on the equ a t o r i a l tides of the f i r s t week were quite d i f f e r e n t from those found on the t r o p i c t i d e s during the second week, so data from the two weeks have not been averaged together. To allow examination of the data from a d i f f e r e n t viewpoint, another computer program was written to produce p l o t s of average v e l o c i t y components as a function of distance from Sand Heads. Each of the graphs displayed i n Figures 4.49 to 4.5^ corresponds to a composite v e l o c i t y f i e l d shown e a r l i e r i n Chapter 4. The data sampled at 0.1 mile i n t e r - v a ls along each f l o a t track were used, and distance from Sand Heads was c a l c u l a t e d as distance from there to the f i r s t point of the track plus distance along the track. Since i t did not seem sensible to average the low v e l o c i t i e s found near the edges of the plume with higher ones measured i n i t s centre, the f l o a t tracks were s u b j e c t i v e l y divided i n t o three groups. On each graph the three traces represent average v e l o c i t y components f o r f l o a t s i n the north, centre and south regions of the plume. The standard deviation of the data used to c a l c u l a t e each point was p r i n t e d out, and an error bar representing a t y p i c a l value of the standard deviation has been p l o t t e d beside each graph. CHAPTER k 36 RESULTS When the Fraser River flows into the S t r a i t of Georgia, the fresh water forms a surface l a y e r above the denser s a l t water. Without the confinement of the r i v e r banks and the Staveston J e t t y , the fresh water spreads out to form a plume, becoming thinner as i t diverges. F r i c t i o n between the two layers decreases i t s speed, and mixing occurs along the i n t e r f a c e between the l a y e r s . I f f r i c t i o n were the only force acting and i f the lower l a y e r were not being advected, the plume would be symmetric. The speed of the outflowing water at Sand Heads would be determined by the runoff into the r i v e r . There are several external forces which a f f e c t the v e l o c i t y of water i n the plume, and prevent the formation of a symmetric flow pattern. The C o r i o l i s force, which i s proportional to the speed of the water, gives i t an ac c e l e r a t i o n to the r i g h t of the o r i g i n a l d i r e c t i o n of flow. As the t i d e r i s e s and f a l l s the currents which i t generates move the s a l t water up and down the S t r a i t , and the f r i c t i o n a l forces between the layers cause the plume to move also. The slope of the surface i n the S t r a i t produces a pressure gradient which acts on the plume. The water l e y e l i n the r i v e r r e l a t i v e to that i n the S t r a i t a f f e c t s the speed of the outflowing fresh water. As the t i d e f a l l s , the speed of water leaving the r i v e r mouth increases u n t i l s h o r t l y before low t i d e , when so much water has l e f t the r i v e r mouth that i t s l e v e l i s lower than that i n the S t r a i t . A numerical model of the Fraser River, developed by Mr. A. Ages of the I n s t i t u t e of Ocean Sciences, P a t r i c i a Bay, B.C., p r e d i c t s 37 that the maximum outflow during a t i d a l cycle occurs about one hour before lower low water. As the water l e v e l r i s e s with the f l o o d i n g t i d e , the speed of discharge decreases and fresh water accumulates near the r i v e r mouth. Shortly before high t i d e the speed of the water leaving the r i v e r begins to increase as the continuing discharge makes the surface l e v e l at the r i v e r mouth higher than that i n the S t r a i t . Wind stress acts on the water surface and moderate to strong winds impart enough momentum to the upper layer that the plume's v e l o c i t y i s noticeably a f f e c t e d . The configuration of the banks and the Steveston J e t t y introduce v a r i a t i o n s i n the flow which complicate the s i t u a t i o n even more. This experiment has shown that the flow i n the Fraser plume i s dominated by t i d a l e f f e c t s . The f i r s t week (May 28 to 31, 1974) was a period of equatorial-type t i d e s and most of the data was taken on the small floods and ebbs. During the tropic-type t i d e s of June 4 to 6, observations were made of only the large ebb and f l o o d stages of the t i d e . The data from the two weeks are thus quite d i f f e r e n t and w i l l be discussed separately. 4.1 Week 1 - tracks and v e l o c i t i e s Graphs of the t i d e height and wind speed and d i r e c t i o n for the f i r s t week are shown i n Figure 4.1. The times when the various sets of data were obtained are i n d i c a t e d on i t . Time i s measured i n hours from midnight (PDT) on May 28, 1974. 4.1.1. Sets 2 and 6, near lower low water During the time near lower low water, the speed of the out- flowing water reaches a maximum. The plume i s deflected l e s s by f r i c t i o n a) 2 _ 38 -2 1 1 2 3 4 5 6 7 8 b) Set 1 it—I 1 1 I 1 1 1 M ( I Figure 4.1 a. Tide height at Tsawassen, b. times when the sets of data were taken and c. wind speed and d i r e c t i o n , during the f i r s t week of the experiment. Time i s measured i n hours from midnight, PDT, May 28, 197'4. 39 with the lower layer than at any other time i n the t i d a l c y c l e . The r e s u l t i n g s i m p l i c i t y of the flow at t h i s t i d a l stage makes i t a good place to "begin the examination o f the data. Observations made near lower low t i d e are Sets 2 and 6, which were obtained on the f i r s t and t h i r d days of the week. The f l o a t s i n Set 2 were i n the water from about one-half hour before lower low t i d e u n t i l almost two hours a f t e r i t . The paths of these f l o a t s (Figure h.2) were p l o t t e d from data i n t e r p o l a t e d to one point every f i v e minutes. The f l o a t s are u s u a l l y numbered i n order of i n s t a l l a t i o n , but f l o a t s added to a l i n e which i s some distance from the r i v e r mouth are given numbers consecutive with those of nearby f l o a t s . Set 2 began with the i n s t a l l a t i o n of Float 1, about three miles from Sand Heads, and Float 4, only a mile out. F l o a t s 2 and 3 were added near 1, while 5 5 6, and l a t e r 7 were put i n near 4. Almost an hour a f t e r the set began Floats 8, 9 and 10 were put i n to form a t h i r d l i n e . The f l o a t s i n Set 6 (Figure 4.3) were put i n near the r i v e r mouth about one- h a l f hour a f t e r low t i d e on the t h i r d day of the experiment. As described i n Chapter 3, v e l o c i t y f i e l d s may be generated by d i v i d i n g the area into a g r i d of squares and averaging the v e l o c i t y components of data points f a l l i n g within each square. A vector repre- senting the mean v e l o c i t y may then be p l o t t e d at the centre of the square. To i l l u s t r a t e the v a r i a t i o n s i n the flow over short time periods, each l i n e of f l o a t s i n Sets 2 and 6 was t r e a t e d as a small data set to pro- duce the superimposed v e l o c i t y f i e l d s shown i n Figure 4.4. The s o l i d arrows make up the f i e l d s corresponding to Floats 1 to 3, 4 to 7, and ho 01 -p B 2 • H o -p ir\\D r O H 0 \ 0 \ H J cooooo o-\ ON OA co cd o\cA H r - l r ~ I H H r — I H i — I i — ) H t— t— t— t-— t— t~co t-- co oo r-ir-\r-\r-{rHr-\t-\r-lr-ir-t H W f O j - 1 A \ D h - CO 0 \ 0 • H 6 i H oj o • H -P Figure h.2 Path l i n e s of f l o a t s i n Set 2, beginning at 17.0 hours, ending at 19.4 hours, i n c l u d i n g the time near lower low t i d e . Winds were near west southwest 6 knots. In t h i s and a l l l a t e r path l i n e p l o t s , the s o l i d l i n e at the upper right represents the Steveston J e t t y ; the r i v e r flows out to the south of i t . The path l i n e s are composed of i n t e r - polated points sampled every f i v e minutes. Points on the hour are marked by a box, those on the h a l f hour are indicated by a cross. The f l o a t number- near the beginning of each path l i n e corresponds to one i n the table l i s t i n g times of i n s t a l l a t i o n and removal. Figure 4.3 Path l i n e s of f l o a t s i n Set 6, beginning at 57-0 hours, ending at 58.5 hours, taken just a f t e r lower low t i d e . Winds were about northeast 7- \ \ \ V \ Figure k.h V e l o c i t y f i e l d based on the data from Set 2 (17-0 hours to 19.4 hours) and Set 6 (-57.0 hours to 58.5 hours), near lover low t i d e . The s o l i d arrows are the average v e l o c i t y vectors obtained by t r e a t i n g each l i n e of f l o a t s i n Set 2 separately; the dotted arrows correspond to Set 6. The data were inte r p o l a t e d to one point every f i v e minutes. As i n a l l subsequent v e l o c i t y f i e l d s , the Steveston Jetty i s represented by the s o l i d l i n e at the upper r i g h t . Each arrow represents the average v e l o c i t y of points which f a l l within the half-mile square surrounding the t a i l of the arrow. 43 8 to 10 of Set 2, while the dotted arrows are the velocity f i e ld for Set 6. Differences in average speed for any one square were generally 10% or less among the subsets making up Set 2, while speed variations of as much as 25% occurred between Sets 2 and 6. From the velocity f i e l d the characteristics of the flow may be noted. The greatest speeds, of about 1.7 m/s, were found near the centre of the plume and close to Sand Heads. Farther away from the r iver mouth, near the edges of the plume, speeds as low as .6 m/s were measured. This reduction in speed was probably caused by the f r i c t iona l drag of the salt water layer below, and of the slower moving surface water outside the plume. The small cross-stream component changed gradually from being down the Strait (southwest) to up the Strait (north- east) as the tide changed from ebb to flood over the two and one-half hour period during which the data was collected. The Coriol i s force, acting to the right of the veloci ty , would also be important in causing this shi f t . If the Coriol is force were acting alone on a current with an i n i t i a l speed of 1 m/s at latitude 49°N, i t would cause the water to move in a c i rc le of radius about 9 km or 5 nautical miles. The speed would remain the same, but after an hour i t s cross-channel velocity component would change by about .4 m/s. Fr ic t ion would reduce this effect somewhat, making the results of the calculation f a i r ly consistent with the observed flow. Winds during Set 2 were west-southwest to west at 6 to 7 knots, while east 15 winds were experienced during Set 6. (Since the wind data obtained from AES was in units of nautical miles per hour, this unit w i l l be used for wind speeds throughout the thesis ; 1 knot = 0.52 m/s.) hk Buckley and Pond (1916) suggest that when a well defined surface layer e x i s t s , momentum transfered from the wind to the water stays i n the upper layer and i s d i s t r i b u t e d quite evenly throughout i t . An approx- imate expression for the wind stress i s T = p C_ U 2, where p i s the a D a a i r density, C the drag c o e f f i c i e n t and U the wind speed .With p = 1.2 x 10 3 g cm 3 and C = 1.3 x 10 3 , the wind stress for a speed of 16 knots or 8 m/s i s T - 1 dyne. Acting on the top 3 meters t h i s gives an acceleration of 1 cm s 1 (about one-third of the C o r i o l i s 300 a c c e l e r a t i o n which would act on a 1 m/s current). Over a period of an hour, the wind stress would give a v e l o c i t y of 12 cm/s while a p a r c e l of water moving at 1 m/s moved 2 n a u t i c a l miles. I f the wind speed were halved, the v e l o c i t y change i n an hour would be only 3 cm/s. This change i s not large compared with the t o t a l speed or the C o r i o l i s e f f e c t . Thus the winds during Set 2 would have had l i t t l e noticeable e f f e c t on the flow, and those i n Set 6, by pushing the water s l i g h t l y to the r i g h t o f the plume a x i s , would add to the turning caused by the C o r i o l i s force and the f l o o d i n g t i d e . Figure 4.5 shows the v e l o c i t y f i e l d obtained by averaging together a l l the data i n Sets 2 and 6, using data sampled at five-minute i n t e r v a l s . This type of sampling may not be the best to use, since i t might lead to biased average v e l o c i t i e s . A quickly moving f l o a t i s only represented i n a p a r t i c u l a r h a l f - m i l e square by one or two data p o i n t s , while a f l o a t moving more slowly remains i n the square longer and biases the average toward a lower value. In an attempt to reduce t h i s problem the data were sampled at 0.1 mile i n t e r v a l s along each f l o a t 45 Figure 4.5 Composite v e l o c i t y f i e l d averaging the data from Set 2 (17.0 hours to 19.4 hours) and Set 6 (57.0 hours to 58.5 hours), taken near lover low t i d e . The data were sampled at one point every f i v e minutes. 46 track so that a f l o a t moving at any speed i s represented by about the same number of data points i n each square through which i t passed. Figure 4.6 shows the v e l o c i t y f i e l d averaged from the distance-sampled data for Sets 2 and 6. Although Figures 4.5 and h.6 are very s i m i l a r , the computer printouts which accompanied the plot s show that the speeds i n Figure h.6 are about 1% l a r g e r than those i n Figure 4.5- Since there i s l i t t l e v a r i a t i o n i n speed, among the tracks i n these sets, i t hardly matters which sampling method i s used over t h i s r e l a t i v e l y short time period. Distance sampling does give equal weight to each f l o a t t rack, and so i s a reasonable choice i n the absence of other c r i t e r i a . When averaging i s extended over a longer time period, i n which the flow pattern has changed s i g n i f i c a n t l y , the r e s u l t s from the two methods may d i f f e r quite markedly. Neither average would represent a flow f i e l d which was a c t u a l l y observed. This type of v a r i a t i o n i s noted with reference to Figures h.l6 and 4.17. A representative average over a long time period cannot be obtained i f sampling has been too nonuniform i n time and space. The average obtained i s biased toward those s i t u a t i o n s which were observed, and cannot include those which were not. Morel and Desbois (197*0 recognize t h i s problem i n t h e i r analysis of wind data obtained by tra c k i n g EOLE balloons. 4.1.2 Sets 4, 7, 1 period from lower low water through lower high water to subsequent low water Three sets of data were taken on the small f l o o d and ebb t i d e s . On the second day of the experiment Set 4 began s h o r t l y a f t e r low t i d e , spanning the fl o o d to lower high water, the subsequent ebb, and about Figure U.6 Composite v e l o c i t y f i e l d for Set 2 (17.0 hours to 19-4 hours) and Set 6 (57-0 hours to 58.5 hours), taken near lover l o v t i d e . The data were sampled at 0.1 mile i n t e r v a l s along each f l o a t track. Unless otherwise s p e c i f i e d , a l l subsequent v e l o c i t y f i e l d s w i l l be p l o t t e d from data sampled i n t h i s way. 48 three hours of the next f l o o d t i d e . Set 7 began near lower low t i d e on the t h i r d day and continued through lower high t i d e to higher low water. Operations on the f i r s t day got underway at lower high t i d e and Set 1, which continues u n t i l about an hour before lower low t i d e , i s discussed a f t e r Sets 4 and 75 since i t includes only the ebb. Var i a t i o n s i n winds and t i d a l ranges on the three days lead to differences among the three sets, so they w i l l be examined separately and then compared. The f l o a t tracks i n Set 4 are shown i n Figures 4.7 and 4.8. The f i r s t l i n e of f l o a t s ( l - 3 ) was put i n about one and one-half hours a f t e r low t i d e , followed by the second l i n e (4-10) about an hour l a t e r . While those f l o a t s were s t i l l i n the water a t h i r d l i n e ( l l - l 4 ) was put i n , and a fourth l i n e (15-18) was begun partway up the r i v e r . Just at high t i d e four f l o a t s (19-22) were put i n the water on the northern side of the plume, and over one and one-half hours l a t e r a l i n e (23-30) was put i n across the main part of the r i v e r . Two or three l i n e s were i n the water at most times so information i s a v a i l a b l e about more than one area of the plume at any one time. Figure 4.9 i s the v e l o c i t y f i e l d f o r the time from the beginning of the set to about one hour a f t e r lower high t i d e . The winds during the period were quite l i g h t at f i r s t , but eventually swung from east 4 to south-southeast 11. The flow speeds decreased from 1.1 m/s near the r i v e r mouth to .3 m/s at the western edge of the observed area as the flooding t i d e held back the r i v e r water. The v e l o c i t y was i n i t i a l l y d i r e c t e d s l i g h t l y to the south of a l i n e 49 a) 1 n a u t i c a l m i l e | 1 f l o a t t i m e t i m e b) no. i n out, 1 33.2 ^33. 9 2 3 3 . ^ 33. 9 3 2ft.3 34. 0 f l o a t t i m e t i m e no. i n o ut 4 34.1 38.1 5 34.3 35.8 6 35-3 3 8 . ^ 5 7 35-4 8 3 4 . 6 . / 36.1 9 3 > r f , 1 6 36.1 10 36.2 c) l\\ F i g u r e 4.7 P a t h l i n e s o f f l o a t s i n Set 4, on t h e r i s e t o and ebb fr o m l o w e r h i g h t i d e . a , 33.1 h o u r s t o 34.0 h o u r s , when winds were near e a s t 2 k n o t s , b , 34.1 hours t o 38.2 h o u r s , when winds were e a s t 2 t o s o u t h e a s t 11. c, 35.1 h o u r s t o 40.7 h o u r s , when winds were s o u t h e a s t 4 t o s o u t h e a s t 11. Figure 4.8 Path l i n e s of f l o a t s i n Set 4, from 37-3 hours to 43.6 hours, on the ebb to and r i s e from higher low t i d e . Winds were southeast 8 to east 12. 51 Figure k.9 V e l o c i t y f i e l d f o r Set h (33.1 hours to 38.9 hours) on the r i s e to lover high t i d e . > • 52 p a r a l l e l to the j e t t y , but the C o r i o l i s force and the flo o d i n g t i d e turned the flow toward the r i g h t , and when the wind speed increased, the turning became much more pronounced. The v e l o c i t y f i e l d shown i n Figure 4.10 i s an average of the data from lower high water to about two hours before low t i d e . The north side of the plume showed progressively more clockwise c u r l i n g and slowing, while i n the c e n t r a l and southern parts speeds increased as the t i d e began to ebb and the flow tended s l i g h t l y to the south. Slower moving f l o a t s at the end of the f l o o d t i d e gave r i s e to the smaller speeds fart h e r out i n the plume. Even the f a s t e r moving c e n t r a l part of the plume was kept from turning much to the south as the wind remained near southeast 10. The v e l o c i t y f i e l d f o r the ebbing t i d e (Figure 4.11) shows the remaining part of the floo d time plume s t i l l c u r l i n g to the north, while the drag of the ebb t i d e had overcome the wind and C o r i o l i s forces and turned the main part of the plume s l i g h t l y to the south. Speeds near the r i v e r mouth were about 1 m/s. The ebb was quite a small one and the l a s t few f l o a t s remained i n the water a f t e r the beginning of the next f l o o d , 'so the speeds seen at the end of the period were as low as .2 m/s. Set 7 began with a very large l i n e of f l o a t s (Figure 4.12a) being put i n across the r i v e r . These f l o a t s were further supplemented by those shown i n Figure 4.12b. The f l o a t tracks numbered 21a and 21b i n d i c a t e that the f l o a t was removed from the water for repa i r s and replaced soon a f t e r . The f l o a t s were i n the water from about f i v e hours 53 Figure 4.10 V e l o c i t y f i e l d for Set h (37-0 hours to 40.T hours), near lower high t i d e . Figure 4.11 V e l o c i t y f i e l d f o r Set 4 (38.9 hours to 43.6 hours), on the ebb to and r i s e from higher low t i d e . 55 f l o a t time time no- i n out 1 58.7 61.8 2 58.7 64.3 3 60.2 63.8 4 58.8 63.9 5 58.8 62.2 6 58.8 62.0 T 58.9 61.8 8 60.7 62.7 9 59.0 65.0 10 59.1 64.8 11 59.1 60.7 12 59-2 60.8 13 59.2 60.8 14 60.1 64.7 15 61.4 64-. 6 16 63.3 64.7 1 n a u t i c a l mile b) f l o a t time t ime no. i n out IT 63.6 65.8 18 63.8 65.4 19 63.8 65.6 20 61.7 63.8 21a 61.7 62.3 21b 62.5 63.8 22 61.8 63.3 Figure 4.12 Path l i n e s of f l o a t s i n Set 7, on the r i s e to and ebb from lower high t i d e , a, 58.6 hours to 65.0 hours, when winds were northeast 7 to southwest 7- b, 6l.6 hours to 65.6 hours, when winds were east 4 to southwest 7- The path l i n e s numbered 21a and 21b indicate that the f l o a t was removed b r i e f l y for repa i r s . 56 before high water to three hours a f t e r i t . Another l i n e of f l o a t s (Figure 4.13) was put i n almost two hours a f t e r high t i d e and removed just a f t e r low t i d e . As i n the analysis of Set 4, three average v e l o c i t y f i e l d s were generated: one for the r i s i n g t i d e , one for the time near the change from f l o o d to ebb, and one for the f a l l i n g t i d e . The f i r s t of these (Figure 4.l4) covers the time from the beginning of the set u n t i l just over an hour before high water. The winds during the p e r i o d were northeast 8 to east 4. The f l o a t paths curved much more evenly to the north than i n Set 4, i n which the f l o a t s moved st r a i g h t out and then curled north. Speeds at the core of the plume were about .8 m/s. The t i d a l r i s e i n Set 4 was smaller than that i n Set 7, but Set 7 began l a t e r r e l a t i v e to the low t i d e . The winds at about northeast 6 were too l i g h t to have much e f f e c t on the flow, but i f anything, they tended to oppose the turning. The previous day's winds had increased f a i r l y quickly to enhance i t . By the end of the time period, the f l o o d had slowed as high water approached and the pressure head of the r i v e r was enough to begin to overcome the force of the t i d e pushing i t back. The southern part of the plume began to swing to the south. Figure 4.15 shows the v e l o c i t y f i e l d for the time one and one-half hours before the turn of the t i d e u n t i l two hours afterward. The change i n the flow was very noticeable as the o l d part of the plume was l e f t c u r l i n g slowly around on the north side, while the main flow from the r i v e r moved o f f to the south with the ebbing t i d e . The e f f e c t was l i k e that of swinging a hose back and f o r t h ; the water continued to move i n the d i r e c t i o n the hose was p o i n t i n g when the water l e f t i t . Figure 4.13 Path l i n e s of f l o a t s i n Set 7, from 64.7 hours to 67-5 hours, on the ebb from lover high t i d e . Winds vere near southwest 6. \ Figure h.lh V e l o c i t y f i e l d for Set 7 (58.6 hours to 62.0 hours) on the r i s e to lower high t i d e . 59 igure 4.15 Velocity f i e ld for Set 7 (6l.6 hours to 65.0 hours), near lower high t ide . 6o Near the boundary between the o l d and new plumes the motion of the o l d plume i s slowed to almost nothing by f r i c t i o n (Floats 9 and 17). The f a s t e r speeds near the r i v e r mouth are due to another l i n e of f l o a t s (Figures 4 to 13) which were put i n a f t e r the ebb had begun. The separation of the o l d and new plumes i s much more pronounced than i n Set U, i n which south-southeast wind i n h i b i t e d turning to the south. The d i f f e r e n c e i n the flow between the f l o o d and ebb t i d e s i n Set 7 are marked. In some areas where the speeds had been quite large during the f l o o d they became very small during the turn to the ebb. Averaging over a longer time period i n such a s i t u a t i o n can lead to biases according to which data sampling method i s used. Figure 4.l6 i s a combination of Figures 4.l4 and 4.15 (made using distance-sampled data), while Figure 4.17 shows an average of the time-sampled data set for the same period. The speeds i n the c e n t r a l region are somewhat slower i n the time-sampled p l o t , e s p e c i a l l y i n the square where Flo a t s 9 and 17 remained for a long time. However, while there are di f f e r e n c e s i n d e t a i l , the basic pattern i s the same i n both cases, g i v i n g con- fidence that the o v e r a l l p i c t u r e of the flow i s representative although small d e t a i l s may not.be. By the time the t i d e began to ebb, the wind had swung around to about southwest 6. Such a l i g h t wind had l i t t l e e f f e c t on the flow (Figure 4.18) which moved quite quickly to the south showing some spreading. The low v e l o c i t i e s on the north side are due to the remnants of the slow-moving water along the boundary with the o l d plume at the beginning of the time period. The apparent separation i n t o northern and 61 Figure k.lS V e l o c i t y f i e l d for Set 7 (58.6 hours to 65.0 hours), on the r i s e to and s t a r t of the ebb from lower high t i d e , made from data sampled at 0.1 mile i n t e r v a l s . Figure 4.17 V e l o c i t y f i e l d for Set 7 (58-6 hours to 65.0 hours), on the r i s e to and s t a r t of the ebb from lover high t i d e , made from data sampled at five-minute i n t e r v a l s . Figure 4 . 1 8 Velocity f i e ld for Set 7 ( 6 4 . 7 hours to 6 7 . 5 hours) on the ebb from lower high t ide . 6k southern sections i s caused by the f a c t that' not enough f l o a t s were put i n to f i l l up gaps i n the diverging flow. While the speeds near the r i v e r mouth, at 1 m/s, were about the same as those observed i n Set 4, those i n the southern part of the plume were considerably l a r g e r . Speeds there averaged .7 m/s i n Set 7, compared with .4 m/s i n Set 4. The change i n t i d e height was l e s s i n Set 7, but the east 11 wind blowing at the end of Set 4 may have slowed the southward flow. Set 1 comprises two l i n e s of f l o a t s (Figure 4.19), the f i r s t of which was put i n at lower high water. The second followed about two hours l a t e r and the f l o a t s remained i n the water u n t i l about one hour before low t i d e . The ebb was a l a r g e r one than e i t h e r of the two seen on the following days. The f i r s t l i n e of f l o a t s moved out f a i r l y s t r a i g h t and then turned to the south as the ebb increased, while the second l i n e turned much closer to Sand Heads and showed more divergence. Winds during the period were southwest 4 to 8. The v e l o c i t y f i e l d (Figure 4.20) was very s i m i l a r to that for the ebb i n Set 7 (Figure 4.18). Since the ebb during Set 1 was l a r g e r , the speeds near the r i v e r mouth were higher, reaching 1.2 m/s, but the opposing winds slowed the flow s l i g h t l y so that speeds were very s i m i l a r f a r t h e r out. Composite v e l o c i t y f i e l d s summarize the observations. The flow on the flo o d t i d e from Sets 4 and 7 (Figures 4.9 and 4.14) has been averaged i n Figure 4.21. I t shows the smooth curving to the north found on t h i s t i d a l phase and the beginning of the turn to the south as the r i v e r ' s pressure head overcame the push of the r i s i n g t i d e . To obtain an average flow pattern for a ' t y p i c a l small ebb', the data comprising Figure 4.19 Path l i n e s of f l o a t s i n Set 1, on the ebb from lower high t i d e a, 11.6 hours to 15.7 hours, b, .13-3 hours to 16.7 hours. Winds were southwest h to southwest 8. 66 Figure 4.20 V e l o c i t y f i e l d f o r Set 1 (11.6 hours t o l6.7 hours) on the ebb from lower high t i d e . gure 4.21 Composite v e l o c i t y f i e l d averaging the data on the r i s e to lower high t i d e , from Set 4 (33.1 hours to 38.9 hours) and Set 7 (58.6 hours to 62.0 hours). 68 Figures 4.11, 4.18 and 4.20 were averaged to form a sing l e v e l o c i t y f i e l d . This composite f i e l d (Figure 4.22) shows the turning to the south, the c u r l i n g to the north, and the decreasing speeds as distance from the r i v e r mouth increases which are c h a r a c t e r i s t i c of the flow on t h i s t i d a l phase. 4.1.3 Sets 5, 8 and 3, near higher high water During the nights of the f i r s t week an attempt was made to study the large floods and ebbs. Because of poor weather, the d i f f i c u l t i e s of working i n the dark and the inexperience of some of the people involved, we only managed to track one l i n e of f l o a t s each night. Set 5, c o l l e c t e d during the second night, gives the best representation of the flow. The f l o a t s i n Set 5 (Figure 4.23) were put i n the water about three and one-half hours before higher high t i d e , s t a r t i n g halfway through the f l o o d t i d e . The winds were near east 11 at t h i s time. The f l o a t s moved out and to the r i g h t u n t i l about an hour before the high t i d e , when they began to turn to the south. They continued moving south or southwest u n t i l they were removed, les s than an hour before the lower low t i d e . The data may be divided into two d i s t i n c t flow regimes with the d i v i s i o n occurring about an hour before higher high t i d e . The f i r s t v e l o c i t y f i e l d (Figure 4.24a) shows that the r i v e r discharge was held back by the flooding t i d e , r e s u l t i n g i n speeds as low as .2 m/s by the end of the time i n t e r v a l . The swing to the north was probably due to se\<-eral fac t o r s : the flooding t i d e , the C o r i o l i s force and the east 11 winds a l l encouraged the trend. Figure 4.22 Composite v e l o c i t y f i e l d averaging the data on the ebb from lower high t i d e , from Set 1 (11.6 hours to l6.7 hours), Set 4 (38.9 hours to 43.6 hours), and Set 7 (64.7 hours to 67•5 hours). Figure 4.23 Path l i n e s of f l o a t s i n Set 5, from 45.9 hours t o 54.5 hours, on the .r i s e t o and ebb from higher high t i d e . Winds were east 9 to northeast 15. gure U.2k V e l o c i t y f i e l d s f o r Set 5- a, 4 5-9 hours to 49.0 hours, on the r i s e to higher high t i d e , b, ^9.0 hours to 54.5 hours, on the ebb from higher high t i d e . 72 As "Sets 4 and 7 demonstrated, the pressure head of the r i v e r becomes large enough to overcome the flooding t i d e somewhat before high water. During the time from one hour before high t i d e u n t i l the end of the set (Figure 4.24b) the plume turned to the south, with speeds increasing to .6 m/s as the ebb became stronger. The surface slope i n the S t r a i t and the f r i c t i o n a l e f f e c t of the ebbing tide' would act together to bring about t h i s change i n the flow d i r e c t i o n . The s h i f t of the wind to northeast 12, increasing to northeast 18, brought i t more nearly p a r a l l e l to the flow. As ca l c u l a t e d e a r l i e r , a wind of l6 knots would add,12 m/s to the current over a period of an hour. A comparable increase i n the water speed would be expected to be caused by the wind during the l a t t e r part of Set 5- Water leaving the r i v e r mouth during t h i s time would have begun to move south immediately, forming the main part of the plume to the east of the f l o a t p o s i t i o n s . Speeds i n i t would probably have been somewhat higher than those we observed at the side of the plume. The data i n Set 8, obtained during the t h i r d night, again consist of a sing l e l i n e of f l o a t s (Figure 4.25). They were put i n s l i g h t l y over four hours before the higher high t i d e , s t a r t i n g about a t h i r d of the way through the flood. Since the preceding low t i d e had been quite a b i t higher than the one the previous evening, the flood was not as strong and the flow speeds near the r i v e r mouth (Figure. 4.26) were about .8 m/s, s l i g h t l y l a r g e r than the corresponding ones i n Set 5 (.6 m/s). The increased speed must have been due to Figure 4.25 Path l i n e s of f l o a t s i n Set 8, from 69.7 hours to 79-0 hours, on the r i s e to and ebb from higher high t i d e . Winds were near southeast 5. —j F i g u r e 4.26 V e l o c i t y f i e l d f o r Set 8 (69.7 hours to 76.0 hours), on the r i s e to and beginning of ebb from higher high t i d e . 75 differences i n the t i d e , since the winds during Set 8 were very l i g h t ( l e s s than 6 knots), while the winds during Set 5 should have enhanced the flow. By high water most of the f l o a t s were over f i v e miles from Sand Heads. They were l e f t moving out with a s l i g h t curve to the north, while the main plume near the r i v e r mouth probably turned to the south as observed i n Set 7- The f l o a t s continued outward, curving to the ri g h t under the influence of C o r i o l i s force and slowing because of the f r i c t i o n a l drag between the surface and lower l a y e r s . F i n a l l y , they appeared to s t a l l , probably because the fresh water l a y e r had spread out so t h i n l y that the f l o a t s were influenced considerably by the lower layer of s a l t water. Two to three hours a f t e r higher high t i d e the f l o a t s began to move again as the ebb i n the S t r a i t became stronger (Figure 4.27). Even a f t e r t h i s change, the speeds were s t i l l small (.2 m/s) but appeared to be increasing. On the f i r s t night, the f l o a t s i n Set 3 (Figure 4.28) were i n s t a l l e d l e s s than two hours before higher high tide. The winds at the time were northwest 12, so the f l o a t s began to move to the south quite soon. The s i t u a t i o n corresponds to the second parts of Sets 5 and 8, which took place on the ebbing t i d e . The winds dropped to 5 knots for a few hours, but then r a p i d l y increased to northwest 19 by 28.0 hours. The rough seas which accompanied the wind made work very d i f f i c u l t , so f l o a t tracking stopped by 27.0 hours. Float 1 could not be located, but l a t e r washed up on Mayne Island, on the west side of the S t r a i t of Georgia. 76 Figure 4.27 V e l o c i t y f i e l d for Set 8 (76.O hours to 79.0 hours) the ebb from higher high t i d e . 1 n a u t i c a l mile N f l o a t time time no. i n out 1 2 2 . 8 2 6 . 3 2 2 2 . 8 2 6 . 7 3 23 .0 2 6 . 6 4 23.1 2 6 . 6 5 2 3 . 3 2 7 . 0 6 2 5 - 5 2 6 . 8 Figure 4 . 2 8 Path l i n e s of the f l o a t s In Set 3 , from 2 2 . 8 hours to 2 7 . 0 hours, on the ebb from higher high t i d e . Winds were.northwest 7 to northwest 1 9 . 78 The v e l o c i t y f i e l d (Figure 4.29) appears to have been strongly influenced by the wind, since the d i r e c t i o n of flow became nearly p a r a l l e l to i t and the flow speed increased. Of course, the ebbing t i d e also encouraged the a c c e l e r a t i n g flow to the south; speeds increased from .4 m/s near Sand Heads to 1 m/s at the end of the observations. When the path l i n e s are compared with a hydrographic chart of the area i t seems that the f l o a t s followed the curvature of the banks of the r i v e r d e l t a . A more t y p i c a l ebb without such strong wind e f f e c t s would be expected to resemble Set 5» showing more divergence of the flow, and l e s s sharp turning to the south. Composite v e l o c i t y f i e l d s o f the flow for the second and t h i r d nights have been prepared for the time before the flow turned (Figure 4.30) and f o r the time a f t e r the turn (Figure 4.31). Set 3 has been omitted from the composite since i t represents a f a i r l y d i f f e r e n t s i t u a t i o n . 4.2 Week 2 - tracks and v e l o c i t i e s The experimental work during the second week was done only during the large ebbs and floods. On the basis of our experience the previous week i t was c l e a r we could not get good coverage during such t i d a l periods and maintain 24-hour operations with the vessels and personnel a v a i l a b l e . Fortunately, these t i d a l periods occurred during the daylight which made the work somewhat easier. Figure 4.32 shows the t i d a l height, the wind speed and d i r e c t i o n , and the times when data were obtained. Time i s i n hours, measured from midnight PDT June 4, 1974. In order to maintain c o n t i n u i t y of the data through the lower low t i d e s , we w i l l examine i t beginning at high t i d e .  Figure 4.30 Composite v e l o c i t y f i e l d averaging the data on the r i s e to higher high t i d e , from Set 5 (45.9 hours to 49.0 hours) and Set 8 (69-7 hours to 76.0 hours) Figure 4.31 Composite ve l o c i t y f i e l d averaging the data on the ebb from higher high t i d e , from Set 5 (49.0 hours to 54.5 hours) and Set 8 (76.0 hours to 79.0 hours). 82 9 10 l l D) Set + - M i 1 12 13 l4 15 I H i — l — i 16 IT 18 I H—If—I Figure 4.32 a, Tide height at Tsawwassen. b, times when the sets of data were taken, and c, wind speed and d i r e c t i o n , during the second week of the experiment. Time i s measured i n hours from midnight, PDT, June 4, 1974. 83 4.2.1 Sets 12 and 16 (before 59-0 hours), f i r s t part of large ebbs The data comprising Sets 12 and 16 were obtained during the ebb t i d e on the second and t h i r d days of the week's work. No data were c o l l e c t e d during t h i s t i d a l phase on the f i r s t day because of high winds. Set 12 consists of two l i n e s of f l o a t s (Figures 4.33a and 4.33b). The f i r s t l i n e was i n s t a l l e d almost two hours a f t e r the high t i d e , with the second l i n e following over an hour l a t e r . The f l o a t s were l e f t i n the water u n t i l about one and one-half hours before the lower low t i d e . The winds were very l i g h t during the ebb, from east 6 to calm. The v e l o c i t y f i e l d for the f i r s t two hours of the set i s Figure 4.34a. The speeds, which were about 0.8 m/s near Sand Heads, were somewhat smaller than those at the beginning of the small ebbs the previous week. This diff e r e n c e was probably due to the fa c t that the lower high t i d e s i n the second week were higher, g i v i n g the r i v e r l e s s of a pressure head. The f l o a t s moved out without much curving, though there was some divergence to the north and south. The f l o a t s i n the centre moved out more quickly than those on the sides, so that they were quite far out by the time the northern f l o a t began to turn south under the influence of the increasing ebb. By the time the second l i n e of f l o a t s was put i n , the flow had begun to swing s l i g h t l y to the south and the speed had increased con- siderably, to 1.1 m/s near Sand Heads (Figure 4.34b). The f l o a t s i n the second l i n e appear to have been put i n to the north of the plume a x i s , since they curved gradually to the north and showed no sign of swinging toward the south as i s t y p i c a l of flow on an ebb t i d e . I t seems l i k e l y that the speed of the water le a v i n g the r i v e r mouth would have continued to increase with the ebbing t i d e u n t i l reaching a maximum about an hour 84 1 n a u t i c a l mile a) f l o a t time time no. i n out 1 30.8 34.1 2 30.9 33.4 3 30.9 31.6 4 30.9 32.3 5 31.0 31.9 6 31.2 32.6 7 32.9 33.8 8 33.0 33.3 b) f l o a t time time no. i n out 9 32.6 34.3 10 32.7 33.3 11 32.8 34.6 12 32.8 34.8 Figure 4.33 Path l i n e s of f l o a t s i n Set 12, at the s t a r t of the large ebb a, 30.8 hours to 34.1 hours, b, 32.5 hours to 34.8 hours. Winds were east 6 to calm. 85 Figure 4.34 Velocity f i e l d s for Set.12, at the sta r t of the large ebb. a, 30.8 hours to 32.7 hours, b, 32.6 hours to 34.8 hours. 86 tiefore the lower t i d e . The turning to the south would have decreased somewhat before that time. Set l 6 , c o l l e c t e d the next day, gives b e t t e r coverage of the ebb. In the time from high water u n t i l about two hours before lower low water, three l i n e s of f l o a t s were put i n the water (Figures 4.35a, 4.35b and 4 . 3 8 a ) . The very end of the second l i n e and most of the t h i r d l i n e w i l l be considered with Set IT, which covers the end of the ebb. The three l i n e s were put i n about one hour, three hours, and four and one-half hours a f t e r high t i d e . The i n i t i a l v e l o c i t y f i e l d (Figure 4 .36a) i s very s i m i l a r to that f o r the beginning of Set 1 2 , although there was l e s s turning to the north. The second f i e l d (Figure 4 .36b) shows speeds s i m i l a r to those i n the second part of Set 1 2 , but the flow d i r e c t i o n was more southerly. The winds which were southwest 13 to southwest 5 probably enhanced the turn to the south. The l a r g e r speeds (about 1.8 m/s) near Sand Heads are derived from the beginning of the t h i r d l i n e of f l o a t s . The speeds of the f l o a t s i n the second l i n e were about 1.5 m/s there. Figure 4.3T i s an average v e l o c i t y f i e l d for the early part of the ebbing t i d e , i n c l u d i n g Set 12 and Set l 6 before 59-0 hours. I t shows the features c h a r a c t e r i s t i c of the flow at t h i s phase of the t i d e . I n i t i a l l y , there i s a s l i g h t swing to the north perhaps caused by the • end of the flooding t i d e as well as the C o r i o l i s force. The flow swings to the south but the speeds remain near 1 m/s decreasing very slowly. 4 . 2 . 2 Sets 16 ( a f t e r 59-0 hours), IT, 13 and 9 , end of large ebbs As lower low t i d e was approached, the r i v e r reached i t s 87 1 nautical mile a) b) float time time no. in out 1 54. 8 57.8 2 54.8 57.6 3 54.9 57.8 4 55.0 57.5 5 55.4 57.7 6 55.5 5>Y 7 56.2 ^51.6 a float time time no. in out 8 56.8 58.3 11 9a 56.8 57.1 9b 57.3 58.8 10 56.8 58.4 11 56.9 59.8 12 56.9 58.9 13 58.2 59.1 14 58.5 58.8 Figure 4.35 N Path lines of floats in Set 16, at the start of the large ebb. a, 54.7 hours to 57.8 hours, b, 56.7 hours to 59.9 hours. Winds were southwest 15 to southwest 4. The path lines numbered 9a and 9b indicate that the float was removed briefly for repairs. Figure 4.36 Velocity f i e l d s for Set 16, at the sta r t of the large ebb. a, 54.7 hours to 56.7 hours, b, 56.3 hours to 59-0 hours. Figure 4.37 Composite v e l o c i t y f i e l d averaging the data from Set 12 (30.8 hours to 34.8 hours) and Set 16 (54.7 hours to 59.0 hours), taken at the beginning of the large ebb t i d e . f l o a t time time no. i n out 15 58.3 58.1+ .16 58.3 58.5 17a 58.3 58.8 17b 59.0 60.8 18 58.7 60.7 19 58.8 60.8 20 59.0. 60.6 21 60.3 60.8 22 60.4 60.8 1 — 1 n a u t i c a l —I mile a) b) f l o a t time time no. i n out 1 59-9 60.5 2 60.0 60.5 3 6o.i 61.7 1+ 6o.i+ 61.8 5 60.1+ 61.8 6 60.9 62.1 7a 61.0 61.8 7b 61.8 62.-1 Figure N Path l i n e s of fl o a t s i n a, Set l 6 , from 58.2 hours to 60.8 hours, b, Set 17, from 59-9 hours to 62.1 hours, taken near lower low t i d e . Winds were south 1+ to southwest 8. The path l i n e s numbered 7a and 7b, and 17a and 17b, i n d i c a t e that those f l o a t s were b r i e f l y removed f o r re p a i r s . o 91 maximum outflow. The flow i n the plume during t h i s t i d a l phase was measured on the t h i r d day i n Set 16 (after 59-0 hours) and Set IT. and on the second day i n Set 13. On the f i r s t day two f l o a t s were put i n the r i v e r beside the j e t t y just a f t e r lower low t i d e (Set 9). Their v e l o c i t i e s w i l l be examined as w e l l . The end o f Set 16 and Set IT cover the time i n t e r v a l from about two hours before lower low water u n t i l about one hour a f t e r i t . The l a s t two f l o a t s from the second l i n e of Set l6 (Figure 4.35b) remained i n the water for a short while, and those of the t h i r d l i n e (Figure 4.38a) were removed h a l f an hour before low water. A new l i n e of f l o a t s (Figure 4.38b) was put i n the water about an hour before the lower low t i d e . Floats 1 and 2, put i n north of Steveston J e t t y , moved very slowly back p a r a l l e l to the j e t t y , while the f l o a t s put i n the main part o f the plume moved out s t r a i g h t at quite a high speed, as the v e l o c i t y f i e l d (Figure 4.39) shows. The speeds (about l.'T m/s near Sand Heads) are considerably higher than they were i n Sets 2 and 6, and the f l o a t s moved out farther before beginning to curve to the north. These differences are due to the f l o a t s i n Set IT being put i n s l i g h t l y before the time o f maximum outflow while those i n Sets 2 and 6 went i n somewhat a f t e r , as well as to the height of the low t i d e being considerably lower. As the sideways p u l l of the ebb t i d e slackened the v e l o c i t i e s of the f l o a t s from the end of Set 16 also swung r i g h t to become nearly p a r a l l e l to the j e t t y . The winds during the three-hour period were l i g h t , being south 4 to southwest 8. 92 Figure 4.39 V e l o c i t y f i e l d f o r Sets 16 and IT (59.0 hours to 62.1 hours), taken near lower low t i d e . 93 Set 13, which began almost two hours before lower low water on the second day, follows the end of Set 12 with a gap of only a few minutes. The f l o a t tracks are shown i n Figure 4.40a, and the v e l o c i t y f i e l d i n Figure 4.41a. Although the winds were very l i g h t (southeast 4), the f l o a t s i n i t i a l l y moved somewhat to the north. This may be due to spreading of the plume and the fa c t that those f l o a t s were on the north- ern side of i t . The i n i t i a l speeds of 2.1 m/s near Sand Heads were somewhat higher than.those i n Set 17 (l«7 m/s), but at distances of three miles or more from Sand Heads, speeds i n the two sets became very s i m i l a r . By the time the f l o a t s were removed about a h a l f hour a f t e r lower low water, the C o r i o l i s force and the e f f e c t of the lower s a l t water l a y e r , which was being pushed up the S t r a i t by the flooding t i d e , had begun to turn the flow to the r i g h t . ^ Set 9 consists of two f l o a t s which were put i n the r i v e r beside the j e t t y on the f i r s t day (Figure 4.40b) at about one-half hour a f t e r lower low water, but while the r i v e r ' s pressure head was s t i l l quite large. Float 1 remained quite close to the j e t t y but F l o a t 2 gradually moved away. It would probably have been i n the "southern si d e " of the plume i f i t had stayed i n the water long enough to move out into the S t r a i t . The f l o a t s moved very quickly, at 2.5 to 2 m/s i n the r i v e r , (Figure 4.41b), but slowed.slightly as they approached the S t r a i t . The slowing was probably due to f r i c t i o n a l drag with the lower l a y e r , which had by then begun to be pushed up the S t r a i t by the flooding t i d e . The surface layer had become t h i n enough that t h i s drag force was f e l t by the f l o a t s . I —1 1 n a u t i c a l mile Figure k.kO Path l i n e s of f l o a t s i n a, Set 13, from 35.1 hours to 37.h hours, when winds were calm to south k, and b, Set 9, from 12.1 hours to 13.1 hours, when winds were near south 10. The data were taken near lower low t i d e . vo 95 < H 13 (35-1 hours to 37.4 hours) and b, Set 9 (12.1 hours to 13.1 hours). 96 The composite flow f i e l d (Figure k.k2) i s an average of Sets 9, 13, 1.6 ( a f t e r 59-0 hours) and 17. I t shows the t y p i c a l features of flow near lower low water. Because of the r i v e r ' s large pressure head, the flow i s quite r a p i d , and moves away from the r i v e r mouth with l i t t l e spreading and only a very gradual curvature to the north. The radius of the i n e r t i a l c i r c l e f o r a 2 m/s current i s about 11 n a u t i c a l miles, which i s consistent with the observed curvature. 4.2.3 Sets 10, 14 and 18, e a r l y part of large flo o d As the t i d e began to r i s e from lower low water, the water moving up the S t r a i t aided the C o r i o l i s force i n swinging the r i v e r plume to the north. Sets 10, 14 and 18 were a l l c o l l e c t e d on the r i s i n g t i d e , s t a r t i n g one to one and one-half hours a f t e r lower low water. The path l i n e s for these sets are shown i n Figures 4.43a, 4.43b, and 4.45a. Figures 4.44a, 4.44b, and 4.45b are the corresponding v e l o c i t y f i e l d s . In a l l three cases, the f l o a t s i n i t i a l l y moved out f a i r l y s t r a i g h t from Sand Heads, but the e f f e c t of the fl o o d i n g t i d e combined with the C o r i o l i s force to turn the flow i n c r e a s i n g l y northward. Floats on the south side of the plume were caught between the flooding S t r a i t water and the outward moving r i v e r water and slowed r a p i d l y . In Set 18, Float 11 moved very slowly at f i r s t , but was l a t e r pushed north more sharply than the fa s t e r moving f l o a t s near the centre of the plume, cut t i n g across t h e i r path l i n e s . By that time the c e n t r a l f l o a t s were more than a mile farther out. Floats on the north-side of the plume . tended to move quite slowly a l s o , and to be pushed north by both the  a) 1 n a u t i c a l mile f l o a t time time no. i n out 1 13.3 13.8 2 13.4 ll+.l 3 13.1+ ll+.k 1+ 13.5 ll+.l 5 13.6 11+.2 6 13.T 111. 6 Figure 1+.1+3 Path l i n e s of f l o a t s i n a. Set 10, from 13.3 hours to 11+.6 hours, when winds were near south 10, and b. Set lk, from 38.2 hours to 1+1.3 hours, when winds were southeast 1+ to east 12. The data were taken near the beginning of the large f l o o d to higher high t i d e . f l o a t time time no. i n out • 1 39.3 1+0.8 2 38.3 1+0.6 3 38.3 1+0.8 1+ 38.1+ 1+0.1 5 38.1+ 39-1 6 38.5 39.6 7 1+0.5 39.6 8 1+0.6 1+1.3 9 1+0.7 1+1.2 CO 99 Figure 4.44 V e l o c i t y f i e l d s f o r data near the beginning of the large f l o o d to higher high t i d e , a, Set 10 (13.3 hours to 14.6 hours) and b, Set 14 (38.2 hours to 41.3 hours). 100 Figure 4.1*5 a, Path l i n e s and b, V e l o c i t y f i e l d f o r Set 18 (62.8 hours to 64.9 hours) taken near the beginning of the f l o o d to higher high t i d e , when winds were southwest 6 to southwest 14. 101 flooding t i d e and the C o r i o l i s f o r c e . The c e n t r a l f l o a t s maintained quite high speeds, since the water l e v e l i n the S t r a i t was low and the r i v e r had quite a large pressure head when they l e f t Sand Heads. Winds were s i m i l a r on the three days: south 10 during Set 10, south-southeast 8 to east 15 during Set lk, and southwest 10 to west-southwest 12 during Set 18. On each day the wind had a component which encouraged the flow to the north with the t i d e . The average v e l o c i t y f i e l d f o r the three sets (Figure k.k6) shows the basic features of the flow at the s t a r t of f u l l f l o o d . The speeds at the centre of the plume are large (near 1.5 m/s) because of the r i v e r ' s pressure head, and they decrease quite slowly as the f l o a t s move away from the r i v e r mouth. F r i c t i o n a l drag slows the f l o a t s near the north and south edges of the plume. There i s gradual curving to the north, caused by the increasing strength of the fl o o d t i d e , the C o r i o l i s force and the encouragement of the wind. k.2.h Sets 11 and 15, approach to higher high water The higher high t i d e s during the second week reached about the same water l e v e l s as the higher high t i d e s observed at night during the f i r s t week. Observations were made on the r i s e to higher high water on the f i r s t and second days of the week, y i e l d i n g Sets 11 and 15. Even though the t i d a l heights were s i m i l a r to those i n Week 1, the preceding low t i d e s were much lower, so the force of the t i d e f l o o d i n g up the S t r a i t was considerably l a r g e r . Set 11 consists o f an i n i t i a l group of three f l o a t s (Figure k.kla) put i n over four hours before high water, followed by a 102 Figure 4.46 Composite v e l o c i t y f i e l d averaging data from Set 10 (13.3 hours to 14.6 hours), Set 14 (38.2 hours to 41.3 hours) and Set l8 (62.8 hours to 6k-9 hours), taken near the beginning of the flood to higher high t i d e . 103 F i g i x r e 4.47 P a t h l i n e s o f f l o a t s i n a, S e t 1 1 , fr o m 15.5 h o u r s t o l6.8 h o u r s , when winds were s o u t h 10 t o s o u t h e a s t 7- b , S e t 11 from 16.8 hours t o 20.1 h o u r s . when w i n d s were s o u t h e a s t 7 t o t o sou t h w e s t 3, and c, S e t 1 5 , fr o m 41.3 h o u r s t o 44.2 h o u r s , when w i n d s were n e a r e a s t 17, t a k e n n e a r h i g h e r h i g h t i d e . 3r 11 N 1 n a u t i c a l m i l e f l o a t t i m e t i m e no. i n o ut 1 15.6 16.3 2 15.8 16.9 7 3 15.9 16.7 4 16.9 18.2 5 17.0 20.0 6 17.3 19-9 7 17.3 19.9 8 17.4 18.8 9 17.4 18.8 10 17.5 20.1 11 18.5 19.8 12 19.0 19.6 13 19.2 19.7 f l o a t t i m e t i m e no. i n o ut 1 41.3 42.8 2 41.4 42.9 3 41.5 44.3 4 41.7 44.2 5 41.8 44.1 6 41.8 43.8 7 41.8 42.7 8 41.8 43.7 9 41.9 43.8 10 41.9 43.7 11 41.9 43.8 12 43.5 44.0 13 43.6 44.0 104 l a r g e r group (Figure 4.47b) put i n from three hours to one hour before the high t i d e . The f l o a t s i n Set 15 (Figure 4.47c) were put i n about three hours before the high t i d e . The flow patterns observed on the two days are quite d i f f e r e n t , but most of the differences may be a t t r i b u t e d to the strong southeast wind which was blowing on the second day. The v e l o c i t y f i e l d s f o r the two parts of Set 11 are shown i n Figures 4.48a and 4.48b. The r i v e r outflow was decreasing as the water l e v e l i n the S t r a i t rose. Float 1 was f a r enough out to be pushed north by the flooding t i d e , but Floats 2 and 3 were caught north of the main flow near Sand Heads, and moved very slowly. The next group of f l o a t s moved quite s t r a i g h t out from the r i v e r mouth, but was g r e a t l y slowed by the r i s i n g water l e v e l i n the S t r a i t . Speeds were 0.2 to 0.3 m/s. The winds during the period were quite l i g h t : south 8 to east 5 to southwest 3. I n i t i a l l y they may have been strong enough to push Float 1 more to the north, but a f t e r that they probably had l i t t l e e f f e c t . When the f l o a t s comprising Set 15 (Figure 4.47c) were put i n the water the r i s i n g water l e v e l i n the S t r a i t made the flow speed of the water l e a v i n g the r i v e r mouth quite low. In t h i s s i t u a t i o n the wind, which was east l 6 to southeast 18, was able to exert a dominant force on the water i n the surface l a y e r . The v e l o c i t y f i e l d (Figure 4.48c) shows that the flow was pushed northwest by the wind, with a l i t t l e help from the C o r i o l i s force. The wind stress increased the speed of the f l o a t s from 0.3 to 0.5 m/s. This f i n d i n g i s consistent 105 N si 4 1 nautical mile 1 meter/second Figure k.kQ Velocity f i e l d s for data taken near higher high t i d e , • a, Set 11 (15.5 hours to l6.8 hours), b, Set 11 (16.8 hours to 20.1 hours) and c, Set 15 (Ul.3 hours to hk.2 hours). 106 with the e a r l i e r c a l c u l a t i o n of the e f f e c t s of wind drag acting on a three-meter-deep surface l a y e r . The 16 knot wind would produce a .2 m/s increase i n speed over about two hours. Since the flow patterns i n the two data sets are so d i f f e r e n t i t seems that there i s nothing to be gained by averaging them together. Set 11 gives the better representation of the flow near higher high water, since i t i s not strongly a l t e r e d by wind e f f e c t s . 4.3 Average v e l o c i t y components versus distance from Sand Heads Another way of presenting the data i s to plo t average v e l o c i t y components ( p a r a l l e l and perpendicular to the Steveston J e t t y ) as a function of distance from Sand Heads. To r e t a i n some of the features of the cross stream v a r i a t i o n , the f l o a t tracks have been a r b i t r a r i l y d i vided i n t o three groups - those on the north side of the plume, those i n i t s c e n t r a l region, and those on the south side. For each f l o a t track, distance was c a l c u l a t e d as the distance from Sand Heads (the o r i g i n of the graphs) to the s t a r t of the track plus the distance t r a v e l l e d along the track. (Note that t h i s i s not the same as the displacement from Sand Heads.) The data used are those sampled at 0.1 mile i n t e r v a l s along each track. Each o f the graphs of v e l o c i t y components versus distance .(Figures 4.49 to 4.54) corresponds to one of the composite v e l o c i t y f i e l d s found e a r l i e r i n the chapter. A l l f l o a t tracks or parts of tracks f a l l i n g within the s p e c i f i e d time i n t e r v a l s were averaged to produce the plo t s f o r the three regions. As i n the previously displayed v e l o c i t y f i e l d s , some of the apparent features of the flow are probably 107 a r t i f a c t s caused by f l o a t s being put i n and~taken out at d i f f e r e n t times and places, and by the lack of simultaneity i n the data sets. The standard deviation was c a l c u l a t e d f or each average, using the formula n E v. n i=l 1 2 Z 2 - (±=±—) vr n ., 1=1 1 2 ( — ) n - l where v^ i s a value of the downstream of cross-stream v e l o c i t y component. To give an i n d i c a t i o n o f the scatter i n the data being averaged, t y p i c a l values o f t h i s standard deviation are shown beside each graph. Since the averaged quantities were observed at s l i g h t l y d i f f e r e n t times and l o c a t i o n s , they are not expected to be measurements of exactly the same thing. The standard deviation i s , therefore, probably a better estimate of e r r o r than the standard er r o r of the mean, which would be c a l c u l a t e d by d i v i d i n g the standard deviation by (n) . 4.3.1 Week 1 In the f i r s t week's data, Sets 2 and 6 cover the times near low t i d e and hence the times of the l a r g e s t discharge. A l l the f l o a t s involved seemed to remain i n the c e n t r a l region of the plume, so only points f o r that region have been p l o t t e d i n Figure 4.49. The corresponding v e l o c i t y f i e l d was shown i n Figure 4.6. The most s i g n i f i c a n t feature of the graph i s the trend toward decreasing speed. This tendency was probably caused by the f r i c t i o n a l drag of the underlying s a l t water on the surface l a y e r forming the plume. Winds during both sets were l i g h t enough (6-8 knots) to have l i t t l e e f f e c t . The trend of the cross-stream component to become 108 Distance ( n a u t i c a l miles) (--7 -6 -5 -4 -3 -2 -1 x centre t y p i c a l standard deviation 'XX 1 f - 3 1 2 -0.5 -1.0 _2_ 5 V ; x (meters/ second) 1 -2.0 1-2.5 XX * * * * * * * X * * * * X x ^ ^'^ V y (meters/ second) i i -7 1 1 1 1 1 ~ A x x -6 -5 -h -3 -2 - l x x i j 0 1 2 .-0.5 Figure k.k9 V e l o c i t y components (v downstream and v cross-stream) as a function of distance from Sand Heads", for the northern, c e n t r a l and southern regions of the plume. Set 2 (17.0 hours to 19.k hours) and Set 6 (57-0 hours to 58.5 hours) were taken near lower low water during equatorial t i d e s . •109 more p o s i t i v e has l e s s s i g n i f i c a n c e , since most of the points f a l l within one standard deviation of zero. The e f f e c t s of the fl o o d i n g t i d e and the C o r i o l i s force would, however, tend to produce such a change. The points f o r both components are generally within one standard deviation of f a l l i n g along a st r a i g h t l i n e . Figure 4.50, which corresponds to Figure 4.21,displays the average v e l o c i t y components for the times when the t i d e was r i s i n g from low to lower high t i d e . The e f f e c t s of the flooding t i d e are found i n the p o s i t i v e (northward) values of cross-stream v e l o c i t y components for most regions of the plume and i n the speeds which are generally at l e a s t 50$ smaller than those measured at the end of the ebb t i d e . Again the graph shows a f a i r l y l i n e a r decrease i n the downstream v e l o c i t y component. The seeming increase i n the downstream component f o r the north side of the plume near the o r i g i n i s probably a r e s u l t of more quickly moving f l o a t s being i n s t a l l e d farther from Sand Heads than the i n i t i a l slow moving ones. Figure 4.51 i s the graph for the small ebb t i d e s , corres- ponding to Figure 4.22. While the flow speeds are somewhat l a r g e r than those for the r i s i n g t i d e , they are s t i l l appreciably smaller than those i n Figure 4.49. The data for i t w^re obtained at the end of the ebb phase of the ti d e s which f e l l to a lower l e v e l . The lower t i d e height during Sets 2 and 6 would permit a l a r g e r outflow and thus higher speeds. Many of the f l o a t s averaged i n p l o t t i n g v e l o c i t y components f o r the north side of the plume were c u r l i n g sharply to the north. Some of them (Set 4) turned far enough to give the downstream component p o s i t i v e values 110 Distance (n a u t i c a l miles) -7 I -5 f- -U -2 x x am -1 —h- O north x. centre ^ south t y p i c a l J standard deviation * x x -a®&e><$ 1-0.5 X X x*-L -1.0 X X K X X 1-1.5 v x (m/s) "-2.0 ..-2.5 Figure 4.50 V e l o c i t y components ( v x downstream and v cross-stream) as a function of distance from Sand Heads, Tor the northern, c e n t r a l and southern regions of the plume. Set 4 (33.1 hours to 38.9 hours) and Set 7 (58.6 hours to 62.0 hours) were taken on the r i s e to lower high water during equatorial t i d e s . I l l Distance ( n a u t i c a l miles) -7 -6 / 5 oo a -2 -1 a aa O north X centre £ south t y p i c a l •f standard deviation X X - 4 4 a a * X * X * " O A * X * X a ° m a ° ^ a -0.5 t-1.0 -1.5 t - 2 . 0 -2.5 TO.5 * * x x y j e V y ° a a ° a ° a a a a g 0 g ' g ' a a a a o r o -b X X . x xxxxxxxxxxftxx 4 4 4 4 4 » 4 A 4 4 4 4 ^ 4 4 4 V , (m/s) (m/s) 0 1 Figure 4.51 V e l o c i t y components ( v x downstream and Vy cross-stream) as a function of distance from Sand Heads, f o r the northern, c e n t r a l and southern regions of the plume. Set 1 (11.6 hours to 16.7 hours), Set 4 (38.9 hours to 43.6 hours) and Set 7 (64.7 hours to 67.5 hours) were taken on the ebb from lower high water during equatorial t i d e s . 112 at a distance of about three miles from Sand Heads along the f l o a t tracks. These f l o a t s were then removed from the water so the average values f o r greater distances s t i l l show outward motion.. The cross- stream components ex h i b i t the divergence of the plume, with the points for the north and south sides showing d e f i n i t e tendencies i n those respective d i r e c t i o n s . In the c e n t r a l region the graph i n i t i a l l y i n d i c a t e s a southward component of the motion, as would be expected on an ebbing t i d e . The p o s i t i v e values at distances greater than four miles are due to the f l o a t s i n Set 4, which remained i n the water f o r up to two hours a f t e r the t i d e turned to the flood. I t was f e l t that Sets 3, 5 and 8, obtained on the r i s e s to and f a l l s from higher high t i d e during the nights of the f i r s t week, were s u f f i c i e n t l y sparse i n coverage and d i f f e r e n t i n character that v e l o c i t y versus distance graphs would probably not be representative. These sets have thus been omitted from t h i s section. 4.3.2 Week 2 The study of the second week's data began with Sets 12 and 16, obtained during the e a r l y stages of the ebb from high to lower low t i d e , f o r which the composite v e l o c i t y f i e l d i s Figure 4.37. The v e l o c i t y versus distance graph for these s e t s , Figure 4.52, shows speeds which are l a r g e r than those found on the small ebbs during the previous week (Figure 4.5l), but speeds comparable to the end of the l a r g e r ebb (Figure 4.49). ' The f l o a t s i n the c e n t r a l region of the plume move considerably f a s t e r than those on each side, which are presumably slowed by l a t e r a l f r i c t i o n with the water outside the plume, as w e l l as f r i c t i o n 113 Distance ( n a u t i c a l miles) -7 -6 -5 -4 -3 -2 -1 a std. dev. t y p i c a l for c e n t r a l region to 3 mi. from Sand Heads •xxxx XX f i t y p i c a l -Lfor other points XXXx x X x X x 01 north % centre A south 0 1 -0.5 -1.0 ---1.5 yx (m/s) -2.0 -2.5 - 0.5 v y (m/s) I i * * x -6 -5 -^xxxxxxxxxs* 4 l 4 4 4 4 4 ' ga aa x 0.5 gure 4.52 V e l o c i t y components ( v x downstream and v y cross-stream) as function of distance from Sand Heads, f o r the northern, c e n t r a l and southern regions of the plume. Set 12 (30.8 hours to 34.8 hours) and Set 16 (54.7 hours t o 59-0 hours) were taken at the s t a r t o f the ebb from lower high water during t r o p i c t i d e s . 114 from below. The cross-stream components show that the plume gradually diverges, e s p e c i a l l y by turning to the south under the influence of the ebbing t i d e . The sudden increase i n t h i s component i n the southern region o f the plume at 3.4 miles from Sand Heads i s caused by the i n s t a l l a t i o n at that point of a quickly moving f l o a t , and by a slower moving f l o a t being just that f a r out at 59.0 hours, the end of the time i n t e r v a l f o r t h i s graph, so i t s e f f e c t s on the average are not seen beyond there. Figure 4.53 displays the v e l o c i t y versus distance graph for Sets 9» 13, 16 ( a f t e r 59.0 hours) and IT, which cover the times near the lower low t i d e s at the end of the large ebbs. As one would guess from looking at the composite v e l o c i t y f i e l d i n Figure 4.42, the speeds i n the c e n t r a l region are l a r g e r than those observed on any other t i d a l phase. The very low t i d e height gives the r i v e r an exceptionally large pressure head and correspondingly high outflow speed. Even the f l o a t s on the north and south sides of the plume move r e l a t i v e l y f a s t i n com- parison with those on other t i d a l phases. I n i t i a l l y , the c e n t r a l f l o a t s show a p o s i t i v e cross-stream v e l o c i t y component, which may be caused by the C o r i o l i s force. Under the influence of the ebbing t i d e , the c e n t r a l f l o a t s then show a smaller negative cross-stream component, which becomes p o s i t i v e again as the t i d e turns and begins pushing up the S t r a i t . The f i n a l graph of v e l o c i t y versus distance, Figure 4.54, displays the averages f o r Sets 10, 14 and 18. The composite v e l o c i t y f i e l d f o r these data, which were obtained on the r i s i n g t i d e j u s t a f t e r lower low water, i s Figure 4.46. The r a p i d r i s e i n the t i d e height was 115 Distance (nautical miles) — I 1 1 1 h -T -6 typical standard xx x***y -5 A -4 -3 -2 A A A 4 Af (3 A deviation x x X X x x , -xx x * xxx, a a. £3 north x centre A south I x x x x *xxxx, i t s " XX x x J -7 A A A A * 0 1 - -0.5 t - i . o * A A A -1.5 v x (m/s) ._ -2.0 *xx> XX -2.5 T 0.5 v y (m/s) A A A A ^ f * * x 0.5 Figure 4.53 Velocity components (v x downstream and Vy cross-stream) as a function of distance from Sand Heads, for the northern, central and southern regions of the plume. Set 9 (12.1 hours to 13.1 hours), Set 13 (35.1 hours to 37-4 hours), Set 16 (59-0 hours to 60.8 hours) and Set 17 (59.9 hours to 62.1 hours) were taken near lower low water during tropic tides. 116 Distance (na u t i c a l miles) 1 1 1 h 3 ( - -7 -6 -5 -4 -3 -2 m -1 H h a « 4 T t y p i c a l ; i standard X deviation t3 north x centre 4i south x x x x x x x x CP 0 1 -0.5 -1.0 & A A A A , x x x X x x x x x x x x X ) ( -1.5 v x (m/s) -2.0 T - 1.0 i x a H 1 1 h I 1 —+ -7 -6 -5 -4 -3 -2 -1 * A Vy (m/s) 0 1 10.5 Figure 4.54 V e l o c i t y components ( v x downstream and Vy cross-stream) as a function o f distance from Sand Heads, for the northern, c e n t r a l and southern regions of the plume. Set 10 (13.3 hours to 14.6 hours), Set l 4 (38.2 hours to 4l.3 hours) and Set 18 (62.8 hours to 64.9 hours) were taken at the s t a r t of the flo o d to higher high water during t r o p i c t i d e s . 117 accomplished by a strong f l o v of water up the S t r a i t , which caused the lar g e s t cross-stream component values observed i n the whole experiment. The f l o a t s on the north side of the plume turned sharply enough to make the downstream component become p o s i t i v e before they were removed. As i n a l l the graphs i n t h i s s e r i e s , the t o t a l speeds of the f l o a t s i n the ce n t r a l region decrease quite smoothly, approximately l i n e a r l y , with distance. The observed v e l o c i t i e s i n Sets 11 and 15 were considered to be s u f f i c i e n t l y d i f f e r e n t that a graph of average v e l o c i t y components versus distance would not be very representative. Preliminary attempts at such a graph d i d i n d i c a t e that, although the di r e c t i o n s of motion i n the two sets were almost at r i g h t angles, the t o t a l speeds were quite s i m i l a r . Those i n Set 15 d i d move s l i g h t l y f a s t e r . k.4 Comparison with other observations In reading the l i t e r a t u r e on observations made i n the S t r a i t of Georgia one finds very l i t t l e data taken i n the area of the Fraser plume which can be r e a d i l y compared with the r e s u l t s of the IOUBC experiment. Included i n the data published by Tabata et al (1970), however, i s a set of current meter data taken i n the Fraser plume during freshet. Current v e l o c i t y measurements were made from a wooden-hulled ve s s e l , anchored 6 km from Sand Heads i n the d i r e c t i o n i n d i c a t e d by the Steveston J e t t y . A Hydro Products Model U65 meter with remote read-out was used to make hourly measurements of the current at a number of depths on May 23-27, 19^7. The seventy-five hour period included three cycles of t r o p i c t i d e s . The data taken at a depth of lm were assumed to be comparable to those which would be observed by drogue t r a c k i n g . 118 To f a c i l i t a t e comparison, the v e l o c i t i e s were resolved into components p a r a l l e l and perpendicular to the Steveston J e t t y , and phase averaged to show v a r i a t i o n s over a si n g l e t i d a l cycle (Figure U .55'). The t i d e heights were found i n Canadian Tide and Current Tables (1967). S i m i l a r t i d a l conditions occurred during the second week of drogue tr a c k i n g , but i n that week drogues entered the h a l f - m i l e square around the current:meter s t a t i o n on only four occasions. V e l o c i t y components for each of those periods of up to an hour were averaged and p l o t t e d i n Figure 4.55 at the appropriate t i d a l phase. Drogues reached the area of the current meter s t a t i o n only on the large ebb t i d e . Their speeds are comparable to those measured by the current meter but they had smaller cross-stream v e l o c i t y components and l a r g e r downstream ones. Differences i n wind are probably responsible for the v a r i a t i o n s . The t i d a l amplitudes during the IOUBC experiment (dotted l i n e s i n Figure 4̂ 55) were s l i g h t l y smaller than those occurring when the current meter data were taken. The discharge from the Fraser River was s l i g h t l y l a r g e r during the 1967 measurements. k.5 Estimates of entrainment A further c a l c u l a t i o n based on the experimental data provides an i n t e r e s t i n g comparison with the r e s u l t s of a study i n v o l v i n g scale models of a r i v e r with an arrested s a l t wedge. While the s i t u a t i o n i n the Fraser plume i s d i f f e r e n t i n many respects from the model, i t i s i n t e r e s t i n g to note that there are apparent s i m i l a r i t i e s i n the mech- anism of entrainment. Figure 4.55 a, V e l o c i t y components as a function of time, phase averaged from hourly observations over three t i d a l c y c l e s . The v e l o c i t i e s were measured with a current meter at a s t a t i o n s i x kilometers from Sand Heads on May 23-27, 1967• They have been resolved i n t o components p a r a l l e l and perpendicular to the Steveston J e t t y . V e l o c i t i e s observed during my experiment near the current meter s t a t i o n have been p l o t t e d at the appropriate t i d a l phase and marked with a c i r c l e (June 5) or a box (June 6). b, Average t i d e height at Tsawwassen f o r May 23-27, 1967 ( s o l i d l i n e ) and June 4-6, 1974) dotted l i n e .  121 The fresh water discharged from the mouth of the Fraser River i s no longer h o r i z o n t a l l y constrained, and forms a spreading plume with non-zero h o r i z o n t a l divergence. Since, i n an incompressible f l u i d , there can be no net divergence, s a l t water i s entrained from below to maintain the continuity of the upper l a y e r . The con t i n u i t y equation i s ,. ' 9u 9v ^ 9w _ div U = T— + r — + T — = 0 — 9x 9y 9z where the v e l o c i t y i s U = (u,v,w). The v e r t i c a l v e l o c i t y w must be zero at the surface, z = 0. While i t i s quite probable that the h o r i z o n t a l divergence, d i v U = 9u_ + _9v , varies with the depth, no 9x 9y estimate of the v a r i a t i o n can be obtained from the experimental data. Since the surface layer i s reasonably w e l l mixed and probably quite turbulent, i t i s reasonable to assume that any entrained f l u i d i s mixed throughout the la y e r quite quickly. I t thus seems reasonable to assume that d i v U i s independent of depth over the surface l a y e r , from n— z = 0 to z = -h. Integrating v e r t i c a l l y , we obtain an expression for the v e r t i c a l v e l o c i t y at the i n t e r f a c e , U . v ' m ' — • dz = 1 - d i v n dz o 9z o H— -h -h w | = ^iv^U z | Um = h d i v R U LJJJ i s , of course, an average value since the ph y s i c a l processes which 122 accomplish the entrainment are non-uniform. I f the process i s s i m i l a r to the one described by Keulegan (1966), then entrainment i s caused by parcels of s a l t water being introduced into the fresh l a y e r at the apices of breaking i n t e r n a l waves. The s i t u a t i o n discussed by Keulegan (1966) i s that of an arrested s a l t wedge intruding into the channel of a r i v e r which empties into a t i d e l e s s sea. Although the wedge remains stationary, s a l t water may be entrained by the moving fresh water above i f i t s speed exceeds a c r i t i c a l value. This c r i t i c a l speed U c, depends on the r e l a t i v e densities of the two l a y e r s , p andp-£p , the kinematic v i s c o s i t y of the lower l a y e r , v , gr a v i t y , and a p r o p o r t i o n a l i t y constant, C : 2 U = C ' ( ^ v g ) l / 3 ' c p 2 where g i s the acceleration due to gravit y . The e m p i r i c a l l y determined value of C i s 7-3 for an arrested s a l t wedge. To study s a l t wedges Keulegan constructed small scale models of r i v e r channels with rectangular cross sections. Based on measurements of the flow i n these models, he gives an empirical formula for the entrainment v e l o c i t y at the i n t e r f a c e : U = k' (U-U ). m c k' i s a p r o p o r t i o n a l i t y constant which he evaluated by measuring the amount of s a l t mixed into the upper layer and U = ( u 2 +v 2)' 2 i s the speed of the upper layer. The measurements were done with three d i f f e r e n t 123 density r a t i o s , using a model channel 5-3 cm wide and 11.2 cm deep. His value f o r k' i s 2.12 x 10_t*. To compare Keulegan's r e s u l t s with the s i t u a t i o n i n the Fraser plume, the two expressions f o r U , the v e r t i c a l v e l o c i t y at the i n t e r f a c e , may be equated, g i v i n g h div„U = k' (U-U ) . H— c Evaluating U c f o r the Fraser plume y i e l d s a value of approximately 3 cm/s, which i s so much smaller than t y p i c a l speeds found i n the plume that t h i s term may be neglected. Thus h div T TU If a reasonable estimate i s made f o r the value of h, the expression on the r i g h t may be evaluated from the composite v e l o c i t y f i e l d s . The only measurements of the surface layer thickness i n the IOUBC experiment were those obtained with the CSTD. Unfortunately, the depth data are not s u f f i c i e n t l y r e l i a b l e near the surface to show var i a t i o n s i n h due to p o s i t i o n and t i d a l phase. Based on the CSTD data, a uniform layer thickness of 3 m has been assumed; t h i s assumption probably introduces no l a r g e r errors than other approximations made i n doing the c a l c u l a t i o n s . 124. Div HU — - — was evaluated f o r the composite v e l o c i t y f i e l d s shown i n Figures 4.6, 4.21, 4.22, 4.37, 4.42 and 4.46. In order to estimate 9u 9v Au Av values of — and — at g r i d points where u and v are known, -— and — 3x 3y B ^ Ax Ay were ca l c u l a t e d from the values of u and v at the points on e i t h e r side of the point i n question. The r e s u l t s of these c a l c u l a t i o n s give a scattered c o l l e c t i o n of values f o r k' at the various g r i d p o i n t s , as Figure 4.56, the sample c a l c u l a t i o n based on Figure 4.6, demonstrates. The average values and standard errors of the mean for the composite v e l o c i t y f i e l d s are Figure # points k' T i d a l phase 4.6 12 (2.67± .74)xl0 - 1 + End of ebb 4.21 19 (l.26±1.25)xlO _ L f Small f l o o d 4.22 38 (2.47± .95)xlO - l t Small ebb 4.37 20 (4.89± .98)xl0 _ I t Start of large ebb 4.42 31 (1.76± .50)xl0 _ t* End of large ebb 4.46 16 (3.40±1.02)xl0_lt Start of large f l o o d The o v e r a l l average of the 136 points gives an estimate of k' = (2.62+ ,40) xlO \'which i s remarkably close to Keulegan's value of 2.12 x 10 . Within each composite there were negative values of k', i n d i c a t i n g areas o f convergence and downward v e r t i c a l v e l o c i t y . That s i t u a t i o n did occur near the north side of the plume when i t curled sharply around,- and along the boundary between o l d and new sections of the plume. However, some apparent instances of convergence were probably caused by the data d i s t r i b u t i o n and the averaging procedure. For 125 .017 + .232 .249 * . 8 l 0 .307 -.309 -.243 -.120 -.110 -.060 -.130 + .273 + .321 + .403 + .347 + .280 + .334 -.036 .078 .283 .237 .220 .204 * . 8 5 l *1.04 * 1 . 0 8 -1.15 * l . l 8 v l . 21 -.042 .075 .263 .205 .185 .168 -.111 -.192 -.315 -.030 .291 + .232 + .224 + .244 + .282 + .278 .121 .032 -.071 .252 .569 v.901 -.949 * 1 . 0 8 v l . 2 6 *1.13 .134 .034 -.066 .200 .506 Figure 4.56 Sample c a l c u l a t i o n of Keulegan's constant k', based on the composite v e l o c i t y f i e l d Figure 4.6. Each box corresponds to a g r i d point and contains Au Av and the Ax' Ay and the h o r i z o n t a l divergence Au Av, - 1 . - 1 ^ — + — (ms xmi 1 ) , the Ax Ay ho r i z o n t a l speed U (ms 1)and k' — = Au Av / . — 1 \ h — + — (mi 1 ) . Ax Ay U To obtain the dimensionless constant k', these values of k'/h were averaged, and the average was m u l t i p l i e d by h = k* = .164 mi" 1 x 3 m = 2.67 x 10~h -I - 3m x 1 mi 1853 m. 1853 m mi 126 example, the track of a quickly moving drogue might end, le a v i n g only more slowly moving ones to form the average v e l o c i t y i n the next square. Despite the differences between Keulegan's small scale model of an arrested s a l i n e wedge i n a t i d e l e s s r i v e r channel and the experi- mental s i t u a t i o n of a spreading surface l a y e r o v e r r i d i n g a s a l t l a y e r i n a t i d a l s t r a i t , the nearness of the two estimates of k' ind i c a t e s that the process of entrainment i n the two cases may be quite s i m i l a r . From observations of the change of s a l t content i n the Fraser plume, de Lange Boom (1976) obtained an average value f o r k' of 2.h x 10 4 which i s also very close to Keulegan's r e s u l t . 127 CHAPTER 5 SUMMARY AND CONCLUSIONS The examination of the data c o l l e c t e d i n the drogue tr a c k i n g experiment showed that t i d a l forces were us u a l l y the dominant fa c t o r i n determining the pattern of flow i n the Fraser plume. Winds (unless quite strong) and C o r i o l i s force had l e s s e r e f f e c t s . Discharge from the r i v e r remained r e l a t i v e l y constant during the experiment. To summarize the r e s u l t s , the composite v e l o c i t y f i e l d s from Chapter 4 have been c o l l e c t e d here. B r i e f comments w i l l be made on t h e i r main features. Data covering the small f l o o d and ebb stages of the eq u a t o r i a l t i d e s were c o l l e c t e d during the days of the f i r s t week (Figure 5-l)- Throughout most of these periods the winds were l i g h t enough (speeds not over 10 knots) that they had l i t t l e e f f e c t on the flow (Figure 4.1). Sets 2 and 6 (Figure 5-la) occurred near lower low t i d e , when the discharge from the r i v e r was at i t s maximum for the week 1 t i d a l c ycles. The small amount of cross-stream motion observed was probably caused by the C o r i o l i s force and the beginning of the subsequent f l o o d t i d e . Observations of the small f l o o d t i d e comprise the f i r s t parts of Sets 4 and 7 (Figure 5.1b). Discharge from the r i v e r was held back by the r i s i n g t i d e , so outflow speeds decreased and the plume was pushed up the S t r a i t . Just before the high t i d e , the r i v e r ' s pressure head became large enough to overcome the r i s i n g t i d e and the southern f l o a t s began to move south. The small ebb stage of the t i d e was observed during Set 1 and the f i n a l parts of Sets 4 and 7 (Figure 5.1c). The f a l l i n g t i d e l e d to a gradual turning to the south, while the c u r l i n g * * 1" Figure 5.1 Composite v e l o c i t y f i e l d s f o r the small f l o o d and ebb stages of equatorial t i d e s , a, Set 2 -(17-0 hours to 19.4 hours) and Set 6 (57.0 hours to 58.5 hours), near lo v e r low t i d e , b, Set 4 (33-1 hours to 38.9 hours) and Set 7 (58.6 hours to 62.0 hours), on the r i s e to lower high t i d e , c, Set 1 (11.6 hours to 16.7 hours), Set 4 (38.9 hours to 43.6 hours) and Set 7 (64.7 hours to 67.5 hours), on the ebb from lower high t i d e . (—1 co 129 on the north side of the plume was a remnant of the flow from the pre- ceding f l o o d t i d e . During the nights of the f i r s t week of the experiment observations were made of the r i s e to and ebb from higher high t i d e . Only one l i n e of f l o a t s was tracked each night. The winds during Set 3 were strong enough (northwest 19 knots) to a f f e c t the flow considerably and to make conditions bad enough that f l o a t t r acking was stopped early. During Set 5 the winds were s u f f i c i e n t l y strong (increasing to north- east 17) to t r a n s f e r some momentum to the flow, but Set 8 was unaffected by the l i g h t winds of that night. The flow has been divided i n t o two regimes: that on the f l o o d t i d e and that which occurred a f t e r the flow turned with the ebb t i d e . On the f l o o d t i d e the f l o a t s moved out from Sand Heads with very l i t t l e turning or divergence, though t h e i r speed decreased quite markedly (Figure 5.2a). When the ebb began, the three l i n e s of f l o a t s were at d i f f e r e n t distances from Sand Heads, so the v e l o c i t y f i e l d (Figure 5.2b) shows how the strength of the ebb v a r i e d across the S t r a i t . Of course, wind conditions for the three sets were so d i f f e r e n t that the data cannot be considered synoptic; the f l o a t s i n Set 3 (nearest Sand Heads) were p a r t i c u l a r l y a f f e c t e d by the high winds. The large ebbs and floods of t r o p i c t i d e s occurred during the days of the second week of the experiment (Figure 4.32). Observa- tions were not made of the small floods and ebbs during the nights. High winds delayed the s t a r t of operations on the f i r s t day, and winds were strong enough to a f f e c t the observed flow during Sets lU and 15- Figure 5.2 Composite v e l o c i t y f i e l d s f o r the large flood and ebb stages of equatorial t i d e s . a, Set 5 (45.9 hours to 49.0 hours) and Set 8 (69.7 hours to 76.0 hours), on the r i s e to higher high t i d e , b, Set 3 (22.8 hours to 27.0 hours), Set 5 (49.0 hours to 54.5 hours) and Set 8 (76.O hours to 79-0 hours), on the ebb from higher high t i d e . o 131 The composite v e l o c i t y f i e l d s based on the week's observations comprise Figure 5-3. Sets 12 and 16 (before 59-0 hours) which cover the early part o f the ebb (Figure 5-3a) show some divergence and turning to the south under the influence of the ebbing t i d e . Speeds are r e l a t i v e l y small; the high speed indi c a t e d near Sand Heads i s due to the f i r s t f l o a t of a new l i n e put i n l a t e r on the t i d a l c y c l e . The flow near the end of the ebb (Sets 9, 13, 16 ( a f t e r 59-0 hours) and IT, Figure 5-3b) exhibits the l a r g e s t speeds measured during the experiment. There i s l i t t l e divergence i n the flow, which moves almost s t r a i g h t out from Sand Heads. (The arrows on the south side represent f l o a t s which were moving south near the beginning of the i n t e r v a l . ) The s l i g h t curvature to the r i g h t i s consistent with the predicted e f f e c t of the C o r i o l i s force. The measurements i n the r i v e r were made just a f t e r lower low t i d e , so those f l o a t s were slowed near Sand Heads by the beginning of the f l o o d t i d e . The f l o o d from lower low to higher high t i d e began during Sets 10, 14 and 18 (Figure 5.3c). The measurements near Sand Heads were made on the e a r l y stages of the f l o o d , when the r i v e r ' s pressure head was large enough that the outflow was not slowed too much. The flo o d i n g t i d e d i d , however, turn the plume sharply up the S t r a i t . Winds during a l l three sets were from the south or southwest at speeds near 10 knots. Such winds would be strong enough to add s l i g h t l y to the northward turning caused by the t i d e . Near higher high t i d e f r e s h water c o l l e c t s near the r i v e r mouth, as i l l u s t r a t e d by the very low speeds observed i n F i g u r e 5-3 Composite v e l o c i t y f o r the l a r g e ebb and f l o o d stage of t r o p i c t i d e s , a, Set 12 (30.8 hours t o 34.8 hours) and Set l6 (54.7 hours to 59-0 hours), at the s t a r t o f the l a r g e ebb. b, Set 9 (12.1 hours t o 13.1 ho u r s ) , Set 13 (35.1 hours t o 37-4 ho u r s ) , Set 16 (59-0 hours to 60.8 hours) and Set 17 (59-8 hours to 62.1 ho u r s ) , at the end of the l a r g e ebb. c, Set 10 (13.3 hours t o 14.6 h o u r s ) , Set 14 (38.2 hours t o 41.3 hours) and Set 18 (62.8 hours t o 64.9 ho u r s ) , at the s t a r t o f the l a r g e f l o o d , d, Set 11 (15-5 hours t o 20.1 hours) and Set 15 (41.3 hours t o 44.2 h o u r s ) , at the end of the l a r g e f l o o d . 133 Sets 11 and 15 (Figure 5.3d). The wind conditions made the flow patterns of the two sets quite d i f f e r e n t . During Set 11 the east 5 wind had l i t t l e e f f e c t on the flow, which moved out from Sand Heads with l i t t l e turning, but the southeast IT wind during Set 15 was the predominant f o r c e , turning the flow sharply up the S t r a i t . Average v e l o c i t y components were p l o t t e d as a function of distance t r a v e l l e d from Sand Heads. Graphs corresponding to Figures 5.1a, b, c and 5.3a, b, c, were shown i n Chapter h, Section 3. Generally, the component i n the d i r e c t i o n along the j e t t y dominated (except f o r the f i e l d of Figure 5-3c). This component was strongest for the c e n t r a l region of the plume and showed an approximately l i n e a r decrease with distance from Sand Heads. Examination of the h o r i z o n t a l divergence l e d to estimates of the entrainment v e l o c i t y consistent with those of Keulegan's (l°66) formula based on laboratory scale models and of de Lange Boom's (19T6) estimate derived from s a l t conservation i n the Fraser plume. A f t e r an experiment has been completed, i t i s u s u a l l y possible to suggest improvements which could be made i n subsequent experiments. Some changes are r e l a t i v e l y minor, while others involve major r e v i s i o n s . Experience showed that the l o g sheets used to record the Mini-Fix data could have been better organized. Space should be pro- vided f o r the name of the vessel as well as the names of the operators. The vessel number and the information about the type of f i x ( i n s t a l l i n g , removing or just checking the f l o a t ) and the f l o a t number should come f i r s t . Next should be the p o s i t i o n coordinates, followed by the time. 135 Even better coverage could p o s s i b l y be obtained with the use of f l o a t s equiped with transmitters. Each f l o a t would send out a d i s - t i n c t i v e s i g n a l , allowing i t to be i d e n t i f i e d . Such f l o a t s have been used i n other experiments (e.g. the SOFAR f l o a t s which were used to follow subsurface currents i n MODE, the Mid Ocean Dynamics Experiment). Obtaining or b u i l d i n g the transmitters and receivers necessary f o r such an experiment would involve considerable expense, but such a system would have many advantages. The vessels would only be needed to i n s t a l l and remove the f l o a t s , allowing more f l o a t s to be tracked. The chance of l o s i n g f l o a t s would be greatly reduced, and the d i f f i c u l t y of d i s - t i n g u i s h i n g them from other objects which appear on a radar screen would be eliminated. 134 Having the information in this order would make recording, transmitting and preliminary plotting of the data easier. During the experiment we tried to measure the velocities of the floats over short distances by taking pairs of fixes separated by only a few minutes, with intervals of twenty minutes or so between successive pairs of positions for each float. This procedure was probably not worthwhile. The method of interpolation of positions and velocities which was eventually chosen would have given good results even without the double fixes, and the time could have been better spent in following more floats. Major changes could be suggested in the basic design of the experiment. Tracking floats with Mini-Fix does have disadvantages, since having to v i s i t each float to measure i t s position severely limits the number of floats which can be handled with the available vessels. Altern- ative methods might allow better coverage. For an area l i k e the Fraser River plume, radar tracking was considered impractical because we wanted to examine more of the flow than the three-mile range of the radar set would permit. A practical alternative might be to use radar tracking near the river mouth and Mini- Fix positioning when floats moved farther out. This combination of methods would c a l l for good organization of the vessels to ensure that floats were taken over for Mini-Fix tracking when they reached the edge of the area of radar coverage. The early stages of the data reduction would be complicated by having data from two sources to be combined. However, a significant improvement in coverage of the area might be obtained with equipment already available. 136 LIST OF REFERENCES BUCKLEY, J.R. 1977. The currents, winds and t i d e s of northern Howe Sound. Ph.D. Thesis. U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. 225 pp. BUCKLEY, J.R. and S. POND. 1976. Wind and the surface c i r c u l a t i o n of a f j o r d . Journal of the Fisheries Research Board of Canada, 33(10): 2265-2271. CANADA. Department of the Environment. Marine Sciences Di r e c t o r a t e . Canadian Hydrographic Service. Canadian Tide and Current Tables 1974, Volume 5, Juan de Fuca and Georgia S t r a i t s . CANADA. Department of Mines and Technical Surveys. Marine Sciences Branch. Canadian Hydrographic Service. Canadian Tide and Current Tables. 1967, Volume 5, Juan de Fuca and Georgia S t r a i t s . DE LANGE BOOM, B. 1976. Mathematical modelling of the c h l o r o p h y l l d i s t r i b u t i o n i n the Fraser River plume, B r i t i s h Columbia. M.Sc. Thesis. U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. 140 pp. EKMAN, V.W. 1905. On the influence of the Earth's r o t a t i o n on ocean currents. Arkiv foer Matematik, Astronomi och Fysik. 2(11): 1. FRASER, CM. and A.T. CAMERON. 1916. V a r i a t i o n s i n density and tem- perature i n the coastal waters of B r i t i s h Columbia. Contributions to Canadian Biology} 1914-1915, pp. 133-143. GI0VAND0, L.F. and S. TABATA. 1970. Measurement of surface flow i n the S t r a i t of Georgia by means of f r e e - f l o a t i n g current followers. F i s h e r i e s Research Board of Canada, Technical Report No. 163, 69 pp. HUTCHINSON, A.H. and C.C. LUCAS. 1931. Epithalassa of the S t r a i t of Georgia. Canadian Journal of Research, 5: 231-284. KEULEGAN, G.H. 1966. The Mechanisms of an Arrested Saline Wedge. Estuary and Coastline Hydronamics3 A.T. Ippen, Ed. McGraw- H i l l , New York. pp. 546-574. MADDEROM, P. 1974. Curve f i t t i n g using cubic s p l i n e s . U n i v e r s i t y of B r i t i s h Columbia Computing Centre, Technical Note 17, 6 pp. MOREL, P. and M. DESBOIS. 1974. Mean 200-mb c i r c u l a t i o n i n the southern hemisphere deduced from EOLE balloon f l i g h t s . Journal of the Atmospheric Sciences, 31(2): 394-406. 137 LIST OF REFERENCES (continued) REINSCH, CH. 1971. Smoothing by spline functions, II. Mathematik, 16: 1+51-454. Numerische TABATA, S. 1972. The movement of the Fraser River - influenced surface water in the Strait of Georgia as deduced from a series of aerial photographs. Pacific Marine Sciences Report 72-6, 69 pp. TABATA, S., L.F. GIOVANDO and D. DEVLIN. Current velocities in the vi c i n i t y of the Greater Vancouver Sewerage and Drainage District's Iona Island Outfall - 1968. Fisheries Research Board of Canada, Technical Report No. 263, 110 pp. TABATA, S., L.F. GIOVANDO, J.A. STICKLAND and J. WONG, 1970. Current velocity measurements in the Strait of Georgia - 1967. Fisheries Research Board of Canada, Technical Report No. 169, 2 4 5 pp. TULLY, J.P. and A.J. DODIMEAD. 1957. Properties of the water in the Strait of Georgia and influencing factors. Journal of the Fisheries Research Board of Canada, l4(3): 241-319• VACHON, W.A. 1974. Improved drift i n g buoy performance by scale model drogue testing. Marine Technology Society Journal, 8 ( 8 ) : 58-62. WALDICHUK, M. 1957. Physical oceanography of the Strait of Georgia, British Columbia. Journal of the Fisheries Research Board of Canada, 14(3): 321-486. WALDICHUK, M. 1958. Drift bottle observations in the Strait of Georgia. Journal of the Fisheries Research Board of Canada, 15(5): 1065-1102.

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