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The influence of the spring-neap tidal cycle on currents and density in Burrard Inlet (Vancouver harbour),… Isachsen, Pål Erik 1998

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T H E I N F L U E N C E OF T H E SPRING-NEAP TIDAL C Y C L E ON CURRENTS A N D DENSITY IN B U R R A R D INLET ( V A N C O U V E R H A R B O U R ) , BRITISH C O L U M B I A , C A N A D A by Pal Erik Isachsen B . A . S c , The University of British Columbia, 1995 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E S T U D I E S E A R T H A N D O C E A N S C I E N C E S ( O C E A N O G R A P H Y ) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September 1998 © Pal Erik Isachsen, 1998 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Earth and Ocean Sciences (Oceanography) The University of British Columbia 2075 Wesbrook Mall Vancouver, BC Canada V6T 1Z1 Date: Abstract The physical oceanography of Burrard Inlet/Vancouver Harbour in British Columbia, Canada, is studied. Particular focus is given to tidal mixing through First and Second Narrows, two constrictions that separate the western harbour from the coastal waters outside and the eastern harbour from the western harbour, respectively. The mixing at these two narrows is believed to be a significant controlling factor on the density field within Burrard Inlet and also within Indian Arm, the northern extension of this estuary. During the 1995 spring, current meters which also measure temperature and con-ductivity were moored at 6 m and 16 m above the bottom at three locations: outside First Narrows, inside First Narrows and inside Second Narrows. During spring tides, currents at depth are as high as 1.5 m/s; small floods bring outside water through the narrows relatively unmixed which sinks down to depth; large floods result in intrusions of highly mixed water up to 1 kg m~3 lower in density. During neap tides currents at depth are generally small, density decreases slowly and vertical diffusion is believed to be the dominant process at depth. Analysis of vertical diffusion near the bottom at one station during neap tides produces estimates of the vertical eddy diffusivity which are somewhat higher than those from similar studies in other B.C. fjords. Harmonic analyses of pressure time series from two of the current meters and tide gauge records are used to estimate the total energy loss from the barotropic tide over First and Second Narrows. Comparison with previous studies is in good agreement; however, there appears to be some seasonal variation. Conditions in the harbour were investigated by CTD and ADCP during the 1997 spring. CTD casts suggest that internal-tide resonance within the harbour during neap ii tides may be a contributing factor to the weak currents at depth during such periods. ADCP transects through Second Narrows reveal the presence of strong vertical velocities, possibly associated with hydraulic jumps, downstream of the narrows during large floods. The flow through the narrows is indeed supercritical with respect to the first baroclinic mode on large floods. Estimates of the dissipation rate of turbulent kinetic energy from current meter casts in the most turbulent regions give e of 1-50 cm2 s - 3 which is as large or larger than any previous estimates in the ocean. iii Table of Contents Abstract ii List of Tables vii List of Figures viii Acknowledgements xii 1 Introduction 1 1.1 General Description of Study 1 1.2 Physical Description of Study Area 4 1.3 Previous Work 6 1.3.1 Descriptive studies 6 1.3.2 Modelling studies 7 1.4 Rationale and Organization of Thesis 9 2 The Field Data 12 2.1 The IA-95 Mooring Program 12 2.1.1 Methodology and instrumentation 12 2.1.2 Data processing 14 Clock drift 14 Trimming and averaging of velocity and scalars 14 Correction for offset and drift in scalars . . 15 2.2 The VH-97 Survey 24 iv 2.2.1 Methodology and instrumentation 24 2.2.2 Data processing 28 Compass corrections of A D C P horizontal velocity estimates 28 Pitch and roll corrections of A D C P vertical velocity esti-mates 30 A note on GPS accuracy 33 3 Results from the IA-95 Mooring Program 35 3.1 Synoptics 35 3.1.1 Seasonal trends 35 3.1.2 The spring-neap tidal cycle 43 3.1.3 Daily details during spring tide 47 3.2 Energy Loss from the Barotropic Tides in the Narrows 52 3.2.1 The barotropic flux model 53 3.2.2 Results 56 3.3 Kinetic to Potential Energy Transfer in the Narrows 59 3.3.1 Density jumps at lower instruments over floods during spring tide 60 3.4 Vertical Diffusion at Depth during Neap Tides 65 3.4.1 The budget method 66 3.4.2 Results 68 4 Results from the VH -97 C T D / A D C P Survey 73 4.1 Conditions in Vancouver Harbour during the 1997 Spring 73 4.1.1 Overview of C T D casts 73 4.1.2 Background estuarine flow in the harbour 83 4.1.3 The tidal prism in the harbour 87 4.1.4 Blocking of the flow at the entrance to sills 88 v 4.1.5 Internal resonance in the harbour 89 4.1.6 The spring-neap variability of density structure and circulation in the harbour 92 4.2 The Flow Behaviour in Second Narrows 94 4.2.1 Field observations 96 4.2.2 Interpretation in terms of internal hydraulics theory for uni-directional flow 103 Elements of the theory 105 Application to Second Narrows 108 4.2.3 The details of mixing in Second Narrows 113 4.3 Turbulent Dissipation in Second Narrows 118 4.3.1 The spectral theory of turbulence 118 4.3.2 Results from 7 May 123 4.3.3 Comparison with results from 1996 127 5 Conclusions 133 5.1 Summary of Results 133 5.2 Suggestions for Further Work 135 Bibliography 137 A Monthly CTD Casts during IA-95 Study 145 B Raw IA-95 Time Series 149 vi List of Tables 2.1 S4 clock drifts 14 3.1 Phase difference of barotropic tide 57 3.2 Seasonal variability in phase shifts 58 4.1 Baroclinic wave speeds vs. depth-averaged east-west velocity through Sec-ond Narrows 113 vii List of Figures 1.1 Estuarine circulation in a typical fjord 2 1.2 The study area 5 2.1 The IA-95 mooring 13 2.2 S4 vs. C T D calibration at QB 17 2.3 S4 vs. C T D calibration at Stn-66 18 2.4 S4 vs. C T D calibration at Stn-48 19 2.5 Temperature and salinity differences between the bottom and top instru-ments at QB 21 2.6 Temperature and salinity differences between the bottom and top instru-ments at Stn-66 22 2.7 Temperature and salinity differences between the bottom and top instru-ments at Stn-48 23 2.8 The M V Noctiluca 25 2.9 Bottle and S4 cast 26 2.10 A D C P mounted off the starboard side of the boat 27 2.11 Correction of A D C P compass by comparison with GPS 29 2.12 Pitch and roll effect on A D C P vertical velocity readings 30 2.13 The A D C P co-ordinate system 31 2.14 Correction of A D C P vertical velocity for pitch and roll effects by regression 34 3.1 Tidal height, speeds and densities for whole record 36 3.2 Tidal height, temperature and salinity for whole record 38 viii 3.3 River discharge during mooring deployment 39 3.4 TS-diagram for station QB 40 3.5 TS-diagram for station STN-66 42 3.6 TS-diagram for station STN-48 42 3.7 Conditions at QB 30 m for 20 days in may 44 3.8 Conditions at Stn-66 60 m for 20 days in May 45 3.9 Conditions at Stn-48 60 m for 20 days in May 46 3.10 Conditions at Stn-66 for 4 days during spring tides in May 49 3.11 Conditions at Stn-48 for 4 days during springs in May 50 3.12 TS diagram from lower instruments at all three stations for 4 days during springs in May 51 3.13 Schematic of the barotropic energy loss across the sill in an inlet 55 3.14 The Continuous Wavelet Transform of density at Stn-48 60 m 61 3.15 Density jumps at Stn-66 at floods during a spring tide 62 3.16 Density jumps at Stn-48 at floods during a spring tide 63 3.17 Density jump vs. square of tidal range over floods during springs at Stn-66 and Stn-48 60 m 64 3.18 Period when vertical diffusion is dominant at Stn-48 69 3.19 Box model of the hole at Stn-48 for vertical diffusion estimate by the budget method 70 3.20 Vertical diffusivity vs. buoyancy frequency during low-advection periods at Stn-48 71 4.1 The tide in Vancouver Harbour during the 1997 spring 74 4.2 C T D casts from 21 February 75 4.3 C T D casts from 7 March 77 ix 4.4 CTD casts from 10 March 79 4.5 CTD casts from 7 May 80 4.6 CTD casts from 8 May 81 4.7 CTD casts from 16 May 84 4.8 East-west velocities in the harbour at early stages of a flood on 16 May . 86 4.9 Density gradient between Stn-66 and Stn-56 on 16 May 91 4.10 Ship tracks through Second Narrows during CTD tow-yos 97 4.11 ADCP and CTD data from tow-yo on 10 March 99 4.12 ADCP and CTD data from tow-yo on 7 May 101 4.13 ADCP and CTD data from tow-yo on 8 May 102 4.14 ADCP and CTD data from tow-yo on 16 May 104 4.15 Density profiles at beginning of each tow-yo through Second Narrows . . 109 4.16 The CTD data, profile by profile, from the tow-yo on 7 May 115 4.17 Gradient Richardson number estimates from tow-yos on 7 May 117 4.18 Sketch of the turbulent energy spectrum 121 4.19 S4 velocities on 7 May 124 4.20 Turbulent energy spectra from 7 May 125 4.21 S4 velocities on 16 March 1996, first cast 128 4.22 S4 velocities on 16 March 1996, second cast 129 4.23 Turbulent energy spectra from 16 March 1996: first cast 130 4.24 Turbulent energy spectra from 16 March 1996: second cast 131 A . l CTD casts at QB during IA-95 program 146 A.2 CTD casts at Stn-66 during IA-95 program 147 A. 3 CTD casts at Stn-48 during IA-95 program 148 B. l QB 20 m 150 x B.2 QB 30 m 156 B.3 Stn-66 50 m 162 B.4 Stn-66 60 m 168 B.5 Stn-48 50 m 174 B.6 Stn-48 60 m 180 xi Acknowledgements I would like to acknowledge some of the people who have helped me through the process of putting this work together. My supervisor Stephen Pond loves to share his knowledge from a long research career with anyone who shows curiosity and interest in learning about this subject. I want to thank him for showing me that there actually is a connection between the real data we gather and the algebraic equations from the G F D and turbulence classes. I also thank him for always taking his job as supervisor extremely seriously. My two committee members, Susan Allen and Richard Pawlowicz, also gave me comments and ideas on the work every time I asked; I want to thank them for their genuine interest. Thanks also to David Farmer, Gregory Lawrence and Roger Pieters for useful discussions and to David Jones, Denis Laplante, Carol Leven and Joseph Tarn for endless technical advice. Special thanks go to Peter Baker, for offering us his boat for this study, but mostly for all the time he voluntarily put in. Without Peter I would not have had the data on which half of this thesis is based. I am indebted to Richard Marsden of the Royal Military College in Kingston, Ontario, who lent us the A D C P used in this work, and to Fred Stephenson and Bodo de Lange Boom of the Institute of Ocean Sciences in Sidney, B.C. , who let me have access to tide-gauge data from the harbour. The National Science and Engineering Research Council (NSERC) provided research support for this project and, along with the Norwegian State Educational Loan Fund, provided personal support. Finally, warm thoughts go to my family and friends. Some have lived in the same house as me here, others on the other side of the planet. They have all made these last two years in Vancouver my best ones ever. xii Chapter 1 Introduction 1.1 General Description of Study This is an observational study of tidal mixing processes around the silled entrance region of a fjord-type estuary. Pritchard (1967) gives the accepted definition of an estuary as . . . a semi-enclosed coastal body of water which has a free connection with the open sea and within which sea water is measurably diluted with fresh water derived from land drainage. There are various types of estuaries, and classification schemes are typically based on geological processes leading to their formation or on gross features of the salinity structure and estuarine flow (e.g. Dyer, 1973, pp. 4-14). A discussion of their past, evolution and future is given in Schubel et al. (1978). Fjords, or inlets, are estuaries created when glacially carved valleys become submerged as sea levels rise after an ice age. They can be several hundred meters deep, often deeper than the continental shelf, and usually have steep sidewalls. At the entrance of many fjords sedimentary deposits left behind as the glacier receded form shallow and sometimes narrow parts of the estuary which are termed banks or sills. In the classic description of estuarine circulation (e.g. Thomson, 1981) the long term, steady-state, flow is driven by an input of fresh water from one or more rivers. One major river may be located at the head of the inlet, but often there is freshwater input from 1 Chapter 1. Introduction 2 smaller tributaries all along the fjord. In this classic description the input of fresh water raises the sea level in the fjord slightly at the head and the resulting along-fjord pressure gradient causes the fresh surface water to travel in the seaward direction. Velocity shear between this top layer and the denser water below causes mixing of denser water into the top layer by the process of entrainment (e.g. Turner, 1986). There is a net transport of water from the salty lower layer into the brackish upper layer. The water lost from the lower layer must be replenished by flow towards the head of the estuary at depth (Figure 1.1). Figure 1.1: Estuarine circulation in a typical fjord. From Thomson (1981). In many fjords the circulation pattern is more complex than that described above. The daily (diurnal) and/or twice-daily (semi-diurnal) flooding and ebbing of the tides through constrictions and over banks and sills result in large velocities. Some of the Chapter 1. Introduction 3 kinetic energy of the flow will be transferred to potential energy of the water column through turbulent mixing processes that occur in these regions. Turbulence may result from several processes, e.g. velocity shear at the bottom, breaking of internal waves radiating away from the sill and from other types of adjustments if the sill imposes hydraulic control1 on the flow. Depending therefore on the strength of the tidal forcing, the geometry of the sill region and the density structure of surrounding waters, the tidal mixing in the sill region may be more or less important in modifying the density structure of the waters in the rest of the fjord. It may be that tidal mixing in one or two such energetic regions is so effective that it essentially dictates the circulation in the entire fjord system. One aspect in particular which may be controlled by such sill processes is the renewal of deep water in a fjord. The water in the fjord at depths greater than the sill depth can only be replaced when even denser water from the coast outside manages to cross the sill. The horizontal pressure gradients that drive the estuarine flow in combination with the tidal forces are the sources of energy required to lift dense water from the outside up to the sill. However, the high velocities in the sill region will often cause turbulent mixing there which in turn may cause the water entering the fjord to be too light to sink and replace the existing deep water there. The fjord studied in this thesis has a very active sill region where tidal mixing is vigorous. The bottom water sometimes remains stagnant for several years before being completely replaced during winter. Sometimes there is replacement during two or three consecutive winters. The inter-annual differences depend on the last replacement and the density of the source water. 1 The concept of hydraulic control on flow due to influence of bottom topography is introduced and discussed in relation to mixing processes in First and Second Narrows in section 4.2. Chapter 1. Introduction 4 1.2 Physical Description of Study Area The Burrard Inlet - Indian Arm system forms a fjord-type estuary on the southern coast of British Columbia (Figure 1.2) and is connected to the North Pacific via the Strait of Georgia. The Greater Vancouver Region, which has more than one and a half million people, is partially built up around Burrard Inlet, the outer portions of the estuary. INDIAN A R M has some of the typical characteristics of a fjord. It is long (approxi-mately 22 km) and narrow (average width 1.3 km), has steep sidewalls and a deep basin which stretches 3/4 of the total length and has a maximum depth of more than 200 m. Its freshwater input, however, is low for a B.C. fjord. The total annually averaged dis-charge into the Indian Arm - Burrard Inlet system is somewhere between 40 and 100 m 3 /s (Davidson, 1979; Dunbar, 1985). The primary inputs to Indian Arm are the Indian River at the head of the fjord and a controlled output from Buntzen power plant at the eastern bank. Indian Arm is separated from Burrard Inlet by a sill 26 m deep. B U R R A R D INLET, which on charts from Canadian Hydrographical Service is termed Vancouver Harbour, can be thought of as an extended entrance region to Indian Arm although it is about 20 km long. The maximum depth is about 65 m, but most of the inlet is much shallower. Most of its freshwater input comes from Capilano and Seymour rivers and Lynn creek draining from steep mountains along the north shore. Fraser river which flows into the Strait of Georgia south of Pt. Grey is the dominant freshwater source in the Strait. Some of its water which is drawn into Vancouver Harbour on flood tides must also be considered. The entrance to Burrard Inlet is FIRST N A R R O W S , a 15 m deep, dredged channel which is heavily used by ships entering Vancouver Harbour. SECOND N A R R O W S is a 19 m deep, dredged channel that separates the main (western) harbour from the eastern portions of Burrard Inlet which lead to Port Moody and Indian Arm. In both of these Chapter 1. Introduction 5 Figure 1.2: Map and longitudinal profile of the study area. Burrard Inlet and Indian Arm make up the two parts of a British Columbia fjord-type estuary. The numbered station names represent twice the distance in kilometers from the inlet head. From de Young and Pond (1987). Chapter 1. Introduction 6 narrow and shallow channels, tidal currents are strong, and the regions around them are the primary focus of this study. 1.3 Previous Work 1.3.1 Descriptive studies Early studies of B.C. inlets can be found in Carter (1934) and Pickard (1961 and 1975). Early studies more specific to the Burrard Inlet - Indian Arm system include Campbell (1954), Gilmartin (1962), Waldichuk (1965) and Tabata (1971). These studies focus on annual mean or annual cycles of properties. The first study to give more specific attention to Burrard Inlet and which also investigated shorter time scale fluctuations, down to tidal periods, was done by Davidson (1979). He studied property distributions in Burrard Inlet and Indian Arm during several ebb cycles and noted that tidal fluctuations were small compared to seasonal variations in properties for all depths below the top 3-5 m of the water column. AdditionaL.aspects of the deep water circulation in Indian Arm were investigated by Burling (1982). Data for more recent studies were obtained with profiling current meters (cyclesondes) and CTDs (Conductivity, Temperature and Depth profiling instrument) during the win-ters of 1982/83, 1983/84 and 1984/85. The nature of the internal tide 2 in Indian Arm was first investigated by de Young and Pond (1987). The internal tide is one of the identified sinks of barotropic3 tidal energy in fjords, along with bottom friction and high-frequency internal waves (Freeland and Farmer, 1980). de Young and Pond (1987) found that as 2 The internal tide is comprised of internal waves of tidal frequencies which may be generated from interaction of the currents associated with the surface tide with bottom topography, e.g. a sill. 3The terms barotropic and baroclinic are both jargon from geophysical fluid mechanics. Various definitions exist (see e.g. Cushman-Roisin, 1994, p. 54 and p. 182; Pond and Pickard, 1983, p. 87). A flow in which isopycnals (surfaces of constant density) are parallel with isobars (surfaces of constant pressure) is termed barotropic. If isopycnals are inclined with respect to isobars the flow is termed baroclinic. A flow which is depth independent, e.g. the astronomical tide, is considered to be barotropic. Chapter 1. Introduction 7 much as 18% of the barotropic tidal energy entering Burrard Inlet is lost, about 9% at each of the two narrows (but since the barotropic energy flux through Second Narrows is smaller due to loss upstream, the relative loss there is higher than at First Narrows). In comparison, the energy lost across the Indian Arm sill was estimated to be around 3% of what enters First Narrows. The partition of energy loss from the barotropic tide in Indian Arm (as well as in two other B .C . fjords) was more closely studied in de Young and Pond (1989). They used energy budget methods (Farmer and Freeland, 1983) to get estimates of the fractions of the barotropic energy that are lost to the internal tide, bottom friction and high-frequency internal waves, respectively. Their quantitative results focused on the loss across the Indian Arm sill rather than on losses in Burrard Inlet. However, they also suggested that some energy is lost to the generation of an internal tide over First Narrows, but that most of the loss in the harbour as a whole is due to bottom friction. The deep water exchange cycle in Indian Arm was studied in de Young and Pond (1-988). Among the topics investigated were the vertical diffusion of salt and heat at depth during quiescent periods and the possibility of the Indian Arm sill exerting hy-draulic control on the exchange flow in the inlet. A main conclusion was that deep-water replacement occurred during neap tides4 when tidal currents through the narrows are generally low. 1.3.2 Modelling studies Two attempts have been made at developing computer models of the circulation in In-dian Arm. The rationale for creating such models is threefold. First, comparison between 4Neap tides, or neaps, are smaller tides which occur when the Earth-Moon-Sun system form a right triangle (the moon being in its first or last quarter). Spring tides, or springs, are extra large tidal ranges which occur when the three bodies align (full moon or new moon). The period of this oscillation is approximately 14 days. Chapter 1. Introduction 8 model results and field observations can immediately indicate whether the approximate equations used in the model actually represent the real physical processes. Second, a modeller is able to turn on and off various types of external forcing, e.g. wind, tides, and buoyancy inputs (e.g. rivers) to investigate both the individual contribution from each on the circulation and perhaps also some of the non-linear interactions between them. The experimental oceanographer does not have such luxuries. Finally, a model which appears to do a good job at simulating the dynamics in the estuary may be used for case studies related to practical problems, e.g. tracking of a pollutant introduced to the waters. The first model of the Indian Arm circulation was written by Dunbar and Burling (1987). The outer boundary of the model was at Stn-66 in the middle of Vancouver Har-bour, so the effect of First Narrows was not accounted for. The model was 2-dimensional (laterally integrated in the across-inlet direction), had multiple depth levels, and was time-varying. It included advective terms, horizontal and vertical turbulent diffusion of momentum and salts, and variations in width and depth. Stacey et al. (1991) compared model simulations with observations from Indian Arm, and found that tidal flow could be simulated reasonably well if horizontal and vertical diffusion coefficients were tuned and freshwater runoff taken into account. The model did poorly however at simulating a deep-water renewal event which was observed for the winter 1984-85. The simulated density field became too homogeneous and the ability to simulate the diurnal and semi-diurnal tides for such periods was reduced. Dunbar and Burling (1987) recognized that besides a too simple parameterization of the eddy diffusivities5, the major limitation of the model was in the coarse spatial resolution. Specifically, the model was unable to ac-curately resolve the thin fresh layer at the surface, so important in resolving the estuarine circulation. A surface layer was added later. 5 Eddy diffusivity and eddy viscosity are concepts introduced in the turbulence literature to close the Reynold's equations which aim to describe the effect of turbulent fluctuations on the mean flow. The turbulent spreading of a scalar is thought of as an enhanced molecular diffusion. Chapter 1. Introduction 9 Another laterally-integrated, time-dependent model, written by Nowak, successfully simulated the circulation of Knight Inlet, another B.C. fjord (Stacey et al, 1995). Achiev-ing satisfactory simulations of the Indian Arm - Burrard Inlet region with the same model has been more difficult (Pond et al, 1998). The model has a variable vertical grid and the grid resolution can be changed locally in the horizontal; thus, the thin surface layer is resolved well, and important regions such as sills have better horizontal resolution. The vertical eddy viscosity and diffusion coefficients also have a more complex parameteriza-tion than in Dunbar's model. They are made to depend on both the local velocity shear and water column stability. The model is able to simulate the diurnal and semi-diurnal tides quite well, but still has problems with the deep-water exchange. Renewal events are simulated by the model, but at the wrong time. As reported by de Young and Pond (1988), field observations show that renewal in Indian Arm occurs during neap tides, whereas in the model it occurs during spring tides. The density of waters passing into Indian Arm on flood tides were typically too high compared with field measurements, indicating that the mixing in Burrard Inlet was underestimated by the model. The (bot-tom) drag coefficient was tuned to give the correct amount of friction and phase lag in the barotropic tide across the narrows (see Section 3.2), and eddy diffusivities based on shear and stability were consistent with turbulence observations. The need for tuning the drag coefficient, however, suggests that another source of turbulence and mixing must be unaccounted for in this model. 1.4 Rationale and Organization of Thesis Based on his studies of several ebb tides in Vancouver Harbour, Davidson (1979) concluded that Chapter 1. Introduction 10 . . . at depths greater than 3 m, seasonal distributions of salinity and tempera-ture can be discussed and compared without particular concern for the phase of the tide at the time the distributions were sampled. He did not, however, include flood tides in his study. As will be seen, a main result of the present study is that salinity and temperature at depth in the harbour vary greatly over the course of both flood and ebb tides, primarily due to the mixing in the two narrows. This realisation is not a new one. Oceanographers at U B C have always recognized the importance of the mixing in Burrard Inlet to the determination of property distributions in the whole fjord system. In discussing the specific significance of the tidal currents flowing through First and Second Narrows, Tabata (1971) wrote that these "currents are considered as the dominant agency contributing to the mixing of waters in the inlet". Before attempting further modelling, the processes of mixing in the narrows must be better understood. A model of the Indian Arm circulation which has its outer boundary at the Indian Arm sill, that is, inside of the active mixing region of Burrard Inlet, would have to have time-varying boundary conditions, not only in the barotropic tidal forcing but also in salinity and temperature at the same time scales. A long-term field program at the Indian Arm sill would be required, an approach which would be prohibitive for a model expected to make operational predictions. If on the other hand the model has its outer boundary at some distance outside of First Narrows, the time scales of boundary forcing are much greater (seasonal variability in the Strait of Georgia). However, the mixing that occurs in the two narrows must be properly parameterized and then included for the model to give sensible results. One purpose of this thesis is thus to better resolve some characteristics of the flow in Burrard Inlet from sub-tidal to longer time scales, and especially that of the deep water which is the only source for intrusion to great depths in Indian Arm. This thesis will Chapter 1. Introduction 11 hopefully enable modellers to better parameterize the tidal mixing in that region. In addition, the characteristics of flow in Burrard Inlet and especially in the regions around First and Second Narrows is an interesting topic of study in itself from a fluid-dynamics perspective, de Young and Pond (1988) suggested that internal hydraulic jumps and other adjustment processes might be present and relevant during large parts of the tidal period. The interaction of stratified flow with topography, however, is a complex topic which still is not fully understood (see e.g. Baines, 1995). The flow through each of the narrows must certainly involve several interacting dynamic phenomena, and a second purpose of this thesis is to identify and better describe some of these processes. Two sets of field observations provide the data on which the thesis is based. Current meters which were also able to measure temperature and salinity were moored near the bottom at three locations in Burrard Inlet for nearly four months in the spring of 1995 (field program IA-95). These instruments sampled fast enough to give an excellent time series of currents and water properties at depth in the inlet; both sub-tidal fluctuations and seasonal trends are represented. In order to study some of the processes related to the interaction of the flow with the topography in First Narrows and Second Narrows, multiple passes across the narrows were done with small boat at several occasions during the spring of 1997 (field program VH-97). The instrumentation consisted of a profiling current, temperature and conductivity probe, an acoustic doppler current profiler, and a ship-mounted echo sounder. Chapter 2 describes the observational techniques and the data reduction for each of the two field programs. Chapter 3 and 4 present findings from IA-95 and VH-97, respectively. Finally some concluding remarks along with suggestions for further work are given in chapter 5. Chapter 2 The Field Data 2.1 The IA-95 Mooring Program 2.1.1 Methodology and instrumentation In March of 1995, three moorings were deployed along Burrard Inlet: the first outside First Narrows near a traffic buoy, the second in the deepest hole inside (east of) First Narrows and the third in the deepest hole inside Second Narrows. These stations will be termed QB, Stn-66 and Stn-48, respectively, and are shown in Figure 1.2. The names Stn-66 and Stn-48 are based on CTD-station ordering with the numbers indicating twice the distance from the head of Indian Arm in kilometers. QB is near a traffic separation buoy outside First Narrows. Each mooring consisted of two S4 electromagnetic current meters (InterOcean, 1994) placed 6 m and 16 m above the bottom, with anchoring and flotation as shown in Figure 2.1. The six instruments will be termed QB 20 m, QB 30 m, Stn-66 50 m, Stn-66 60 m, Stn-48 50 m and Stn-48 60 m to indicate the approximate depth of the instruments below tidal datum 1 (as opposed to the height above the bottom). In addition to horizontal velocities, all S4's observed temperature and conductivity, and the 60 m instruments at Stn-66 and Stn-48 also measured pressure. Only the instrument at QB 20 m was equipped with tilt sensors from which horizontal velocity measurements could be corrected. The tilts at this mooring were small, 2-3 degrees, thus tilts at the other locations were also believed to be small since the moorings were short and the 1 Depth soundings on hydrographic charts are given in depth below datum, which is mean lower low water. 12 Chapter 2. The Field Data buoyancy quite high. 13 F i g u r e 2 .1 : The IA-95 moorings placed at QB, Stn-66 and Stn-48 during the spring of 1995. The entire mooring was anchored to the bottom with a railway wheel, while an acoustic release was used to recover the valuable parts of the mooring later. The instruments were deployed on 6 March and recovered on 28 June 1995. Horizontal velocity, temperature, and conductivity (and pressure for Stn-66 60 m and Stn-48 60 m) were stored every 15 minutes. Each 15-minute velocity reading was an average of 120 readings taken over one minute while the scalars were individual readings at the end of such one-minute periods. The S4 at QB 20 m was an exception in that scalars were also Chapter 2. The Field Data 14 120-point averages. 2.1.2 Data processing When moorings are operating in the field for over three and a half months, one may expect a certain amount of measuremen drift. Calibration of instruments before deploy-ment and after retrieval are discussed in the following. Clock drift A l l S4 internal clocks were calibrated against Pacific Standard Time (PST) in the lab before and after the experiment. Results (Table 2.1) show that clock drift was small, generally in the order of a minute over the whole deployment period. Station Instrument Deviation Deviation Average # # 5 March 28 June deviation (sec) (sec) (sec) QB 20 m 69 1 -61 -30 QB 30 m 51 2 -51 -24 Stn-66 50 m 45 1 -89 -44 Stn-66 60 m 56 2 -46 -22 Stn-48 50 m 46 0 -96 -48 Stn-48 60 m 57 1 -44 -22 Table 2.1: S4 clock drifts over the deployment period. Positive and negative deviations correspond to fast and slow S4 clocks, respectively. A l l S4 clocks were on average less than a minute off correct time. Trimming and averaging of velocity and scalars The raw conductivity records from most instruments contained spikes at irregular intervals, most likely due to biological material near the S4 conductivity electrodes. Most spikes were removed by running a rectangular window, five data points wide, along the Chapter 2. The Field Data 15 time series, calculating the median and the median absolute deviation (MAD) within the window, then replacing the center data point with the median if more than three M A D away from the median. A few remaining spikes, usually much wider than five data points, were removed manually and replaced with the characteristics of the time series around the spike. By doing such a subjective correction to the record one risks removing real physical phenomena; for this study, however, single points do receive individual attention. For some of the remaining analysis, hourly values of velocities, temperatures, salinities, densities and pressure were made from the 15-minute raw records. A rectangular window, seven data points long, was moved along the time series, the biggest and the smallest value within the window were rejected and an hourly mean value from the remaining five readings were calculated. Correction for offset and drift in scalars For studies of long time-scale variations in the density field and as well the vertical den-sity gradient, any relative offset or drift in the temperature and conductivity instruments must be tracked. The water salinity is calculated from temperature and conductivity, and finally density is calculated from temperature and salinity 2. For instance, salinity and temperature gradients between instruments at Stn-66 and Stn-48 were used to make estimates of vertical eddy diffusivity (Section 3.4). Small errors in the gradient due to instrument offsets will affect the results considerably. Plots of temperature and salinity readings of the S4's versus similar measurements taken with a C T D during monthly cruises in Burrard Inlet are shown in Figures 2.2 through 2.4 (all monthly C T D casts are shown in Appendix A) . The C T D was also calibrated against temperature and salinity readings in the laboratory and reversing 2The current equation of state for seawater writes density as a polynomial of temperature, salinity and pressure (UNESCO, 1998). Chapter 2. The Field Data 16 thermometers and water taken from bottle samples during the same cruises, and values were found to be in good agreement (within 0.01 for both T and S). Comparison be-tween S4 and CTD data show mostly good agreement in temperature for all stations, but indicates offsets in some of the S4 conductivity sensors and drift in others. All S4 temperature and conductivity sensors were calibrated before and after the experiment. A polynomial correction (2nd order for thermistor temperatures and 1st order for resis-tance temperatures and conductivity) was applied to each instrument based on these calibrations. Temperature corrections were within 0.02 from before and after calibra-tions but conductivity showed differences up to 0.3 in salinity as seems typical for these instruments. S4 temperature differences should be accurate to 0.02 or better (and the temperatures themselves to 0.03 or better). S4 salinities should be good to about 0.2 and salinity differences to about 0.3 consistent with CTD comparisons. The offsets and drifts observed may be caused by combinations of instrument aging and growth of biologic material on the electrodes. At QB 20 m, some S4 salinities are lower than CTD values, however the CTD casts show that considerable vertical concentration gradients existed at a depth of 20 meters at the time of the casts. At QB 30 m on the other hand, S4 salinities were consistently higher than CTD values even for casts where the gradient at this depth was negligible. At Stn-66 50 m, S4 salinities are higher than CTD values at the beginning of the record, then lower towards the end. Only one CTD cast reached 60 meters at this station, but three more data points were extrapolated from 55 m. For these, both temperatures and salinities were in good agreement. At Stn-48 50 m, S4 salinities for most of the duration of the record were lower than the CTD values. Only three CTD casts reached 60 meters; temperatures and salinities were in good agreement for these. Figures 2.5 through 2.7 show the time series of temperature and salinity differences (as the bottom minus the top values) from the S4 instruments at QB, Stn-66 and Stn-48. Chapter 2. The Field Data 17 QB 20 m QB 20 m 8 9 CTD temp (°C) QB 30 m 8 9 CTD temp (°C) w 29.5 29.3 29.3 29.4 29.5 29.6 29.7 29.8 CTD sal (psu) QB 30 m 29.3 29.3 29.4 29.5 29.6 29.7 29.8 CTD sal (psu) Figure 2.2: S4 vs. CTD calibration at QB. During monthly cruises CTD casts were taken at the mooring stations for instrument calibration of the S4 temperature and conductivity sensors. Legend: • = 9 March, O = 5 April, A = 4 May, y = 2 June and o = 23 June. The diagonal line has slope 1:1. Chapter 2. The Field Data Stn-66 50 m Stn-66 50 m CTD temp (°C) CTD sal (psu) Figure 2.3: S4 vs. CTD calibration at Stn-66. Same as in Figure 2.2 Chapter 2. The Field Data 19 Stn-48 50 m Stn-48 50 m CTD temp (°C) CTD sal (psu) Figure 2.4: S4 vs. CTD calibration at Stn-48. Same as in Figure 2.2 Chapter 2. The Field Data 20 Part of the QB salinity difference may be attributed to the consistently high salinities at QB 30 m. The conductivity drift at Stn-66 50 m mentioned above is particularly apparent, especially in early parts of the record. The salinity differences at Stn-48 also show drift, as well as an offset, presumably related to the low 50 m salinities also noted above. In the early part of the records the deeper instruments report slightly higher temperatures than the shallower ones; this is consistent with results from the CTD casts and the fact that the surface is colder than the deep water in the winter. As the surface warms up AT changes sign. It appears that AT is accurate to at least 0.02 as the laboratory calibrations indicate. To correct for some of these drifts, the assumption of complete mixing at depth inside First Narrows and Second Narrows after the completion of big floods was made. As shown in Section 3.1 the velocities at depth are high during the big floods of spring tides and the density drops. The CTD casts mentioned above indeed show that gradients between 50 and 60 m at Stn-66 and Stn-48 were often vanishingly small at such times. This assumption was not made for QB, being outside First Narrows and thus away from the direct influence of the mixing processes occuring there. During floods QB can be taken to represent the source water, i. e. water from the Strait of Georgia, and one would expect there to be a density gradient at depth. During ebbs even if there were strong mixing just outside First Narrows, the flow would likely become stratified by the time it reaches QB. The offset indicated by the S4-CTD comparison was used to adjust QB 30 m salinities. For Stn-66 and Stn-48 the salinity difference between the 50 and 60 m instruments at the end of floods during spring tides were used as corrections. For a general removal of the salinity drift at the 50 m instruments over the entire record, a low-order polynomial was fitted to the salinity difference after such flood tides. This correction was then added to the 50 m instrument (see Figures 2.6 and 2.7). In addition, where short period events Chapter 2. The Field Data 21 70 110 120 130 Julian days (b) Figure 2.5: (a) Temperature and (b) salinity differences between the bottom and top instruments at QB. A positive difference means higher reading at the lower instrument. The solid line in (b) represents a consistent high salinity reading in the 30 m instrument (as shown in Figure 2.2). This offset was subtracted from 30 m salinities. Chapter 2. The Field Data 2 2 Stn-66 120 130 Julian days (b) Figure 2.6: (a) Temperature and (b) salinity differences between the bottom and top instruments at Stn-66. A positive difference means higher reading at the lower instru-ment. A polynomial fit to the salinity difference, shown as solid line in (b), was added to the 50 m salinity to account for drift in that instrument. Chapter 2. The Field Data 23 Stn-48 0.5 h 1 1 .... . , ! , , i i i i i 11 1 1 1 I I 1 1 1 1 1 1 70 80 90 100 110 120 130 Julian days (b) 140 150 160 170 Figure 2.7: (a) Temperature and (b) salinity differences between the bottom and top instruments at Stn-48. A positive difference means higher reading at the lower instru-ment. A polynomial fit to the salinity difference, shown as solid line in (b), was added to the 50 m salinity to correct for drift in that instrument. Chapter 2. The Field Data 24 were studied, e.g. vertical diffusion over a few days of quiescent conditions, an average value of the flood-tide salinity differences taken a few days before and after the event was either added or subtracted to the data of one of the instruments, in effect 'clamping' the salinities of this instrument to those of the other instrument locally. 2.2 The VH-97 Survey 2.2.1 Methodology and instrumentation A 34-foot boat, the MV Noctiluca (Figure 2.8), was used to conduct a number of one-day surveys of Vancouver Harbour during the spring of 1997. The focus of these investigations was the detailed flow behaviour in the regions around Second Narrows, although on more than one trip some attention was also given to the circulation through First Narrows. Typically a cruise would start at low slack and last for the duration of the flood. Hence, conditions just before and after the flood were also studied, although most effort was put into capturing currents downstream of the narrows at maximum flood. The boat was fitted with a winch-mounted S4 current meter which acted as a CTD probe with 2 Hz sampling interval (Figure 2.9). Density profiles were collected at various locations up and downstream of the narrows for various phases of the tide. In addition, some attempts were made at measuring the 2-D density field for a limited region by tow-yo'ing the S4 when the boat was drifting with the currents downstream of the bridges at the narrows. The second primary instrument on board was a 153.6 kHz narrow-band ADCP3 (RD Instruments, 1987). The ADCP was mounted to one side of the boat by an aluminum post with the transducer head one meter below the surface (Figure 2.10). Water velocities were obtained in 2 m depth-averaged bins, starting at 4 m depth and extending to the bottom. 3 A n Acoustic Doppler Current Profiler measures currents along a profile of the water column by first emitting an acoustic signal then monitoring the doppler shift of the reflection from various depths. Chapter 2. The Field Data 25 Figure 2.8: The 34 ft. MV Noctiluca was the platform for the VH-97 field program. She was equipped (not shown here) with a hydraulic-powered winch for CTD casts, an ADCP, echo sounder and GPS. Photo by Peter Baker. The bottom 15% of the velocity profile will be influenced by side-lobe contamination and is discarded from the analysis. The short-term velocity accuracy (defined as the statistical uncertainty in the velocity measurement for a one second measurement interval) was quoted by the manufacturer to be 45 cm/s. Eight acoustical "pings" were grouped together to form "ensembles" spaced 11-12 seconds apart. As the error goes down as the square root of the measurement interval, the velocity error for each ensemble should be 13 cm/s. In order to resolve velocities in earth co-ordinates as opposed to ship co-ordinates, the ADCP also recorded ship compass heading from an external flux-gate compass, and pitch and roll from tilt devices. Ship position and course was also recorded synchronously by GPS. Due to calibration offsets and drift in the flux-gate compass, post-experiment corrections had to be performed to regain true north-south and east-west horizontal velocities. In addition, tilt and roll effects on vertical velocities as recorded by the ADCP were not corrected for in real time during measurements; hence, appropriate Figure 2.9: S4 casts were done off the port side of the boat. A sample bottle was included with some S4 casts for calibration of the S4 temperature and conductivity probes. Figure 2.10: An ADCP (Acoustic Doppler Current Profiler) was mounted off the star-board side of the boat via a metal tube clamped to the side. The transducer head is below water while the pitch and roll sensors are in the box on top of the rod. Chapter 2. The Field Data 28 post-processing had to be done to recover vertical water velocities. The boat was also fitted with a 50/200 kHz echo sounder. Sound speed gradients as well as other acoustic scatterers in the water, e.g. air bubbles, and various forms of biological organisms, can give an indication of the depth of the pycnocline4 and thus of some of the major flow features. The echo sounder image was recorded on Hi-8 video tape for certain transects and later digitized in the lab. Unfortunately the quality of this data set was no better than the backscatter intensities as recorded by the ADCP. 2.2.2 Data processing Compass corrections of A D C P horizontal velocity estimates The flux-gate compass had anomalies for various headings, presumably due to distor-tions of the magnetic field from metals in the boat structure. Corrections to the compass heading and to all horizontal ADCP velocities thus had to be performed after the cruises. Comparison was made with the course over ground (cog) as indicated by GPS velocities. The GPS receiver, in addition to giving the boat position at each ADCP ensemble, also calculates and stores a smoothed velocity estimate, based on an exponentially weighted average of velocity measurements over the course of the 11-12 seconds between each ensemble. This GPS velocity estimate becomes progressively more reliable for higher speeds. For each ADCP data set, the difference between the GPS course over ground and flux-gate compass heading was plotted for each record versus compass heading, and the points corresponding to GPS speeds higher than 300 cm/s were marked (Figure 2.11). From the observation that the compass deviation was cyclic over the whole azimuthal range a sinusoid AH(h), with the argument h ranging from 0 to 360 degrees, was fitted, in the least squares sense, to the data points corresponding to high speeds. Such a fit is 4 An estuary often has a brackish surface layer lying on top of saltier and colder (thus denser) water below. The depth in the water column where the density gradient is highest is called the pycnocline. Chapter 2. The Field Data 29 shown in the figure. It was found that the compass offset for some data sets varied by as much as 20 degrees over the whole azimuthal range. The compass heading was then changed by this angle H(h)=H(h)+AH(h) (1) and all east-west (u) and north-south (v) velocities were rotated accordingly u(h) = u{h)cos(AH(h)) + v{h)sm(AH(h)) (2) v(h) = -u{h) sm(AH(h)) + v{h) cos(AH(/i)) (3) For a few cases when only a very few data points in a small azimuthal range corresponded 400 -350 -300 -1 0 0 - . ' " ' ' -50 -': 0 I £ ; l • ' ' • l ' ' ' ' 0 50 100 150 200 250 300 350 Heading (deg) Figure 2.11: The ADCP flux-gate compass had different anomalies for different head-ings. These were corrected by comparison with GPS course over ground (cog). The difference between GPS cog and compass heading is plotted vs. compass heading. A sinusoidal fit of the difference (dashed line) was found by regression through values cor-responding to speeds > 300 cm/s (big circles). to high GPS speeds, a least squares fitting algorithm could not be expected to give reasonable results, and a constant offset for all compass headings was chosen instead. Chapter 2. The Field Data 30 2 . 2 . 2 . 2 Pitch and roll corrections of A D C P vertical velocity estimates Figure 2.12 shows how, if the ADCP mount is tilted at some angle off the vertical, the vertical velocity estimate will be corrupted by horizontal currents. A tilt angle of 4 degrees will induce an apparent vertical velocity of more than 10 cm/s for a horizontal current of 150 cm/s. The ADCP software included an option for accounting for this effect in real time, but the feature was disabled for this study. However, since vertical water velocities were of interest for this study, a correction of the ADCP vertical velocities based on recorded pitch and roll values had to be done during post processing. z * i z Figure 2 . 1 2 : Pitch and roll will set up a vertical velocity component from horizontal water velocities. Here the ADCP is aligned in the east-west direction. Due to the non-zero pitch angle (P) a positive east-west water velocity (u) will produce a vertical ADCP velocity (Vz). First, horizontal velocities were rotated from earth co-ordinates to ship co-ordinates. Chapter 2. The Field Data 31 The +Y direction points towards the bow of the ship, the +X direction to starboard, and the +Z direction up as shown in Figure 2.13. Figure 2.13: The ADCP co-ordinate system: The +X direction points starboard, the +Y direction towards the bow of the boat and the +Z direction upwards. For pitch and roll corrections the horizontal water velocities must be rotated from earth co-ordinates to XYZ (ship) co-ordinates. If the bow of the ship points at an angle 9 measured clockwise from north, then the relationship between velocities in earth co-ordinates (u, v and w) and ship co-ordinates ( 1 4 , Vy and Vz) are Vy = u sin(0) + v cos(0) (4) Vx = ucos{0) -usin(0). (5) Chapter 2. The Field Data 32 Furthermore, if tilt angles are defined in such a way that positive pitch and roll angles, P and R, correspond to respective lifting of the +Y and +X axes from the horizontal plane, then positive P, R, Vy and Vx will induce negative vertical velocities. In the small-angle approximation: Vz = w - VyP - VXR (6) where Vz and w are the apparent and actual vertical velocities, respectively and angles are measured in radians. Rearranging to solve for the actual vertical velocity gives w = Vz + VyP + VXR. (7) The ADCP also measures three components of bottom-track (BT) velocities, effectively the movement of the bottom with respect to the ADCP. To recover absolute water ve-locities BT velocities must thus be subtracted from the raw water velocities which are velocities relative to the transducer. Comparisons between the integral of vertical BT velocities (a measure of vertical distance) and the recorded sea-bed profile showed that vertical BT velocity is not affected by the ADCP moving over a sloping bottom. Vertical BT velocity should in other words be identically zero (with some random noise) at all times for an ADCP moving on a flat sea surface. Thus, (6) should read for the BT velocities VzBT = 0-VyBTP-VxBTR (8) or 0 = VZBT + VBTP + VBTR. (9) However, a test of this relationship showed that it would often not hold. A better result was gained by allowing for offsets a and 3 in the pitch and roll, giving for vertical velocities w = Vz + Vy(P + a) + Vx{R+8) (10) Chapter 2. The Field Data 33 and for BT velocities 0 = VZBT + VyBT(P + + VXBT(R + B). (11) This last equation is linear in the two unknown parameters a and /?, and can be solved by standard least squares minimization methods (see for example Wonnacott and Won-nacott, 1981: pp. 417-421). Such a routine was written, and an example of its use is shown in Figure 2.14. Subtracting the influence from horizontal BT velocities does not set the vertical BT velocity identically zero, but will make it fluctuate around a mean value of zero. The standard deviation of the corrected BT velocity in Figure 2.14 is around 2-3 cm/s, much smaller than the expected errors in water velocities of 13 cm/s. Confident that this procedure was well suited to pick out offsets a and (3 in the pitch and roll sensors, the vertical water velocities were then determined from (10). A note on GPS accuracy A hand-held GPS unit with C/A-code accuracy (coarse aquasition) was used to de-termine ship position. Differential corrections (from e.g. Coast Guard beacons) were not available. A test of the accuracy of such a receiver was performed at the University of British Columbia (Richard Pawlowicz, personal communication) in which an ordinary GPS receiver was mounted on a building on campus for some weeks. The results showed that the GPS position undergoes oscillatory drift of ± 50-70 m with period 5-10 minutes and smaller-amplitude random noise on top of this drift. The uncertainty in the boat position when compared to features found in hydrographic charts of the study area must thus be seen in light of the above observed drift. Chapter 2. The Field Data 34 1270 1280 1290 1300 1310 1320 1330 1340 1350 Ensemble # Figure 2.14: Correction of ADCP vertical velocity for pitch and roll effects. Least squares regression is used to find offsets in the ADCP pitch and roll sensors which will make the bottom track (BT) vertical velocity as close to zero as possible in the least squares sense. Solid line = raw vertical velocity, dashed line = pitch effect and dash-dot line = roll effect. The corrected BT vertical velocity is shown below. Also shown is the compass heading. Note that for a large part of this transect the boat's heading is due north. As the flow is primarily eastward, the roll effect is largest. Chapter 3 Results from the IA-95 Mooring Program 3.1 Synoptics The following section will give a descriptive overview of the data gathered by the IA-95 moorings in Burrard Inlet. The mooring time series reveal that the variability in the density at depth inside of both First and Second Narrows is as large over tidal time scales as the total change over the entire spring season. During spring tides, the mixed tides in the region (the principal constituents of which are the diurnal mixed lunar and solar K\ constituent and the semi-diurnal lunar M 2 constituent) create alternating strong and weak flood currents through the narrows with strong and weak associated mixing, respectively. The observations however also reveal variability of longer time scales. The daily changes in density due to tidal mixing depends strongly on the spring-neap tidal cycle and other monthly and seasonal variability. 3.1.1 Seasonal trends Figure 3.1 shows the hourly averaged tidal record over the measurement period from early March to late June as recorded by the pressure sensor at the deeper of the two instruments at Stn-66. Seven complete spring-neap periods are covered, and the monthly and seasonal variation in the nature of the spring-neap cycle can can be seen. The spring tides are alternatingly big and small with the largest tidal ranges seen towards the end of the period. The difference between spring tides and neap tides is smallest in March. 35 Chapter 3. Results from the IA-95 Mooring Program 36 1 April 1 May 1 June 60 80 100 120 140 160 180 Julian days Figure 3.1: Mooring data from the deeper instruments over the whole measurement period: (a) tidal height at Stn-66, (b) water speeds and (c) densities at all three stations. Chapter 3. Results from the IA-95 Mooring Program 37 Figure 3.1 also shows hourly averaged speeds and densities from the deeper instru-ments (6 m above the bottom) at all three stations. Clearly the daily density variations are as large as the total change over the entire spring season. Conclusions of previous studies that were based on samples taken at weekly or monthly intervals must thus be re-evaluated, since each one unique density sample might have been different by as much as 1 kg m - 3 had it been sampled a few hours earlier or later in the tidal cycle. The record is not stationary; the strongest variability in the density occurs during spring tides and is correlated with very high velocities at depth. The neap periods on the other hand are of-ten associated with small or even negligible velocities and gradually decreasing densities, especially at Stn-66 and Stn-48. The temperatures and salinities for the three deeper instruments are shown in Figure 3.2. The temperature records show a clear seasonal trend: the gradual warming of waters as the spring progresses into summer. As the water column attains an increasingly strong temperature gradient due to increased heat flux through the surface later in the season, strong daily variability associated with spring tides is seen, whereas in the beginning of the record the weak temperature stratification give no indication of the mixing during springs. The salinity records look quite similar to the density records except that densities decrease due to the seasonal temperature trend. Figure 3.3 shows daily discharge from both local rivers and the Fraser river over the same period. The correlation with the temperature records and the onset of the spring freshet as seen in the Fraser river discharge is striking. However, both are associated with seasonal warming rather than being directly related; the salinities at depth in the harbour appear to have little overall trend, suggesting that Fraser river water does not have a big effect on the density field in Burrard Inlet and Indian Arm. Chapter 3. Results from the IA-95 Mooring Program 38 1 April 1 May 1 June T 1 1 r 60 80 100 120 140 160 180 Julian days Figure 3.2: Additional mooring data from the deeper instruments over the whole mea-surement period: (a) tidal height at Stn-66, (b) temperature and (c) salinity at all three stations. Note that at the start of the record Stn-48 has the lowest temperature and QB the highest temperature. Chapter 3. Results from the IA-95 Mooring Program 39 Figure 3.3: Discharge from mayor rivers into the Burrard Inlet/Indian Arm system. The Indian river at the head of Indian Arm is small but correlated to Capilano river (see e.g. Dunbar, 1985). Also shown is Fraser river discharge. Some water from this river may enter Burrard Inlet during flood tides. Data sources are Water Survey of Canada, Inland Waters division of Environment Canada, and B.C. Hydro. Chapter 3. Results from the IA-95 Mooring Program 40 Figures 3.4 through 3.6 show TS-diagrams1 of the hourly averaged records from the instruments at QB, Stn-66 and Stn-48 respectively. Isopycnal lines (constant density) are Figure 3.4: TS-diagram for station QB (a) 20 m and (b) 30 m. also drawn in the diagrams as dotted lines. The TS-diagrams from both QB 20 m and 30 m in one end show high density water from a relatively constant source. Climatological data from the Strait of Georgia (Waldichuk, 1957) in fact show that the high density end of the TS-diagrams correspond closely to Strait water from approximately 50 m. The salinity of this water is fairly constant whereas temperature increases considerably over the spring season. At the other end of the TS-diagram can be seen a highly variable 1 TS-diagrams are one of the classic ways to present a water sample. The position of a water sample in such a diagram, which has salinity along the horizontal axis and temperature along the vertical axis, uniquely characterizes the dynamic properties of the sample. A common feature of TS-diagrams is that a scatter of water samples which form a line in the diagram indicate the mixing of two distinct water types, one from each endpoint of the scatter line (Pickard and Emery, 1990: pp. 144-146). Blobs of points indicate quiescent conditions with little activity or well-mixed conditions. Hence, TS-diagrams can often say something about the origin of the water masses present and about the nature of the mixing processes that take place. Chapter 3. Results from the IA-95 Mooring Program 41 low density source: surface water from inside First Narrows (possibly with some water from the Fraser river) with increasing temperatures and decreasing salinities as the spring season progresses. The scatter plot appears to consist of mixing lines between these two water types. When the individual points in the TS-diagram for QB 30 m and QB 20 m are plotted chronologically, a few features become apparent. There is a gradual warming of waters during the course of the spring. Surface water, which is marginally cooler than deeper water in the first few days of the record, warms up much faster than the Georgia Strait deep water, and whereas in the first half of the record salinity variations primarily de-termine the density structure of the water, the last weeks of May and June show an increased importance in the effect of the temperature gradient between the surface water and deeper water. Plotting the points chronologically also shows that the lowest density water generally is found at ebbs during spring tides. TS-diagrams from Stn-66 and Stn-48 follow the same major features as mentioned for QB. Mixing lines appear to converge towards a relativly constant source, although the range of temperature for high density water is much bigger than for QB, indicating the effect of First and Second Narrows in mixing the water. The temperature of the low-density water also increases faster than the high density water. The deep water at Stn-48, however, show some qualitative difference in its spring-neap behaviour from that at QB and Stn-66. Whereas QB and in particular Stn-66 show low density water appearing irregularly, as low-density "fingers" or "pulses" during spring tides, such features are harder to distinguish at Stn-48, especially towards the end of the record (higher temperatures). Evidence of such a difference can not, however, be easily detected from Figures 3.1 and 3.2. As will be shown in Section 3.1.3, a third water mass (in addition to Indian Arm surface water and Georgia Strait water) emerges at Stn-48 at the end of big ebbs during spring tides in late spring. This third water mass has a Chapter 3. Results from the IA-95 Mooring Program 42 Figure 3.5: TS-diagram for station Stn-66 (a) 50 m and (b) 60 m. STN-48 50 m (a) V1 . . 25 26 27 28 29 Salinity 30 31 13 12 O 11 cu | 10 ci5 o . E ,a> 9 STN-48 60 m (b) 25 26 27 28 29 30 31 Salinity Figure 3.6: TS-diagram for station Stn-48 (a) 50 m and (b) 60 m. Chapter 3. Results from the IA-95 Mooring Program 43 density similar to the other water masses present but considerably lower temperature. This results in the considerable "scatter" in the TS-diagram from Stn-48, making the low density pulses during spring tides harder to detect. 3.1.2 The spring-neap tidal cycle Figures 3.7, 3.8 and 3.9 show twenty days in May (Julian days 129-48) of the original, non-averaged record (15-minute sample interval) from the deeper instruments at QB, Stn-66 and Stn-48, respectively2. This window begins with neap tides then goes through an entire spring-neap period plus a few extra days into the next spring tides. For two to three days during neap tides in early May, velocities near the bottom at Stn-66 and especially at Stn-48 are very small compared to spring-tide velocities. Throughout these days (10-12 May) density is also slowly decreasing, an indication that the dominant process at depth during this time may be vertical turbulent diffusion of heat and salt. Then as the spring tide builds up, at Stn-48 there is a sharp drop in salinity and density at a big flood on 12 May. Both velocity components take on small-scale fluctuations at this time too, a possible indication of turbulence. At both stations in the harbour the first big pulse of advection does not come at depth until the next big flood (late on 13 May), and with it, high frequency oscillations in the pressure record. The following is seen at the deeper instrument at Stn-48 (Figure 3.9). Strong advective pulses come at each flood tide, both big and small floods. The pulses have positive mean u (along-channel) and v (across-channel) components for the big floods while the mean v component is generally close to zero for small floods; there is in other words some differ-ence in direction of the currents. Possibly there is more steering by bottom topography during small floods. The u component is also stronger at 60 m than at 50 m for small floods, suggesting that a turbulent gravity current sinks along the bottom, guided by the 2 Similar plots from all instruments throughout the spring are given in Appendix B Chapter 3. Results from the IA-95 Mooring Program 44 65 £ 60 Q_ CD Q 5 5 Sf 100 E o (a) 0 LD - 1 0 0 100 E o > CO z - 1 0 0 CD > (b) I I I I I I I 1 1 1 (c) , 1 1 i i 1 1 I I I co 2 4 E * - 2 2 "(e) 10/5 12/5 14/5 16/5 18/5 20 /5 Date (day/month) 22/5 24 /5 26 /5 28 /5 Figure 3.7: Conditions at QB 30 m for 20 days in May. (a) Tidal elevation (as measured at Stn-66), (b) east-west and (c) north/south velocities, (d) temperature and (e) density. Chapter 3. Results from the IA-95 Mooring Program 45 10/5 12/5 14/5 16/5 18/5 20/5 Date (day/month) 22/5 24/5 26/5 28/5 Figure 3 .8 : Conditions at Stn-66 60 m for 20 days in May. (a) Tidal elevation, (b) east-west and (c) north/south velocities, (d) temperature and (e) density. Chapter 3. Results from the IA-95 Mooring Program 46 6 5 £ 60 o . Q 55 | 100 > (a) L U ~ 100 (b) , 1 & 100 r .10 10/5 12/5 14/5 16/5 18/5 20/5 22/5 24/5 26/5 28/5 Date (day/month) Figure 3.9: Conditions at Stn-48 60 m for 20 days in May. (a) Tidal elevation, (b) east-west and (c) north/south velocities, (d) temperature and (e) density. Chapter 3. Results from the IA-95 Mooring Program 47 topography (plots from the 50 m instrument may be seen in Appendix B). Between the strong advective pulses there are periods of relatively quiescent waters and other periods of weak outflow. The inflow velocity pulses have more small-scale fluctuation on the big floods, just as much in the v component as in the u component. However, the leading edge of the small-flood pulses often have a big spike in them, possibly indicating that a highly turbulent region just behind the head of a gravity current (e.g. Baines, 1995: pp. 101-103) is passing the instrument. A few days later (starting on 22 May), the kinetic energy associated with neap tides is too low to cause the extreme mixing in the narrows, hence low density water does not reach the instruments at depth. However, the density of the water in the hole at Stn-48 is low enough so that pulses of denser outside water are pumped in during each small flood, and the density here gradually increases as a result. The mixing in the narrows during floods throughout this period probably results in water of intermediate density which adjusts itself to a level higher in the water column, thus passing above the instruments near the bottom. The behaviour at Stn-66 is similar to what is seen at Stn-48. However, the currents during the spring tide period are somewhat weaker and the stratification stronger at depth, suggesting that the mixing is a little less intense across First Narrows. 3.1.3 Daily details during spring tide Figures 3.10 and 3.11 show raw (15-minute sample interval) data from Stn-66 and Stn-48 taken over a few tidal cycles during spring tides in May. Velocities are not necessarily in quadrature with pressure. In particular, at Stn-48 there is often a weak outflow at depth which starts towards low slack after a big ebb and lasts two to three hours into the following big flood. This outflow is associated with water of unusually low temperature. Halfway into the big flood, the turbulent water mass reaches the instruments and brings Chapter 3. Results from the IA-95 Mooring Program 48 with it the mixed waters of very low density. The following small ebb generally brings weak outflow at depth, and the water which is brought in on the small flood does not reach the instrument until 2-3 hours after the barotropic tide has turned. The current at 60 m is stronger than at 50 m during the small flood, suggesting a bottom-intensified density current. A TS-diagram of the data from the deeper instruments at QB, Stn-66 and Stn-48 taken over these same days is shown in Figure 3.12. The main mixing line between fresh surface water and the Georgia Strait source water can be seen. Note that this line is curved, a property which has been associated with heat exchange through the surface (Pawlowicz, 1998). All the Stn-66 data lie on this main mixing line, as does the data from QB. At Stn-48, however, the data points span a triangle, which indicates that a third water type is mixed in at some period of the tide. Plotting the TS-diagram chronologically while noting the corresponding velocities in Figure 3.11 gives an idea of the behaviour of water in the hole at Stn-48: Starting with a big ebb, the water present at Stn-48 60 m is dense water from the-main mixing line, i.e. dense water which was brought in during the previous small flood. Then towards the very end of the big ebb, a third water mass enters the hole. This water is advected to the hole by the pulse of outflowing water as noted above. Half way into the following big flood, a strong and turbulent flow brings in low density mixed water from the main mixing line. Velocities are nearly zero during the following small ebb and the water in the hole unchanged. Then as the tide turns again, there is a short period of mixing between water from the main mixing line and the third water type before the hole is again completely dominated by denser water from the outside. This third water type, whose source was identified from the monthly CTD surveys to be Indian Arm water from below sill depth, is only present at the Stn-48 hole in the second half of the record. It also gradually disappears towards the end of each spring-tide Chapter 3. Results from the IA-95 Mooring Program 49 651 Q. Q 6 0 K 55 10 E 9 8 7^23 E g22 200 _ 100 In I ° 3 - 1 0 0 - 2 0 0 200 100 ,(a) I . I I I I I i i ,(b) i p i -,(c) (d) Upper Lower - 1 0 0 -200 1 o ^ ^ ^ •inrv _ ' (e) 16/5 17/5 18/5 Date (day/month) 19/5 Figure 3.10: Conditions at Stn-66 for 4 days during springs in May. (a) Tidal elevation, (b) temperature, (c) density, (d) east-west velocity and (e) north/south velocities. The time is in PST. Thick line = 50 m and thin line = 60 m. Note that salinities have not been corrected for instrument offsets and drift in these raw data (15 minute sample interval). Chapter 3. Results from the IA-95 Mooring Program 50 o) ^20 19 E o -100 -200 200 _ 100 I 0 > -100 -200 (e) 16/5 17/5 18/5 Date (day/month) 19/5 Figure 3.11: Conditions at Stn-48 for 4 days during springs in May. Tidal elevation (a), temperature (b), density (c), east-west velocity (d) and north/south velocities (e). The time is in PST. Thick line = 50 m and thin line = 60 m. Note that salinities have not been corrected for instrument offsets and drift in these raw data (15 minute sample interval). Chapter 3. Results from the IA-95 Mooring Program 51 11 | 1 : 1 r 1 ; 1 1- r j i : i j 1 : L 26 26.5 27 27.5 28 28.5 29 29.5 30 Salinity Figure 3.12: TS diagram from lower instruments at all three stations for 4 days during springs in May. A third water type is being mixed in at Stn-48 60 m during late stages of big ebbs and early stages of the following big flood. Chapter 3. Results from the IA-95 Mooring Program 52 period, as seen in the temperature record in Figure 3.11. Presumably the whole region between Second Narrows and Indian Arm sill is becoming gradually more mixed after several days of the very strong tidal currents through the narrows. 3.2 Energy Loss from the Barotropic Tides in the Narrows The barotropic tide is an important factor in determining the circulation of some fjords; tidal modulation may overshadow the underlying estuarine circulation. At various locations along the inlet energy may also be extracted from the tide, some of which will cause mixing of waters which may then affect both the horizontal and vertical density field. The barotropic tide thus may have an indirect control on the overall circulation at time scales much longer than tidal. Some different sinks of barotropic tidal energy in an inlet have been identified: frictional dissipation in the constricted entrance or sill region where tidal velocities are high, the generation of an internal tide which will propagate away and be dissipated somewhere else, and the generation of high frequency internal waves and/or kinetic energy flux of turbulent tidal jets. (Farmer and Freeland, 1983; Tinis, 1995). This energy will eventually dissipate into heat and mixing. The barotropic tide propagates along a coastline as a Kelvin wave (e.g. Gill, 1982). However for fjords whose transverse scales are small compared to the external Rossby radius3 and whose lengths are short compared to a wavelength, the tide in a fjord can be modelled as a standing wave neglecting rotation. When the tide has to work against friction and other energy sinks in the inlet, a small progressive wave component must be added. The surface elevation and the along-channel tidal velocity will in other words have an offset from quadrature. It is this phase difference, if it can be measured, that may be used to make estimates of the energy loss of the barotropic tide as will be shown 3 The external Rossby radius of deformation is a lengthscale of the system over which the earth's rotation is important to the propagation of low-frequency waves. Chapter 3. Results from the IA-95 Mooring Program 53 below. In extremely shallow and narrow sill regions where tidal currents reach very high values, the loss from the barotropic tide may be big enough to cause a decrease in the tidal range inside of the sill. A term has been coined which appropriately describes the phenomenon: tidal choking (see e.g. Farmer and Denton, 1985). The barotropic energy flux into Indian Arm was studied from historical tide-gauge data by de Young and Pond (1987, 1989). By calculating the phase lag of harmonic constituents across three sections in Burrard Inlet and Indian Arm, they were able to infer estimates of the barotropic energy loss at these locations. This section aims to retrace the method used by that study using pressure data from the IA-95 records, both to verify the results from the previous study and to refine their conclusions. 3.2.1 The barotropic flux model The common way to measure the energy loss from the barotropic tide over a sill or a narrows is to measure the phase difference of the tide between the two sides of the constriction. The mathematical derivation was presented by Garrett (1975) and is based on the expression for the energy balance for the barotropic tide in a fjord derived from the Laplace tidal equations. For most fjords of moderate size the dominant balance is where p is the density, u is the horizontal along channel velocity component, r\ is the surface displacement, g is the gravitational acceleration, H is the depth, F represents the combined energy losses, n is the normal perpendicular to an element ds, and the overbar indicates a time-average over a tidal period. The left-hand side is the (depth-integrated) inward flux of tidal energy integrated over the mouth, and the right-hand side is the rate of working by frictional forces integrated over the area up-inlet of the mouth, i.e. the loss that we want to determine here. Farmer and Freeland (1983) also point out (12) Chapter 3. Results from the IA-95 Mooring Program 54 that it is only necessary that the inlet be subject to linear physics at the section where the left hand side of (12) is evaluated; one may then evaluate the left hand side for each tidal constituent separately and add the results for the total loss further up the inlet. Taking a section perpendicular to the channel, the energy flux through the mouth (or through any cross section) is P — I pgWjds (13) J section This energy flux through a cross section is balanced by the losses up-inlet. As men-tioned earlier, the barotropic tide in a fjord is best modelled as a standing wave. Without friction then, surface elevation and velocity will be in quadrature, and the integral in (13) is zero. Energy losses however will establish a progressive component to the tide, i.e. set up a phase difference between rj and u other than 90°. A schematic of the situation is shown in Figure 3.13. Tidal choking through a constriction may also reduce the ampli-tude of the tide, but in Burrard Inlet this effect is negligible. If the elevation and velocity at section 1 (down-inlet of the sill) are written as Vi(t) = rj0sm(ujt) u(t)i = u0 cos(ut — e) and at section 2 (up-inlet of the sill) as %(*) = ?7osin(a;t- >^i) u2(t) — uo cos(a>£ — (j)2) One may use continuity to show that (13) reduces to P = ^pgV 2Slujsm(e), (14) where Si is the surface area up-inlet of section 1. To solve for the energy flux, angle e must be found in terms of the elevation phase lag between sections 1 and 2 which Chapter 3. Results from the IA-95 mooring program 55 T ^ s m c u t u , c o s ( o j t - € ) Section 1 SILL 7 ] 0 s i n ( c j t - c / ) , ) ! u 2 c o s ( a j t - c £ 2 ) Section 2 Figure 3.13: Schematic of the barotropic energy loss across a sill or a narrows in an inlet. The phase lag of the tide along a "loss line" (the stretch between the two sections) is used to calculate the energy lost to friction and other baroclinic drag effects. From de Young and Pond (1987) Chapter 3. Results from the IA-95 Mooring Program 56 is available from observations. The first derivation was made by Freeland and Farmer (1980). Stacey (1984) generalized the result by allowing for further losses to be possible up-inlet of section 2, then Dunbar (1985) allowed for a variation in the cross-section of the inlet between sections 1 and 2. Each of these result in a relationship for e as a function of fa. Tinis (1995) was even more thorough in the derivation and allowed for the possibility of a change in the surface elevation across the constriction, as he observed across Skookumchuck Narrows in Sechelt Inlet. 3.2.2 Results The data available for this study were pressure data from the two S4 current meters at 60 m at Stn-66 and Stn-48. In addition, hourly tide-gauge data from Pt. Atkinson and Vancouver Harbour (tide stations 7795 and 7735, respectively) were used (from the Geomatics Engineering Group, Canadian Hydrographic Service, Institute of Ocean Science, Sidney, B.C). The phase lag between Pt. Atkinson and Stn-66 (or Vancouver Harbour) were taken to represent the loss across First Narrows, while the lag between Stn-66 and Stn-48 were taken to represent the loss across Second Narrows. Harmonic analyses (e.g. Godin, 1972: pp. 207-212) were performed on the hourly elevation records with a program written by Mike Foreman of IOS (Foreman, 1977). The tidal-height phase differences fa across each of First and Second Narrows from the K\ diurnal and the M 2 semi-diurnal tides (the two dominant tidal constituents in the area) are presented in Table 3.1. Corrections have been made to the phases of the S4 instruments since each reading every 15 minutes actually was recorded at the end of a one-minute period which started every quarter of an hour. The phase difference between the S4 at Stn-66 and the tidal gauge at Vancouver Harbour was less than one degree. This difference corresponds to about 4 minutes at M2 and 2 minutes at K\, smaller than the quoted time accuracy of the IOS gauges (± 5 minutes). The tidal-height phase Chapter 3. Results from the IA-95 Mooring Program 57 Stretch M 2 Ki Pt. Atkinson - Vane. Harb 7.3 4.1 Stn-66 - Stn-48 8.1 4.9 (a) Stretch M 2 Kx 1983-84 Pt. Atkinson - Vane. Harb 5.0 3.8 Vane. Harb - Sill (CI) 7.9 4.6 Sill (CI) - Basin (C3) 2.4 1.6 1984-85 Pt. Atkinson - Vane. Harb 6.8 3.8 Vane. Harb - Sill (CI) 7.9 3.6 Sill (CI) - Basin (C3) 2.1 / (b) Table 3.1: Phase difference (in degrees) of surface elevation for K\ and M 2 tide in (a) IA-95 study and (b) study by de Young and Pond (1987). differences resulting from the study of de Young and Pond (1987) are also shown in table 3.1 for comparison. The topography otherwise being the same for the two studies, the only important result to investigate is fa; the phase angle e and the energy flux P can be derived from fa. The estimates given by de Young and Pond were averages of four separate months of data, taken during the winter period, and the standard deviations were quoted to be about 10-15% of the mean. The results of the IA-95 study show phase lags a little higher than the previous study, but they are both within the given error limits. The two studies thus correspond well. The phase lags calculated for this study are averages taken over almost four months of data. Stacey (1984) however noted that there was a seasonal trend in similar energy flux estimates for Observatory inlet. He found that the increase in freshwater runoff in late spring was correlated with an increase in P. Boundary friction should be the Chapter 3. Results from the IA-95 Mooring Program 58 Stretch M 2 Kx Pt. Atkinson - Vane, harb 7 March - 10 April 5.3 3.2 11 April - 17 May 7.4 4.0 18 May - 22 June 8.1 4.5 Stn-66 - Stn-48 7 March - 10 April 8.3 4.3 11 April - 17 May 6.8 4.6 18 May - 22 June 9.6 5.2 Table 3.2: The surface elevation phase lags (in degrees) for three successive 35-36 day periods during the spring of 1995. same throughout the season, whereas sill processes due to increased stratification as the spring progresses may be responsible for an increased loss. The freshwater run-off is quite small in Indian Arm itself; however, the increased local heat flux in the spring combined with the onset of the spring freshet in the Fraser river does increase the stratification in Burrard Inlet. Table 3.2.2 shows the phase lags 4>\ calculated for three periods of approximately 35 days each. There seems to be a trend towards higher phase lags in the end of the time series. The increasing trend is more pronounced across First Narrows which can be expected since the stratification is stronger here than in the area around Second Narrows. Another interesting detail to note is that whereas in the previous study the second "loss-line" (the stretch between the two sections that are compared) was from Vancouver Harbour to just inside the Indian Arm sill (see Figure 1.2), in this study the "loss-line" was a much shorter one: the stretch between the harbour and the deep hole just inside of Second Narrows. The results discussed above strongly suggest that the barotropic tide loses energy as it passes through Second Narrows but little or nothing across the broad Chapter 3. Results from the IA-95 Mooring Program 59 Indian Arm sill itself. Then, judging from de Young and Pond (1987), there is a small additional loss over the stretch from just inside the IA sill to the basin and this loss presumably occurs in a narrow region about 2 km inside (northeast) of the sill. 3.3 Kinetic to Potential Energy Transfer in the Narrows As can be seen in Figures 3.1, 3.8 and 3.9 there is a diurnal signal in the density in the holes at Stn-66 and Stn-48 during spring periods. Relatively small flood tides bring dense water from outside over the sill, and this water then probably sinks down as a gravity current, finally reaching the instruments in the holes. The big floods also bring denser water to sill depth, in fact they have even more kinetic energy available to lift up dense water. However the density at the holes inside of the narrows drops during big floods. The outside water which is brought to the sill is vigorously mixed with the surface water to create a resulting water mass with lower density which eventually reaches the instruments. Now we look for indications of a correlation between the kinetic energy of the water introduced at the sill at each flood and the density change which is seen at the instruments on the inside. In other words we are looking to quantify the transfer of kinetic energy of the in-flowing tide to a change in potential energy of the water column inside. Although the change in density of the water that reaches the deep holes inside each narrows is related to the available kinetic energy of the water reaching the narrows, the relationship will probably not be linear. The turbulent mixing processes that take place around the sill regions are very non-linear, and in addition to being dependent on the velocities and velocity shears of the flow, they must also be related to the nature of the stratification present. However, a first step is to identify a relationship between the strength of the tide and the size of the density changes at depth. Chapter 3. Results from the IA-95 Mooring Program 60 3.3.1 Density jumps at lower instruments over floods during spring tide The IA-95 dataset had no measurements of currents in the narrows. An indication of the currents can be inferred from the recorded sea level variations by use of conservation of volume. If assuming that the surface area S of the inlet above the mouth is constant, then the flow rate Q through the mouth is Q = av = (15) where a is the cross sectional area of the mouth, v is the velocity through the mouth and h is the water level in the inlet. The velocity through the mouth is thus proportional to the rate of change in the surface water level. By approximating the time derivative by the average change over the entire flood cycle, dh Ah _ hhigh - hi ow dt At tfoigfo tlQW an expression for v averaged over the entire flood tide becomes v = (16) Thus v is proportional to Ah, and the depth-integrated kinetic energy of the flow (as-suming homogeneous conditions), KE= f° - pv2 dz=\ p H v7 J-H 2 F 2 H is proportional to (Ah)2. The Continuous Wavelet Transform (e.g. Farge, 1992; Hubbard, 1996) was used to pick out periods in the hourly-averaged records from the 60 m instruments at Stn-66 and Stn-48 around spring tide when the diurnal variability in the density was important. Portions of the record where the CWT of 24-hr time scale was above a certain threshold value were extracted (Figure 3.14). From these periods the magnitudes of density drops Chapter 3. Results from the IA-95 Mooring Program 61 Figure 3.14: Analysis of the density time series from Stn-48 60 m with the Continuous Wavelet Transform (CWT). (a) The density time series, (b) its CWT, and (c) a cut along one row of the CWT matrix showing the magnitude of the 24-hr variability throughout the record. The intensity scale in (b) is arbitrary; dark regions correspond to high wavelet coefficients. The dashed line in (b) shows the 24-hr scale while the one in (c) indicates the threshold value used to identify regions of interest. Chapter 3. Results from the IA-95 Mooring Program 62 or rises over each flood — the period between low water and high water as indicated by the pressure records — were recorded (examples in Figures 3.15 and 3.16). 641 1 1 1 r- 1 r 22.81 1 1 1 1 1 1 1 1 r 1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000 Time (hours) Figure 3.15: Example of density jumps at Stn-66 during a spring tide, (a) Tidal height and (b) density. Tidal range and the corresponding density jump at periods between low and high slack are shown with thicker lines. The diurnal wave trains during spring tides at Stn-48 are fairly smooth, and in fact resemble square waves towards the end of each spring-tide period. In the first half of this particular period, the partial intrusion of a third water mass of intermediate density Chapter 3. Results from the IA-95 Mooring Program 63 Figure 3.16: Same as in Figure 3.15 but for Stn-48. Chapter 3. Results from the IA-95 Mooring Program 64 during the beginning of big ebbs alters the typical square shape. The magnitude of the density jumps Ao~t (taken to be an indication of the change in potential energy) were plotted against the square of the sea-level rise Ah over the corresponding periods (Figure 3.17). (Ah)2 (m2x 1.5 1 0.5 0 -0.5 -1 -1.5 V. * ' t. (b) Stn-48 60 m 10 15 20 25 (Ah)2 (m2) Figure 3.17: Density jumps Aat vs. the square of the tidal range Ah over floods during springs at (a) Stn-66 and (b) Stn-48 60 m. For small floods (where (Ah)2 < 5 m2) the density change is inversly proportional to kinetic energy. For the biggest floods (where (Ah)2 > 10 m2) the density changes level off independent of the strength of the currents. The system is fully mixed. The scatter is large, but some trend can be seen. On the small floods at Stn-48, the rise in density appears to fall off almost linearly with increasing kinetic energy in the narrows. This direct trend also appears to hold true for the smaller of the big floods. However, for the biggest floods the density drops tend to level off around a constant value. This behaviour is more or less the same for both instruments. The result from Stn-66 is more difficult to interpret since high frequency oscillations Chapter 3. Results from the IA-95 Mooring Program 65 were not successfully filtered out from the density record. Still, the density drops during big floods appear to level off around a constant value, independent of the actual strength of the flood. Most of the big floods thus appear to have sufficient kinetic energy to mix the watercolumn completely from top to bottom. 3.4 Vertical Diffusion at Depth during Neap Tides Correct estimates of the strength of vertical diffusion is crucial to the prediction of the evolution of the density field and hence the estuarine dynamics. As an example, the timing of a process like deep-water exchange depends on the conditioning of the deep water density field through turbulent diffusion. Upward diffusion of salts and downward diffusion of heat (in the spring) at depth due to turbulent processes during periods of low advection gradually decreases the density to the point where water entering the fjord system over the sill is heavy enough to intrude into the deep water. This section aims to produce estimates of the strength of turbulent vertical diffusion in the basins at Stn-66 and Stn-48 based on the time evolution of the density field there. Although this region often has strong currents, the background vertical diffusion probably is an important process in determining the density of Vancouver Harbour which in turn controls deep water renewal in the harbour and deep water exchange with Indian Arm. While difficult to do, estimates in such an active outer region of a fjord are of value since they have never been done before. In the latest modelling attempt of Indian Arm (Pond et al. , 1998) vertical diffusion is parameterized by the use of a turbulent eddy diffusivity in order to close the Reynold's equations. The use of this analogy in representing the effects of turbulence may be mis-leading since turbulence is a characteristic of the flow rather than a characteristic of the fluid (Tennekes and Lumley, 1972). More advanced closure schemes exist; however, Chapter 3. Results from the IA-95 Mooring Program 66 the concept of eddy viscosity and eddy diffusivity is still much used in practical oceano-graphic work. Nowadays, instead of using constant eddy diffusivities, values depending on stratification and shear are often used (as discussed below). 3.4.1 The budget method We start with the law of conservation of the mean scalar quantity c per unit mass (see e.g. Gargett, 1984): dc _ ^ dc d dc. p dt 1 dxi dxi 13 dxi The first term on the left is advection of the scalar by the mean velocity field, the second term the turbulent diffusion (molecular diffusion considered negligible in comparison), and the third term represents sources and sinks. If we assume that there is negligible advection, negligible horizontal diffusion, and no sources/sinks, the conservation equation reduces to where Kv is the vertical eddy diffusivity. Whereas molecular diffusivity is a property of the particular fluid in question and will be different for each scalar in question (e.g. it is bigger for heat than for salts), the eddy diffusivity should be considered a property of the flow structure, i. e. the dynamics of the eddy field and should be equal for all passive scalars. For some time now it has been accepted that in this parameterization Kv should not be constant but a function of the stratification, which is usually characterized by the buoyancy frequency, N2 = -°-^, p* dzJ where p* is a reference density. Gargett and Holloway (1984) suggest that if the energy for mixing comes from the breaking of internal waves, Kv will be a function of both the Chapter 3.. Results from the IA-95 Mooring Program 67 stratification and the flux Richardson number: Kv = T ^ ^ T V - 2 (19) where the flux Richardson number, Rf, is a ratio of the energy flux working against buoy-ancy over the total mechanical production of energy. The dissipation rate of turbulent kinetic energy e is shown by Gargett and Holloway (1984) to be e = e0Np (20) where p — 1.0 for waves of a single frequency and p = 1.5 for a broadband wave spectrum. If Rf approaches a constant limiting value, the theory thus predicts a relation between Kv and stratification as Kv = CLoN-" (21) where a0 is a site specific constant and 0.5 < q < 1.0. If, on the other hand, Rf also depends on N, then q may have a different range. Gargett (1984) describes three methods for estimating the vertical eddy diffusion Kv for passive scalars. The one followed here is the budget method. Equation (18) is laterally averaged (assuming negligible horizontal gradients) and integrated from the bottom to height h to give: . . £ /0h A(z) cdz = S'%A(h) • ( 2 2 ) where A(z) is the horizontal area at level z. The numerator is the time rate of change of the total amount of c in the control volume and the denominator is the flux through the top surface. Previous studies of vertical diffusion based on the budget method (e.g. de Young and Pond, 1988; Tinis, 1995) have extracted the density field in a basin from CTD profiles taken at weekly or monthly intervals. Other moored data has been used to find periods Chapter 3. Results from the IA-95 Mooring Program 68 of low advection suitable for such analysis. In this study the only information available about the vertical gradients of salt and temperature comes from the two S4's at 6 m and 16 m above the bottom (the 60 m and 50 m instruments, respectively). 3.4.2 Results Figure 3.18 shows a period of 3-4 days during neap tides when advection at the Stn-48 instruments was low and vertical diffusion is assumed to have been the dominant dynam-ical process at depth. During this period density at depth was not strongly modulated by the semi-diurnal tide but decreased monotonically at both instruments. The density decreased at a faster rate at the upper instrument, which is consistent with turbulent adjustment to a pycnocline higher up in the water column. Note that the density changes over 3-4 days are comparable to the changes in the deep water in Indian Arm over a year (de Young and Pond, 1988: their Figure 3). For such periods of low advection, linear fits were made of the time variation of salinity (and temperature) at both depths. Estimates of the vertical profile were then made by fitting parabolas at the beginning, middle and end of each period, to the data at the two depths with the extra assumption of zero vertical gradient at the bottom. The time rate of change of total amount of salt (and heat) within the basin volume was then evaluated between the beginning and end times, whereas the vertical gradient was evaluated at the mid-time. The area function A(z) used was a simple box model (Figure 3.19) where the area between 0-6 m above the bottom was set to equal that of the 60 m contour taken from hydrographic charts, and the area between 6-16 m set equal to that of the 50 m contour. This approximation is crude, but tests showed that the sensitivity of the results to the area function was small compared to other parameters. Despite of what has been noted in the above, the records from Stn-66 rarely support the idea that vertical diffusion was dominant in conditioning the density field at depth. Chapter 3. Results from the IA-95 Mooring Program 69 Figure 3.18: Period at Stn-48 when water velocities are weak and vertical diffusion is assumed to be the dominant dynamical process at depth, (a) Depth, (b) water speed and (c) density. Thick line = 50 m instrument and thin line = 60 m instrument. Chapter 3. Results from the IA-95 Mooring Program 70 Figure 3.19: Box model of the hole at Stn-48 for vertical diffusion estimate by the budget method. The volumes between 0-6 m and 6-16 m (above the bottom) are represented by rectangular boxes. The salinity (and temperature) profiles are made parabolic with a no-flux boundary condition at the bottom. They instead suggested that there exists a mixed bottom boundary layer at all times at depth as the salinity and temperature gradients between 50 m and 60 m were very small. Although currents were generally low during neap tides and density at both stations sometimes decreased, pulses of strong advection would often interfere. Except for one event on 9-12 May, density at 50 m did not drop faster than at 60 m, as would be the case if diffusion upwards to a pycnocline above was the dominant process. There may indeed have been a pycnocline above, and diffusion to it, but not between 50 m and 60 m. It appears that at this station the instruments were not high enough in the water column to be out of the bottom boundary layer and thus to detect gradients created by the vertical diffusion. Unfortunately no CTD casts were available at these times to support this hypothesis. At Stn-48 however, five neap tide periods showed evidence of vertical diffusion between 6 m and 16 m. A plot of Kv versus N2 for both salinity and temperature is given in Figure Chapter 3. Results from the IA-95 Mooring Program 3.20. Linear least-squares fits give slopes of —1.2 for salinity and 71 — 1.9 for temperature. 10" 4 : i 1 ; * Indian Arm I * * { \ * Sechelt • ' f r • Saanich * ^ V, \ •+ -e-10" 6 10" 5 1 0 - 4 10" 3 10" 2 N 2 (rad s" 1 ) 2 Figure 3.20: Vertical diffusivity Kv vs. the square of the buoyancy frequency iV2 during low-advection periods at Stn-48. Legend: x = salinity, o = temperature. Bounds on all estimates (thin lines) are based on assumed measurement errors of ±0.05 psu in salinity and ±0.02°C in temperature. Approximate regression lines covering the data from Sechelt Inlet (Tinis, 1995), Indian Arm and Saanich Inlet (de Young and Pond, 1988) are also shown for comparison. As there are no sources or sinks of salt at the bottom boundary, the resulting Kv estimate for salinity is probably more correct than that for temperature. Temperature gradients are also small; salinity changes dominate the density field. However, a major uncertainty in the Kv estimates for salinity is introduced from the corrections made to compensate Chapter 3. Results from the IA-95 Mooring Program 72 for the drift in the conductivity sensor in the 50 m instrument (Section Assum-ing measurement errors in the differences between the 50 m and 60 m instruments of ±0.05 psu in salinity and ±0.02°C in temperature, bounds on the slope estimates were found to be [—1.3, —0.8] for salinity and [—3.5, —0.3] for temperature (with steeper slopes corresponding to stronger gradients). The large range of slopes obtained for diffusion of heat (probably mainly due to weak gradients) suggests that little confidence should be put on this estimate. The range of slopes for diffusion of salts is much smaller. For q = 1.0 theory predicts that if the vertical mixing is primarily driven by the breaking of internal tides, then these waves will be of a single frequency. The results of this study, with q = 1.2 for salinity suggests waves that lie in a narrow frequency band, de Young and Pond (1988) presented estimates of the Kv vs. N2 for the deep basin in Indian Arm from CTD profiles taken at weekly intervals between January and March 1983. The slopes for salinity and temperature were —1.6 and —1.2, respectively, for iV2 ranging from one to two orders of magnitude lower than for this study. They also did a study in Saanich Inlet which resulted in q values of 1.8 and 1.9 for salinity and temperature, respectively. Similar studies in other areas have also generally reported q values between 1 and 2 (e.g. Gade and Edwards, 1980; Tinis, 1995). Approximate linear fits for Kv based on salinity data from Indian Arm, Saanich Inlet and Sechelt Inlet are also shown in Figure 3.20 for comparison. The values from Stn-48 are seen to be higher than those from the three other studies; this indicates that Vancouver Harbour is a relatively energetic region. If mixing is primarily driven by breaking of internal waves, (19) suggests that the turbulence level near the instruments at Stn-48 must be considerable. Chapter 4 Results from the VH-97 C T D / A D C P Survey 4.1 Conditions in Vancouver Harbour during the 1997 Spring CTD casts were collected with an S4 at stations 75, 66, 60, 56, 54 and 48 (see Fig-ure 1.2) throughout the spring of 1997 and also once offshore from the Chevron refinery just east of Stn-54. The times of cruises in relation to the seasonal progression of spring-neap tides are shown in Figure 4.1 and the individual CTD casts are shown in Figures 4.2 through 4.7. Two big floods, one small flood and one big ebb were studied during spring tides. In addition one big flood during the transition from spring tide to neap tide and one small flood during neap tide were covered. The range of conditions thus covered several of the typical regimes observed at depth at Stn-66 and Stn-48 in the IA-95 time-series. From these CTD casts a rough picture of the circulation in the harbour can be inferred. 4.1.1 Overview of CTD casts 21 February - small flood during spring tide: CTD casts were collected at stations 66 and 48 (Figure 4.2). At the onset, 20 minutes into the flood, the water at Stn-66 is weakly stratified below 30 meters, the depth of large parts of the harbour. Above this depth the stratification is stronger; this is the remnant water from the previous small ebb. At Stn-48, one and a half hours into the flood, the water is nearly homogeneous except for a 3-6 m thick fresh layer at the surface. Just 73 Chapter 4. Results from the VH-97 CTD/'ADCP Survey 74 40 60 80 100 120 140 Julian days Figure 4.1: The tide in Vancouver Harbour during the 1997 spring. The dates when CTD casts (and tow-yos) were performed are marked off. Tidal heights were cal-culated by XTide, public software developed by David Flater and available through Chapter 4. Results from the VH-97 CTD/'ADCP Survey 75 Figure 4.2: CTD casts in Vancouver Harbour from 21 February. The line types that are used progress with time as: solid, dashed. The tide at time of the casts is shown below. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 76 after high slack the upper part of the water column at Stn-66 is unchanged, but below 15 m — the depth of the sill at First Narrows — an intrusion of denser water has taken place. At Stn-48 the entire water column is denser at high slack, but a thin fresh layer still exists at the surface. 7 March - big ebb during spring tide: Profiles were collected at stations 66, 60, 56, 54, and 48 (Figure 4.3). The source water at Stn-48 1 hour and 45 minutes into the ebb appears to be nearly homogeneous throughout most of the water column after the previous small flood, but closer inspection reveals that the density actually increases measurably with depth, in agreement with the behaviour seen from the small flood on 21 February. A thin fresh layer exists at the surface. Similar characteristics can be seen around the same time at Stn-54 located just east of Second Narrows, although the water below 18 meters is slightly denser there than at Stn-48. The profile at Stn-66 half an hour into the ebb has the same characteristics as that at the end of the small flood on 21 February with a sharp density increase at 12-15 m. A weak indication of this increase can also be seen at 11 m at Stn-60 one hour into the ebb. Half way into the ebb, two completely homogeneous profiles at Stn-56 indicate intense mixing downstream of Second Narrows. This water, somewhat denser from further mixing with denser water in the harbour, appears to have reached both Stn-60 and Stn-66 at the very end of the ebb. An interesting feature is seen in the last cast made at Stn-56. Five and a half hours into the ebb lighter water occupies depths above 15-16 meters. This water must have its origin some distance up Burrard Inlet or even Indian Arm. The lower tidal currents through Second Narrows at the late stages of the ebb allow this water to pass through relatively unmixed. Another possibility is that the mixing of water ebbing out from Second Narrows is not the same everywhere; the transition to intense mixing occurs near the hole at Stn-56, and depending on the exact location of the casts, the flow may or Chapter 4. Results from the VH-97 CTD/'ADCP Survey 77 Stn-66 Stn-60 Stn-56 Stn-54 Stn-48 10h 20 •30 Q. Q 40 50 60 - 16 :30 - 23 :01 _1 L_ 10 20 30 40 50 60 20 22 o t (kg m - 17:00 - 22:29 I 1 _ 20 22 o { (kg m 10h 20 30 40 50 60 - 19 :59 - 2 0 : 3 3 - 2 1 : 3 6 20 22 o, (kgm ) 10 20 30 40 50 60 - 16 :30 _ l L_ 20 22 a t (kg m Or 10 20 30 40 50 60 - 17 :46 I I 20 22 o t (kg m ) 00:00 12:00 00:00 Time 12:00 Figure 4.3: CTD casts in Vancouver Harbour from 7 March. The line types that are used progress with time as: solid, dashed, dot-dashed. The tide at time of the cast is shown below. Chapter 4. Results from the VH-97 CTD/ADCP Survey 78 may not be turbulent. The repeated casts done in this region in fact suggest that the transition to turbulence occurs not at the Stn-56 hole but a short distance downstream. 10 March — big flood between spring and neap tide: CTD casts were collected at stations 66, 56, at Chevron just downstream of the 40 meter hole east of Second Narrows, and Stn-48 (Figure 4.4). The source water at Stn-66 at low slack shows a continuous stratification except for a density jump at 40-43 m. At Stn-56 the first profile taken less than an hour into the flood shows a water column fully mixed from the previous big ebb. At Stn-48 the profile from this early stage shows a stratified upper 20 m, remnants from the previous ebb, above a homogeneous lower layer. Two hours into the flood the water at Stn-56 has become denser, and particularly dense water, presumably remnants from the previous smaller flood left in the harbour, has intruded to depths below 25 m. The water at Chevron around the same time is fully mixed and a little less dense than that found on the upstream side of Second Narrows. As the flood progresses the density step at depth at Stn-56 is gradually eroded away to give place to a more and more homogeneous water column of progressively higher mean density. The fully mixed profiles at Chevron also show progressively higher densities, and the same can be seen in Stn-48 at all depths. Towards the end of the flood, the stratification is weak enough and the flood strong enough to mix the water reaching Stn-48 nearly completely from top to bottom. And the water which has passed through First Narrows and reached Stn-66 is also quite well mixed at the end of the flood. In this case density near the bottom at Stn-48 increases on a big flood, in contrast to the behaviour seen on most other big floods. This behaviour is in agreement however with the IA-95 time series in which density at depth would rise considerably during floods towards the end of spring tides. 7 and 8 May -big floods during spring tide: Profiles were collected at stations 75, 66, 56 and 48 (Figures 4.5 and 4.6). These two Chapter 4. Results from the VH-97 CTD/'ADCP Survey 79 Stn-66 Stn-56 Chevron Stn-48 •~ 0I 1 L _ 1 1 12:00 00:00 12:00 00:00 Time Figure 4 . 4 : CTD casts in Vancouver Harbour from 10 March. The line types that are used progress with time as: solid, dashed, dot-dashed and thin, thick. The tide at time of the casts is shown below. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 80 Figure 4.5: CTD casts in Vancouver Harbour from 7 May. The line types that are used progress with time as: solid, dashed, dot-dashed. The tide at time of the casts is shown below. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 81 Stn-75 Stn-66 Stn-56 Stn-48 15:08 _ J I l _ 10r 20 -§-30 CL D 40 50 60 - 10:41 - 15 :59 - 19 :03 Or 10h 20 30 40 50 60 14:08 16:25 18:30 _i i i i r 14 16 18 20g22 24 14 16 18 20 „22 24 14 16 18 20 „22 24 14 16 18 20 ,22 24 o t (kgm ) rj, (kg m ) a, (kg m ) a, (kgm ) 00:00 12:00 00:00 12:00 Time Figure 4.6: CTD casts in Vancouver Harbour from 8 May. The line types that are used progress with time as: solid, dashed, dot-dashed. The tide at time of the casts is shown below. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 82 consecutive big floods show similar behaviour at all stations. The source water at Stn-75 consists of a brackish layer, 5-10 meters deep, lying above a weakly stratified lower layer. The two casts from 7 May taken two hours before low slack and three and a half hours into the flood suggest that conditions outside First Narrows for the most part remain fairly similar throughout the flood. About an hour before the flood starts, Stn-66 shows a stratified water column down to about 20 m; this is water which presumably has passed through Second Narrows at earlier stages of the ebb but has become stratified during its course through the harbour before reaching Stn-66. It is however also possible that the ebbing surface water tends to flow along the Northern boundary due to topographic and rotational effects (see Section 4.1.3) and that the water seen at Stn-66 here has been present in the harbour long enough for a stratification to be established. At Stn-48 the profiles taken an hour to an hour and a half into the flood show a brackish surface layer, 3-10 m thick, overlying a weakly stratified, almost homogeneous, lower layer. The previous small flood has however introduced a density increase at 35-38 m. The conditions seen at Stn-66 half way into the flood are not quite similar on the two days. Three hours into the flood on 7 May the stratification at Stn-66 has not changed noticeably from before the flood, whereas at three and a half hour into the flood on the following day, dense water has intruded into the upper part of the water column except for a thin surface layer. On both days however, the conditions at depths below 25 m are unchanged. The mixing through First Narrows is apparently not extensive enough to homogenise the entire water column despite the fact that the flood is bigger than on 10 March. Waters at Stn-56 show a weak stratification at early stages, one and a half to two hours into the flood. As the flood progresses, denser water reaches Stn-56 except for the upper 10 m on 8 May. The much stronger stratification due to increased run-off and Chapter 4. Results from the VH-97 CTD/'ADCP Survey 83 surface heating late in the spring might explain this difference. At the end of the flood, the deep water at Stn-66 has become marginally lighter while the water above sill depth at First Narrows remains strongly stratified as it was at low slack. At Stn-48 however the whole water column is effectively mixed and the deep water is 1 kg m - 3 lighter than the water which was present there at low slack. Mixing in Second Narrows has been extensive. 16 May - small flood during neap tide: Casts were made at stations 75, 66, 56, and 48 (Figure 4.7). The source water at Stn-75 has a fairly similar profile to that seen one week earlier, i. e. a layer of brackish water, 5-10 meters thick, overlying a more or less homogeneous lower layer. The profiles taken at the other three stations show little difference between early and late stages of the flood. An increased density of the water at 5-8 m at Stn-48 suggests that an intrusion of denser water has passed through Second Narrows and adjusted itself to that particular depth. This water may have been drawn from below 8 m at Stn-56 if little or no mixing occurred through Second Narrows, or it may be mixed waters from all depths. The deeper water at both Stn-66 and Stn-48 is untouched altogether. This is in agreement with the quiescent conditions frequently seen during neaps in the IA-95 record. 4.1.2 Background estuarine flow in the harbour The flow in the harbour should, in the absence of strong winds, show evidence of the classic estuarine circulation when tidal effects are averaged out. In the idealized two-layer model, a minute surface slope is established due to river run-off in the eastern parts of the harbour, and this sets up a surface flow out of the harbour. Entrainment at the interface between the two layers creates a positive net vertical flow from the denser layer to the lighter layer. Conservation of volume hence dictates inflow at depth. Although this residual background circulation will only become clear when averages are taken over Chapter 4. Results from the VH-97 CTD/'ADCP Survey 84 Stn-75 Stn-66 Stn-56 Stn-48 Or 10 20 -§-30 CL Q 40 50 09:17 _ l I I - 08:47 60h 13:28 10 20 h 30 40 50 60 - 11:09 -• 12:55 10 20 30 40 50 60 _J I I 10:41 12:26 _ l I 0 10 2Q 30 0 10 2fJ 30 0 10 2fJ 30 0 10 2Q 30 o ( (kg rrf3) o, (kg m"3) a { (kg m"3) a, (kg rrf3) 12:00 00:00 12:00 Time 00:00 12:00 Figure 4.7: CTD casts in Vancouver Harbour from 16 May. The line types that are used progress with time as: solid, dashed. The tide at time of the casts is shown below. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 85 several tidal cycles, traces of it might still be seen in snapshots of the velocities in the harbour. When the depth-averaged horizontal velocities are removed for each ADCP ensemble, the result should have most of the tidal effect removed and give some indication of the residual estuarine circulation. This hypothesis would hold better during low and high slack and away from strong mixing regions. Figure 4.8 (a) shows east-west ADCP velocities collected on 16 May during a transect which starts at Stn-75 at low slack and ends at Stn-48 still at an early stage of the flood. Velocities are seen to be higher through Second Narrows than First Narrows, but the transit time from First to Second Narrows is nearly half an hour and should be taken into account here. With the depth-averaged velocities removed in (b) an indication of the baroclinic circulation may be seen. Both west of First Narrows (ADCP ensembles 300-350) and in regions of the harbour (ensembles 490-520) an outflow (dark blue) can be seen near the surface and inflow at depth (green-yellow). Such behaviour is in agreement with the classic model of the estuarine circulation. Interestingly this behaviour is also seen through First Narrows while being less de-tectable through Second Narrows. The evidence in First Narrows can be taken as an indication that mixing through this narrows itself is weak, at least during such an early stage in the flood. East of both First and Second Narrows however the baroclinic flow structure appears to be opposite to that of an estuarine flow. A snapshot of the flow close to a mixing region gives more information of the baroclinicity due to local mixing than of residual estuarine background flow. Figure 4.8 is based on a single transect through the harbour. Instantaneous measure-ments of this kind should not be taken as a definite picture of mean conditions; still the plot in (b) may give an indication of the level of baroclinicity in the harbour. In order to better resolve the background estuarine circulation, one may want to collect data from Chapter 4. Results from the VH-97 CTD/'ADCP Survey 86 300 350 400 450 500 550 600 650 ADCP ensemble # Figure 4.8: East-west velocities (a) in the harbour at early stages of a flood on 16 May. The depth-averaged velocity has been removed in (b) to give an indication of the baroclinic flow. The thick line in each plot marks the bottom. Note that the x-axis measures time rather than length in these plots. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 87 several similar transects and average the results. 4.1.3 The tidal prism in the harbour The CTD data studied here raise the question of whether water which enters the harbour through First Narrows can be expected to reach Second Narrows on the same flood and conversely on the ebbs. The casts taken on 10 March in particular suggest that this is indeed the case on large floods. Conservation of volume may be used to investigate the excursion of water entering the harbour through one of the narrows. A rough estimate was made by neglecting the rise in surface height over the flood. Assuming an approximate value for the cross-sectional area of First Narrows: Ai ~ 400 m * 15 m = 6000 m2, then peak currents of 2.5 m/s, leading to mean tidal currents through the narrows (in the sinusoidal approximation): 2 Ui ~ — * 2.5 m s ~ 1.6 m s , 7T and the cross-sectional area of the harbour: A2 ~ 2000 m * 30 m ~ 60,000 m2, then a depth-averaged current through the harbour would be U% = Ui^- ~ 16 cm s_1, A.2 and the maximum distance reached over one half a tidal cycle Ax ~ 16 cm s - 1 * 6 hr * 3600 s hr - 1 = 3.5 km. The harbour is approximately 9 km long, two and a half times as long as the estimated displacement. The tidal currents do not spread evenly through the harbour but are Chapter 4. Results from the VH-97 CTD/ADCP Survey 88 consentrated in jets along the South and North sides during floods and ebbs, respectively, due to topographic and possibly also rotational effects. Surface currents in these jets can reach 1 m/s (Canadian Hydrographic Service, 1981), thus waters should be able to pass through the entire harbour over half a tidal cycle during big floods and ebbs. This may not be the case during all of the smaller floods and ebbs. 4.1.4 Blocking of the flow at the entrance to sills The observations of 16 May raise the question of whether tidal currents are strong enough to raise water from below sill depth, against the strong stratification during neaps, and up high enough for it to pass through the narrows. This question can be studied in terms of the phenomenon of blocking. A density layer in the flow is said to be "blocked" when its kinetic energy is not large enough to lift the water up through the ambient stratification to the height of the sill. The blocking phenomenon can be explained in terms of energy relations for flow passing over an obstacle. Following Gill (1982: pp. 293-294), an equation describing conservation of energy of two-dimensional steady flow along a streamline (Bernoulli's equation) is where P, p and U indicate conditions sufficiently far upstream of the obstacle. If the flow along the streamline barely makes it to the top of the obstacle, where p = p0 and velocities are zero, we have p + -p(u2 + w2)=P + -pU2 (23) po = P + l-pU2 (24) and so the increase in pressure of this flow is pU2- (25) Chapter 4. Results from the VH-97 CTD/'ADCP Survey 89 To see what height displacement h this change in pressure corresponds to, we assume linear stratification so the hydrostatic equation can be integrated to give p0-P = - [kg^-ti dti (26) Jo dz or 1 po - P = ^pN2h2, (27) which by substitution of (25) gives Approaching the problem with dimensional analysis, assuming the two important pa-rameters are the upstream velocity and ambient stratification, also leads to a similar result: ^ ^ - i . (29) V P* dz At Stn-75 and Stn-56 on 16 May, however, the really strong stratification is above sill depth in both places. At Stn-56 the density changes by less than 2 kg m - 3 from 20 to 40 meters. Still, for a mean current at depth of 50 cm/s, the blocking depth (depth below sill level) should be approximately 0.5 m s-1 h /~~10 m s~2 2 kg m - 3 V 1000 kg m - 3 20 m h ~ 15 m. Considering that the sill depths at First and Second Narrows are 15 m and 19 m, re-spectively, the above result suggests that water below 30-35 m may be prevented from reaching the sills due to buoyancy forces. 4.1.5 Internal resonance in the harbour The fact that currents at the holes of Stn-66 and Stn-48 as seen in the IA-95 record are often found to be weak for several days during neaps may be due to tilting of the Chapter 4. Results from the VH-97 CTD/'ADCP Survey 90 isopycnals at intermediate depth that sets up an along-harbour baroclinic pressure gra-dient in opposition to the barotropic pressure gradient. Showing such a relationship with the sparse CTD coverage in this data-set will be difficult. Account must also be taken of mixing, e.g. in the bottom boundary layer between two stations. Still, a comparison of densities at Stn-66 and Stn-56 towards the end of the flood on 16 May (Figure 4.9) shows that isopycnals from about 2 to 20 meters in fact tilt weakly upwards to the east; a pressure gradient is set up which results in horizontal forces at depth working against the direction of the flood. Integrating the hydrostatic equation from depth z to an assumed flat upper surface: and then plotting the difference between this "internal" hydrostatic pressure at each station also shows an indication of a baroclinic pressure gradient towards the east below 20 m. Below this depth the gradient changes sign. However this is also approximately the maximum depth of the shallower parts of the harbour which separates these two stations. Hence, a comparison of hydrostatic pressures of the two stations will not be indicative of the force balance below 20 m. The horizontal hydrostatic pressure gradient shown in the figure also assumes a flat surface. In reality the surface will have a weak upward tilt towards the west during flood, and stagnant conditions at depth require that the effects of this tilt be cancelled by the baroclinic pressure gradient or by a combination of it and other terms in the horizontal momentum equation. If a two-layer approximation is made of the density structure in the top 20 m, then based on the profile from Stn-56 the baroclinic shallow-water wave speed would be •o (30) or 10 m s - 2 * 1000 kg m-3 10 m + 10 m 5 kg m - 3 10 m * 10 m = 50 cm s , - i Chapter 4. Results from the VH-97 CTD/'ADCP 'Survey 91 Figure 4.9: The horizontal density gradient between Stn-66 and Stn-56 (contours of ot) on 16 May results in a horizontal pressure force towards the west. The hydrostatic equa-tion is integrated at each station, and the pressure difference, AP = Pstn-66 — Pstn-56, is plotted (thick solid line). Since the bottom gets shallower than 25 m at some places between the two stations, neither the 22 kg m~3 contour nor the pressure gradient line below 25 m should be trusted. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 92 The corresponding wavelength at semi-diurnal frequency would be A = c T (32) or A ~ 0.5 m s_1 * 12 hr * 3600 hr s - 1 = 22 km. If we think of Vancouver Harbour as an enclosed embayment and consider the possi-ble internal resonant motion, or "seiche", in a two layer fluid there, the along-channel standing wave modes would have 7 ^ = cT, A; = 0,1,2,... (33) where L is the length of the embayment. For the fundamental mode, k = 0, half a wave-length fits inside. A comparison of the estimated wavelength above with an approximate length of the harbour of 9 km thus suggests that the fundamental mode of the pycnocline in the harbour during neaps could quite possibly be excited by the semi-diurnal tide. A similar stratification existed at Stn-48 on 16 May, and since the distance from Second Narrows to Port Moody is comparable to the length of the harbour, internal resonance there may also affect the flow at depth. In Chapter 3 it was shown, in fact, that currents at depth during neap tides are weaker at Stn-48 than at Stn-66. More observations would be needed for a closer investigation of this possibility. 4.1.6 The spring-neap variability of density structure and circulation in the harbour A classification of flows in the harbour based on a simple distinction between spring tides and neap tides will be a primitive one. The difference between springs and neaps are less dramatic in February-March than both before and after. A rough sketch of Chapter 4. Results from the VH-97 CTD/'ADCP Survey 93 conditions in the harbour within this spring-neap subdivision may nevertheless be made based on the structure of the CTD casts and the discussion of these given above. Big floods and ebbs during spring tides mix waters thoroughly over a period of several days, and the over-all stratification in the harbour drops. This gradual lowering of density gradients as spring tides progress can be seen in the IA-95 data. The mixing around First Narrows during springs may or may not be complete on each big flood; CTD data show that the water column at Stn-66 is never homogenised from top to bottom except during the transition from springs to neaps. Mixing through Second Narrows is certainly very effective on the big floods during springs and causes the entire water column at Stn-48 to be homogenised with water of progressively lower density. For small floods during spring tides mixing through First Narrows is weaker, the water exiting is probably still stratified and settles at appropriate depths at Stn-66. Hence, the low-density water from the previous big flood at the bottom of Stn-66 is replaced by heavier water. A similar weaker mixing and settling of the outflow at various depths depending on density possibly also takes place through Second Narrows. On each big flood however, the over-all density in the harbour decreases. Towards the end of spring tides, the difference in tidal range is smaller for consecutive floods and consecutive ebbs. Over the course of one of the smaller floods dense water enters the harbour and settles as a pronounced dense layer at depth. This water does not reach Second Narrows during the small flood. At the next flood, a bigger one, mixing is stronger in both narrows. Since the over-all stratification is weak after several days into the spring tide, the waters leaving the narrows are completely mixed. The dense water left in the harbour since the previous smaller flood is mixed through Second Narrows to produce water considerably denser than what exists at Stn-48. Two to three days of passing relatively dense water through First Narrows and into the harbour and then mixing it through Second Narrows will cause the density there to rise as the tides enter Chapter 4. Results from the VH-97 CTD/'ADCP Survey 94 the neap period. The absence of the very big floods and ebbs during neap tide enables the stratification in the harbour to build up. Each flood and ebb will for a few days have near equal amplitude, and if the tide interacts with baroclinic effects, possibly including an internal oscillation of the pycnocline close to semi-diurnal frequency, the motion at depth may be damped during both floods and ebbs. This is the time when vertical diffusion may have a chance to dominate at depth. Eventually the asymmetry of tides — and mixing through the narrows — becomes more pronounced again, the resonance between the tide and stratification in the harbour is lost. 4.2 The Flow Behaviour in Second Narrows The detailed flow behaviour through First and Second Narrows will be affected greatly by the complex topography found there. Previous numerical model results (Pond et al. 1998) have shown that turbulence parameterized by bottom friction alone was insufficient in mixing the water flowing through Second Narrows. The modelled inflow to Indian Arm was much denser than what was seen in field observations. Other sources of mixing must exist in the narrows, and this section aims at identifying some of these. The general topic of stratified flow over topography is of interest not only to oceanog-raphers but also to atmospheric scientists and civil engineers. In both the atmosphere and the ocean the influence of topographic forcing will propagate as internal waves away from the source of the forcing and may have a considerable effect on the overall dynamics and energy balance. Interaction with a nonuniform stratification (Sutherland, 1996) and boundaries (Maas et al. 1997) may cause initially small-amplitude waves to steepen and break either close or far from their source. The topographically-induced baroclinicity exerts form drag on the mean atmospheric Chapter 4. Results from the VH-97 CTD/'ADCP Survey 95 and oceanic flow. This form drag accounts for up to 50% of the total drag on the atmosphere (Palmer et al. 1986), hence a good understanding of the mechanisms involved is essential for successful modelling of the large-scale circulation of the atmosphere and ocean. A knowledge of topographic effects on stratified flows is also important for the interpretation of phenomena at smaller scales. In the atmospheric boundary layer, the flow over mountain ranges may result in severe downslope winds (e.g. Smith, 1985). Similar behaviour in the world's coastal regions and estuaries, e.g. the interaction of tidal flows with fjord sills (Farmer and Armi, 1998) can be a major source of turbulent mixing and hence affect the coastal circulation. One approach to the theoretical modelling of layered, uni-directional, flow through contractions and over sills has been that of internal hydraulic analysis (Farmer and Denton, 1985; William and Armi, 1991; Armi and Williams, 1992; Lawrence, 1993). Although much used in practical engineering-type applications, this description is not complete since the approach assumes steady flow and thus does not directly account for propagating waves or other flow transients. Other approaches which do include finite-amplitude wave motion (e.g. Long, 1953, 1954, 1955; Peltier and Clark, 1979; Wurtele et al. 1996) are leading towards useful results describing large-scale, finite-amplitude, behaviour (see Baines, 1995, for a summary). The current theories however are typically limited to idealized topographies, velocity and density structures; one is not able to reproduce in detail the flow seen in nature based on any one of these models alone. Nevertheless, internal hydraulic theory has been successfully used in a more qualitative sense, e.g. in the description of the exchange (bi-directional) flow through the Strait of Gibraltar (Armi and Farmer, 1988; Farmer and Armi, 1988). Chapter 4. Results from the VH-97 CTD/ADCP Survey 96 4.2.1 Field observations Four tow-yos with the S4 were performed in Second Narrows during various flood tides. The purpose was to identify regions in the narrows where large-scale mixing takes place and to look closer at the mechanisms involved. By lowering and raising the S4 repeatedly while drifting with the flow, one may obtain enough density information from the S4 and velocity information from the ADCP to obtain a picture of the major flow features and processes present. However, in this study, the relatively low resolution of the ADCP (one averaged reading, an ensemble, per 11-12 seconds, in 2 m depth bins) and the limitation on the spatial resolution of CTD data due to the nature of the tow-yo, limited our ability to see details. The ship tracks during tow-yos through Second Narrows are shown in Figure 4.10. They occurred during big floods on 10 March, 7 and 8 May and during a small flood on 16 May (CTD casts at various stations during these days are shown in Figures 4.4 through 4.7). Due to other ship traffic, the tow-yos generally began downstream of the Second Narrows bridges; hence upstream conditions were not measured. As can be seen in Figure 4.10, even with GPS uncertainty taken into account, the ship tracks were not identical for the different tow-yos. It is thus more difficult to judge consistency between the different tracks. On the other hand, this provides some information about spatial variability. Composite plots which show ADCP velocity vectors, ADCP back-scatter intensities and S4 density contours were made (Figures 4.11 through 4.14). Note that the horizontal axis in these figures measure the distance travelled along the track of each transect1, not a distance in any particular compass direction. ADCP velocities are shown as vectors with a horizontal component along the direction 1 A D C P ensembles come at 11-12 second intervals. The distance travelled over each such ensemble was taken to be this time interval multiplied by the boat's speed over ground during the ensemble. Chapter 4. Results from the VH-97 CTD/'ADCP survey 97 Figure 4.10: (a) Ship tracks through Second Narrows during CTD tow-yos and (b) on an expanded scale with depth contours (in meters). The two bridges (railway bridge to the east) are also shown. Tow-yos were performed on 10 March (solid line), 7 May (dashed line), 8 May (dash-dot line) and 16 May (dotted line). Note that the aspect ratio is not 1:1 in (b). Chapter 4. Results from the VH-97 CTD/'ADCP Survey 98 of the boat's drift and the vertical component. The shallowest ADCP depth bin is at 4-5 meters; however, velocity readings from this depth often looked devious and were disregarded. Also, velocities in the bottom 15% of the water column are affected by side-lobe contamination and should not be trusted. The ADCP backscatter intensity is shown in the background; a non-linear gray scale (cosine-shaped) has been used to enhance the contrast. Strong backscatter, corresponding to a high level of turbulence, will result in a dark region in the plot. Two topographic features immediately west of Second Narrows were of particular interest: a small hole, 35 meters deep, some 700 meters downstream of the bridges, then a rise in the topography, followed by a deeper (45 meters) hole about 500 meters downstream of the first hole. Hydraulic theory of stratified flow over topography predicts a shift in flow behaviour in the vicinity of such features, and indeed, as will be shown below, such shifts were often observed. 10 March - 4 1/2 hours into a big flood at spring-neap transition The transect (Figure 4.11) began about 700 meters downstream from the Second Narrows bridges, along the Southern edge of the first hole, and then continued in a fairly straight line along the centre of the channel, passing directly over top of the second hole, and ending up some three hundred meters downstream of it. Some distance into the transect the surface waters showed indication of very turbulent conditions within the water column. "Boils" as wide as 20-30 meters would bring deep water up to the surface and other more calm areas would indicate down-welling convergence zones. The stratification is very weak and there are indications of local overturning right from the start. The flow at first follows topography and isopycnals up to the top of the topographic rise 300 meters into the transect. It then plunges down along the downward slope of the feature, and at the same point the isopycnals diverge markedly. Downstream, at about 650-700 m, the flow at depth rises again before levelling out. The water column Chapter 4. Results from the VH-97 CTD/'ADCP Survey 99 Cast number 5 6 7 8 9 10 11 12 13 14 15 16 200 400 600 800 Transect length (m) 1000 1200 Figure 4.11: ADCP and CTD data from tow-yo on 10 March. Backscatter intensity is shown in the background with dark patches indicating turbulent regions. Arrows indicate ADCP velocities in the plane of boat drift (Two arrows at the lower-right corner indicate horizontal and vertical currents of 100 and 10 cm/s, respectively). The tow-yo casts (dotted line) are numbered on the top of the figure. The phase of the tide is also shown. The density contours have interval 0.05 kg m~3. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 100 is essentially homogeneous from top to bottom from this point on. Back-scatter intensity shows heavy turbulence activity starting just downstream of the top of the topographic feature and persisting throughout the rest of the transect. After about 800 m the flow is downwards everywhere, presumably because the boat, drifting without engine power, was trapped in a convergence zone at the surface. 7 May - 4 hours into a big flood during spring tide The transect (Figure 4.12) began in the centre of the channel about 500 meters down-stream of the bridges. It commenced to the South of the first hole and ended up at the beginning of the second hole, also near the South side. Vigorous boils were seen on the surface some distance into the transect. The stratification is stronger and the flow follows topography and isopycnals which slope down into the first hole. Back-scatter intensity shows that the flow gets turbulent right from the beginning of the drop into the hole. The isopycnals at 5-10 meters gradually diverge right from the start. At around 650 meters into the transect, the bottom is still flat, but the flow at depth rises abruptly. The back-scatter indicates strong turbulence extending all the way to the bottom, and downstream from this point the stratification has all but vanished. A complex and unordered velocity field further downstream may indicate the presence of boils extending throughout the water column. 8 May - 3 1/2 hours into a big flood during spring tide The transect began about 100 meters downstream from the bridges, followed the centre of the channel, passed the first hole along its Northern edge, then curved right and ended up on the South side of the second hole. Surface boils dominated the flow downstream. The flow is well stratified from the start, and remains stratified as the flow follows the topography well past the first hole. There is however evidence of turbulence as the flow dips into the first hole, both indicated by strong back-scatter intensities and by some isopycnal spreading. The flow follows the topographic rise and goes down into the second Chapter 4. Results from the VH-97 CTD/'ADCP Survey 101 Cast number O1 _ i i i i i 1 1 1 1 1 — 100 200 300 400 500 600 700 800 900 1000 Transect length (m) Figure 4.12: Same as in Figure 4.11 but from 7 May. Two arrows at the lower-right corner indicate horizontal and vertical currents of 100 and 10 cm/s, respectively. The density contours have interval 0.2 kg m - 3. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 102 Cast number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18192022223242526 200 400 600 800 1000 1200 Transect length (m) Figure 4.13: Same as in Figure 4.11 but from 8 May. Two arrows at the lower-right corner indicate horizontal and vertical currents of 100 and 10 cm/s, respectively. The density contours have interval 0.2 kg m - 3. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 103 hole. As the boat makes a sharp turn to the North along the 40 meter contour (about 1100 meters into the transect) strong upward flow is encountered. Back-scatter is strong in this region and there is flow through rapidly diverging isopycnals. 16 May - 3 hours into a small flood during neap tide This transect started right under the bridges and mostly followed a path along the centre of the channel, just along the Northern edge of the first hole. Unfortunately this transect did not reach the final interesting topographic feature, the downslope into the second hole, which appears to act as a trigger for much of the turbulence in earlier transects. The surface waters around Second Narrows were fairly quiescent during this flood. The shallowest depth in the transect corresponds to an excursion towards the southern boundary of the channel to avoid ship traffic. For the most part the flow near the bottom follows topography and the flow in the interior follows the isopycnals. However, as the flow passes over the first hole, 500-550 meters into the transect, the isopycnals do spread moderately and there is a considerable cross-isopycnal flow. The flow near the bottom in this region is stronger than in the interior and resembles a bottom intensified jet. The interior almost appears to be stagnant. The strongest backscatter is seen in the region of spreading isopycnals. A dominant feature of this transect, however, is that the flow is highly stratified throughout. No extensive mixing over the entire water column is taking place. It must be kept in mind however that this transect did not reach the second hole. 4.2.2 Interpretation in terms of internal hydraulics theory for uni-directional flow The flow of a homogeneous fluid through a shallow or narrow gap has been success-fully described in terms of hydraulic theory (Bachelor, 1967). The difference in reservoir heights on the two sides of the gap and the horizontal pressure gradient they set up Chapter 4. Results from the VH-97 CTD/'ADCP Survey 104 Cast number 1 2 3 4 5 67 8 9 10 11 12 13 14 15 16 17 18 19 100 200 300 400 500 600 700 Transect length (m) Figure 4.14: Same as in Figure 4.11 but from 16 May. Two arrows at the lower-right corner indicate horizontal and vertical currents of 100 and 10 cm/s, respectively. The density contours have interval 1 kg m - 3. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 105 generally dictate the mean flow speed. However, when the downstream reservoir height is below a certain threshold, the flow speed through the gap is so high that the fastest moving waves are unable to travel in the upstream direction. The downstream reservoir thus loses its influence on the dynamics, and the flow is said to be "hydraulically con-trolled" through the gap. The extension of this approach to the description of stratified fluids through gaps has received some attention but the theory is less complete. Elements of the theory Internal hydraulics theory assumes steady, incompressible, inviscid and hydrostatic flow, and its derivation starts with the Bernoulli equation (e.g. Kundu, 1990) which states that for flow along a streamline 1 P - q2 H V g z — const (34) 2 p where q is the flow speed and z is the height above some reference level. The theory also assumes 2-D conditions (one horizontal and one vertical scale) and small vertical bottom slopes (e.g. Lawrence, 1993) so that streamlines are essentially horizontal. Bernoulli's equation then reduces to 1 P - u2 H V g z = const. (35) 2 p As long as the assumptions hold the flow can be solved explicitly everywhere. Non-dimensional parameters are frequently used within hydraulic analysis in distin-guishing various flow regimes. One of these, the Froude number, F, is a ratio of the flow speed to the speed of the fastest infinitesimal shallow-water waves (e.g. Turner, 1973). This number is a measure of the ability of disturbances to propagate against the flow as shallow-water waves to adjust the upstream reservoir conditions. A careful discussion of its definition for layered flows is given by Lawrence (1990). For a homogeneous layer of Chapter 4. Results from the VH-97 CTD/'ADCP Survey 106 velocity u and depth h, the Froude number based on the above definition is given by For flows with two or more homogeneous layers or with a continuous stratification how-ever, the fact that each layer may have a different flow speed makes it less straightforward to write a Froude number with the physical interpretation mentioned above. For a two-layer flow a composite Froude number, G, can be used (e.g. Armi, 1985) which has a similar relevance on the flow characteristics as the Froude number in the single layer case. It is defined as G2 = F2 + F2 - 7 F2 F2 where 7 is the fractional density difference between the two layers, P2 - Pi 7 = , P2 and Fi and F2 are the densimetric Froude numbers of the two layers: where g' is the reduced gravitational acceleration, g' = 7 g, and yi is the thickness of the individual layers. This approach can also be extended to more than two layers (e.g. Farmer and Denton, 1985). The two-layer example shows that for progressively more complex systems a simple dimensionless parameter describing the ability of long waves to move information upstream against the mean flow may perhaps not be possible. For a realistic continuous stratification with velocity shear this will certainly be impossible. However for yet another simplified case, that of a linearly stratified fluid with constant velocity from top to bottom, a Froude number which relates the flow speed to the speed of the first, and fastest, baroclinic mode can be written as Chapter 4. Results from the VH-97 CTD/'ADCP Survey 107 where N is the Buoyancy frequency and D is the depth of the fluid. Based on a series of theoretical and experimental papers by Long (1953, 1954, 1955) flows are traditionally classified as "absolutely subcritical" if the flow speed is lower than the long wave speed everywhere in the domain of interest, "critical" if there exists a confined section where the opposite is true, and "absolutely supercritical" if the flow speed is higher than the long wave speed everywhere in the domain. A flow through a contraction or over a vertical obstacle will typically be subcritical in the upstream reservoir. Then as the cross-sectional area of the channel decreases and velocities increase, the Froude number also grows. For critical two-layer flows theoreti-cal and experimental studies have been done to determine the possible locations of the control, the point in the channel where the Froude number passes from a value less than one to higher than one. For flow through a contraction the control occurs either at the narrowest point or some distance upstream in which case it is termed a "virtual control". Armi and Farmer (1986) introduce this terminology in the context of two-layer exchange flow, i.e. for two layers moving in opposite directions. A depth-averaged mean flow due to the barotropic tide will move the point of control. For flow over an obstacle the con-trol occurs either at the crest of the obstacle, in which case it is termed "crest-control", or some distance upstream in which case it is termed an "approach control". The ver-tical displacement of the interface in a two-layer flow over an obstacle for various flow regimes can be seen in photographs from laboratory experiments by Lawrence (1993: his Figure 7). One central aspect of the flow must be discussed in the context of waves, and as such can not be explained by hydraulic theory alone. Although discussed here in the context of a two-layer flow over an obstacle, the general concepts will also be valid for any type of stratified flow over topography and also to flow through a contraction. Whenever Chapter 4. Results from the VH-97 CTD/'ADCP Survey 108 the flow is supercritical in some region, there will be a pile-up of wave energy some-where downstream. Waves trapped by the flow will steepen and become finite-amplitude waves as a balance builds up between dispersion and non-linearities (e.g. Turner, 1973: Sec. 3.1.2.), but at some point non-linearities will dominate and the waves will break. The turbulence associated with such a stationary "hydraulic jump" in the lee of an ob-stacle can be a source of intense mixing between lighter and heavier fluids. For lower flow speeds the longest waves might be fast enough to pass over the obstacle whereas shorter finite-amplitude waves generated by the vertical displacement of isopycnals as the flow passes the obstacle, may be trapped (e.g. Long, 1955). Dispersion and non-linear effects may balance in such waves to prevent breaking. Application to Second Narrows Figure 4.15 show density profiles taken at the beginning of each tow-yo through Sec-ond Narrows. They show that the flow entering the narrows (taken to represent the up-stream conditions) is neither strictly layered nor uniformly stratified. The stratifica-tion generally falls between these two extremes for various portions of the water column. On 10 March the over-all stratification is weak. The breakdown with depth begins with uniform stratification from the surface down to about 6 meters, then a fairly homoge-neous layer down to 15 meters, followed by a uniform stratification to about 25 meters and a homogeneous layer underneath. These upstream conditions could be crudely ap-proximated by a three-layer fluid. On 7 May a very thin brackish layer exists near the surface. Below this layer the water column is nearly uniformly stratified. On 8 May a thin brackish layer near the surface overlies a strong gradient down to about 5 meters with much weaker stratification down to the bottom. On 16 May a strong nearly uniform stratification exists from about a meter below the surface down to 10-11 meters. Below this depth the stratification is weak. These profiles suggest that a theoretical model of Chapter 4. Results from the VH-97 CTD/'ADCP Survey 109 Figure 4.15: Smoothed density profiles at the beginning of each tow-yo (profile #1) through Second Narrows Chapter 4. Results from the VH-97 CTD/'ADCP Survey 110 the flow must have at least three layers but would more appropriately be able to handle more complex stratification. To compare the speed of infinitesimal long waves to the flow speed, as required by hydraulic theory, the actual density profiles were used to calculate the wave speeds from the numerical solution to the vertical part of the shallow-water equations for a continuous density stratification. We start with the linearized equations of motion for an inviscid and incompressible fluid: du 1 dp m - f v = -J*d-x (36) d-t+fU = -J*lTy <37> 0 = - d/z-9P (38) S + £ + £ - ° W ^ _ PlN2 w = o. (40) dt g v ' Here p* is a reference density while p and p are perturbations of pressure and density from the state of rest. The fictitious Coriolis force, which tend to turn motion clockwise in the Northern hemisphere and counter-clockwise in the Southern hemisphere, is here included using the f-plane approximation; the Coriolis parameter is considered constant, / = 2Qsin(0), where Cl is the angular rotation rate of the Earth and (j) is the latitude. Equations (36), (37) and (38) are momentum equations or the Navier-Stokes equations for the x, y and z directions respectively. Perturbation density is considered small and is only included in the buoyancy term of (38). This is an application of the Boussinesq approximation. Furthermore, vertical acceleration has been neglected in the same equation. This is Chapter 4. Results from the VH-97 CTD/'ADCP Survey 111 the hydrostatic approximation. Equation (39) is conservation of volume, and (40) is a linearized way of stating the incompressibility and non-diffusive assumptions. The theory of normal modes in a continuously stratified fluid uses separation of vari-ables to write each of the variables u, v, w, p and p as sums of orthogonal vertical modes which are functions of z alone, and horizontal separation constants which are functions of £, y and t (e.g. Kundu, 1990: pp. 498-500). If the perturbation pressure is written as CO P = ^2Pn(x,y,t) 1pn(z), n=0 then the structure of (36) through (40) dictates that the remaining variables take the forms: CO n=0 oo v = ^2 vnrb(z)n, 71=0 = YsWn I 1pn(z')dz', n J—H dlpn(z) w n=0 n=0 U Z where un, vn and pn are functions of (x,y,t). By substitution of the expressions above into (36) through (40) and rearranging, an expression can be found which is separable into a vertical and a horizontal part. Taking the derivative with respect to z of the vertical part gives d , 1 dibnx 1 , s ( ^ ) + i * - = °- (41) This differential equation describing the vertical structure of the normal modes is of the "Sturm-Liouville form". The eigenvalue cn is the square of the horizontal phase speed of the wave corresponding to each individual mode (Kundu, 1990: equations 47-51). Chapter 4. Results from the VH-97 CTD/'ADCP Survey 112 It is this wave speed which must be compared to the flow speed when examining the "criticality" of the flow with respect to the various baroclinic modes. For a set of well-behaved density profiles, including layered, linear and exponential profiles, analytical solutions to (41) exist (e.g. Roberts, 1973). For more complex density profiles, solutions may be found numerically. An algorithm based on the "leap-frog" method (e.g. Tinis, 1995) was used in this study. The theory of normal modes in stratified fluids assumes a flat ocean floor. As this section is a study of topographic effects on the flow, the approach of calculating normal modes may seem inappropriate. However, the calculation should still be able to give a local estimate of phase speeds for the possible modes at various locations through the channel. Table 4.1 shows the wave speeds of the first two baroclinic modes as calculated by this method for the first density profile of each series along with the depth-averaged flow speed at the same locations. The flows on 10 March, 7 May and 8 May are clearly supercritical with respect to the first baroclinic mode, thus Second Narrows exerts a control on the flow through it. On 16 May however the speed of the first baroclinic mode is comparable to the flow speed, and the experimental uncertainty involved makes it difficult to state the "criticality" of the flow with respect to this mode. The flow is most probably supercritical however with respect to all higher modes. The flow behaviour during the big floods on 10 March, 7 May and 8 May are indeed indicative of a hydraulic control somewhere in the Second Narrows. On 10 March the rising isopycnals before the crest and dramatic downward plunging on the lee side sug-gest "approach-controlled" flow. On 7 May isopycnals are instead falling towards the topographic rise, thus suggesting a "crest-controlled" flow. Lawrence (1993: Figures 17 and 18) discusses the differences between these two regimes for the two-layer case of flow over an obstacle. On all of the big floods the pronounced upward flow at depth some Chapter 4. Results from the VH-97 CTD/'ADCP Survey 113 10 March 7 May 8 May 16 May cn (cm/s) Mode 1 Mode 2 12 6 11 5 11 5 43 21 Depth averaged east-west velocity (cm/s) 180 230 240 60 Table 4.1: Baroclinic wave speed cn vs. depth-averaged east-west velocity at the location of the first profile in each tow-yo. Depth-averaged velocities are much bigger than phase speeds on 10 March, 7 and 8 May, hence the flow is supercritical through Second Narrows. On 16 May the mode 1 wave speed is comparable to the flow velocity, and the flow may therefore be subcritical with respect to that mode. distance downstream of the lee side, and the mixing in that region, suggests the presence of a hydraulic jump. During the small flood on 16 May there is no indication of hydraulic control in the narrows, but one must keep in mind that this transect did not reach the second hole as did the others. 4.2.3 The details of mixing in Second Narrows The above results suggest that mixing through Second Narrows is not only confined to a turbulent bottom boundary layer. Mixing efficiency by bottom friction increases with velocity and should be strongest at the narrowest point in the channel. The flow observed here however retains its stratification through Second Narrows itself and then turns turbulent a few hundred meters downstream where the channel both widens and deepens. Mixing through the breaking of finite-amplitude shallow-water waves — in a highly turbulent hydraulic jump — is certainly an appealing theory. The most vigorous Chapter 4. Results from the VH-97 CTD/'ADCP Survey 114 mixing does in fact appear to be confined to such a feature of the flow. The ADCP backscatter intensities, however, indicate that relatively intense turbulence is also present some distance upstream of the jumps. The isopycnal splitting at the same locations is also consistent with turbulent mixing upstream. And on 16 May when no indication of a hydraulic jump exists, isopycnal splitting indeed occurs right at the location of high backscatter intensities. Further indications of the spatial distribution of turbulence can be seen in Figure 4.16. It shows profiles of horizontal water velocities with respect to the boat and density from the S4 throughout the tow-yo on 7 May. A comparison with Figure 4.12, profile by profile, shows that the smaller-scale (or higher-frequency) fluctuations correspond to regions of both high backscatter intensity and isopycnal splitting (e.g. profiles 5-8). The immediate effect of mixing on the density profiles can also be seen. Some of the turbulence — and mixing — occurs upstream of the hydraulic jumps, suggesting that mixing also takes place by the breaking of smaller-scale instabilities. In their study mechanisms which lead to the establishment of stratified tidal flow over the sill in Knight Inlet, B.C., Farmer and Armi (1998) conclude that small-scale instabil-ities above and in the neighbourhood of the sill are responsible for a significant portion of mixing. Stratified flow over topography is sheared, and this shear promotes growth of small scale instabilities. They show that entrainment from the breaking of such instabil-ities in Knight inlet gradually leads to isopycnal splitting and the formation of a weakly stratified layer which moves slowly compared to the rest of the flow. The progressively smaller density step between this layer and the underlying flow in turn increases the local Froude number until the bottom layer becomes supercritical. A hydraulic response in the form of an "undular hydraulic jump" forms downstream, but in the case of the Knight inlet sill this undular jump is not the primary source of mixing. Undular jumps have been shown to be quite stable to breaking (e.g. Long, 1955; Lawrence, 1993). Chapter 4. Results from the VH-97 CTD/'ADCP Survey 115 Figure 4.16: The CTD data, profile by profile, from the tow-yo on 7 May: (a) east-west velocities relative to the boat, (b) north-south velocities relative to the boat, and (c) density. Cast numbers are shown on top. Chapter 4. Results from the VH-97 CTD/ADCP Survey 116 Regions in a flow favourable to the growth of small scale instabilities can be located by making estimations of a non-dimensional stability parameter, the gradient Richardson number: This ratio can be studied in the context of linear instability theory (e.g. Kundu, 1990: pp. 384-385) in which it will indicate whether linear disturbances will take on a wave-like form or grow exponentially, or in the context of fully developed turbulence (e.g. Tennekes and Lumbley, 1972: pp. 98-99) in which it compares buoyant production to shear pro-duction of turbulent kinetic energy. A necessary (and usually sufficient) condition for linear instability of inviscid stratified parallel flows is R i < \ . Smoothed profiles (running 5-meter mean with highest and lowest value removed) of the east-west velocity and density from the S4, with finite differences replacing the derivatives, were used to generate rough estimates of Ri at various locations through the transect. Figure 4.17 shows such estimates from the tow-yos on 7 May. The flow is seen to be stable to the growth of small scale instabilities west of the crest. The Richardson number however drops below the critical value where the isopy-cnal splitting starts, suggesting that isopycnal splitting at this early stage occurs due to entrainment from the overturning of small-scale instabilities. Further downstream larger-scale turbulence dominates and the Richardson number is no longer an interesting parameter. The data from Second Narrows show both similarities and differences with the model stipulated by Farmer and Armi. The formation of a slow moving weakly stratified layer above the Knight inlet sill was initially a response to a subcritical flow, and was in fact a requirement for the development of a supercritical flow later on. In Second Narrows Chapter 4. Results from the VH-97 CTD/'ADCP Survey 117 Figure 4.17: Gradient Richardson number estimates from tow-yos on 7 May. X'es and O's indicate Ri > \ (stable flow) and Ri < \ (unstable flow), respectively. Bigger symbols correspond to progressively more stable (or unstable) flow. The flow is stable west of the crest (casts 1 and 2). Immediately to the east of the crest (casts 4 and 5) the Richardson number drops below |; the flow there is unstable to the growth of small-scale instabilities and entrainment causes isopycnals to diverge from this point onwards. Further downstream (cast 6) the flow turns violently turbulent in a hydraulic jump. Thin lines are density contours and background gray scale is acoustic backscatter intensity. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 118 the flow is clearly supercritical at mid-stages of big floods, and although mixing by entrainment appears to take place throughout, most clearly above the crest before the second hole, the entrainment appears to only be an additional source of mixing to the more dramatic overturning of a hydraulic jump downstream. 4.3 Turbulent Dissipation in Second Narrows In the latest modeling attempt of this region (Pond et al. , 1998) it is recognized that the mixing through Second Narrows in the model from boundary-layer turbulence alone is too low. Insufficient mixing during big floods results in water exiting Second Narrows with much higher density in the model than what is observed in the field. Since the model is incapable of reproducing the processes which lead to turbulent mixing in the flow interior, i.e. the asymmetric flow behaviour over complex topography, some parameterizations may instead be added to the model. The central question which must be answered is: how much of the mean flow kinetic energy is dumped into turbulent kinetic energy at various locations along the channel? 4.3.1 The spectral theory of turbulence Due to the enormous range of length and time scales in turbulent flows, the impor-tant variables in such flows, i.e. velocity, density and pressure, are typically treated as stochastic variables (e.g. Kundu, 1990). At the heart of this statistical description of turbulence lies the Reynold's decomposition in which a variable is decomposed into a mean and fluctuating part, e.g. for east-west velocity: u(x, y,z,t) = U + u'(x, y, z, t). The proper average is an ensemble average (average of a variable measured from a set of identical experimental conditions). However, for stationary processes (where the Chapter 4. Results from the VH-97 CTD/'ADCP Survey 119 statistics of a variable are independent of time) and homogeneous processes (where the statistics are independent of space), the corresponding time and space averages are, by the Ergodic hypothesis, taken to represent the ensemble average. Since in geophysical applications a controlled experiment is usually impossible, time or space averages must be assumed to represent the ensemble average. By inserting the mean and average variables into the Navier-Stokes equation, one may study the effect of the fluctuating quantities on the mean flow. Kinetic energy budgets of both the mean and turbulent flow can be derived. If stratification is neglected, the form of the kinetic energy budget of the turbulent flow (fluctuating part) will be (e.g. Kundu, 1990: pp. 433-438) ^ - ^ g 2 = turbulent transport + shear production — viscous dissipation where q2 is twice the kinetic energy of the fluctuating velocity. The first term on the right hand side redistributes turbulent kinetic energy around the flow but does not contribute to the loss or gain of total turbulent energy in the flow. The second term, which tends to increase the amount of turbulent kinetic energy, also exists in the budget equation for mean flow kinetic energy in which it has the reverse sign and acts as a loss term. Finally the third term above is loss of turbulent kinetic energy to viscous dissipation. Thus, if a flow is in steady state, i. e. the level of turbulence being constant over some region in time and space, there will be an approximate balance between the shear production and the dissipation of turbulent energy into heat. An estimate of the dissipation will consequently also be an estimate of the transfer of mean kinetic energy into turbulent kinetic energy. An estimate of the viscous dissipation of turbulent kinetic energy can be obtained by observation of the turbulent kinetic energy spectrum. Such a spectrum (formally the Fourier transform of the autocorrelation of the turbulent velocity) is a decomposition of Chapter 4. Results from the VH-97 CTD/ADCP Survey 120 the turbulent velocity fluctuations into "waves" of different periods or wavelengths with the value of the spectrum at a given frequency or wavelength being the mean energy in that wave (e.g. Tennekes and Lumley, 1972: pp. 210-216). In this description, a turbulent "eddy" is thought of as some disturbance containing energy in some small wave number (or frequency) band. The integral of the spectrum E(k) over all wave numbers, k, is by Parseval's relation equal to the total turbulent kinetic energy: A turbulent kinetic energy spectrum is sketched in Figure 4.18. Energy transfer from the mean flow occurs at low wave numbers (determined by the large-scale flow structure). The biggest eddies will feed off the main flow and will thus be aware of the orientation of the mean flow. The turbulence at small wave numbers are thus anisotropic, i.e. their orientation and extent will be different depending on the geometry. Energy is transferred from big scales to small scales through the "energy cascade", described by Richardson (1922): Big whirls have little whirls, which feed on their velocity, and little whirls have lesser whirls, and so on to viscosity. Smaller eddies extract energy from eddies which are only slightly larger. The anisotropy at large scales (small wave numbers) need therefore not be felt directly at much smaller scales. As pressure fluctuations will tend to equalize velocity fluctuations in the three spatial dimensions, there will then be a wave number above which the turbulent structure of the flow looks the same in all directions. The flow in this "equilibrium range" of the spectrum is isotropic. The spectrum is influenced by the nature of the mean flow at very small wavenumbers and by viscosity at very large wave numbers. If the Reynolds number is sufficiently big (42) Chapter 4. Results from the VH-97 CTD/'ADCP Survey 121 e q u i l i b r i u m range log(k) Figure 4.18: The turbulent energy spectrum, E(k). Turbulent energy is extracted from the mean flow at large scales (small k) and is transferred to progressively smaller scales. Plotted on log-log scales, the spectrum will fall off with a -5/3 slope in the "inertial subrange". Adapted from Kundu (1990). Chapter 4. Results from the VH-97 CTD/'ADCP Survey 122 the range of scales between these two extremes may be so large that yet another sub-regime exists in between: the "inertial subrange". In this part of the spectrum the flow is isotropic. Since the production and dissipation scales are far away in the cascade of energy, neither large flow features nor viscosity are important. The non-linear transfer of energy between scales by inertia forces is the dominant process in this range (e.g. Lesieur, 1990: pp. 137-139). Energy is transferred between scales at a rate equal to the energy dissipated per unit mass and time e (note that the same symbol is used for a different quantity in Section 3.2) by viscosity at higher wave numbers, so that where K has been termed the Kolmogorov constant and has been found by experiments to be equal to about 1.7. This is "Kolmogorov's -5/3 law" for the inertial subrange. A plot of measurements of E(k) vs. k on logarithmic axes should have a slope of -5/3 within the inertial subrange if one exists. Such a plot can then be used to make estimate of the dissipation rate e. E(k) is the three-dimensional spectrum, accounting for turbulent kinetic energy in all three spatial directions. In practice velocity will be measured along a straight line at a fixed time or at a fixed point as a function of time, giving one-dimensional spectra (e.g. Tennekes and Lumley, 1972: pp. 249-256). For measurements along the k\ direction, Fn(ki) is the longitudinal spectrum (velocity fluctuations along the measurement direc-tion) and -£22(^1) is the transverse spectrum (horizontal fluctuations at right angles to the measurement direction). The relations between Fn,F22 and E are complicated in general, but within the isotropic range the relations are E(k) = f(e,k). Dimensional reasoning gives E(k) = Ke^k'V3 (43) E(k) = k3 d . 1 dF1 11 ) (44) dk k dk Chapter 4. Results from the VH-97 CTD/ADCP Survey 123 and d dk\ F22(h) ki d2 ~2dkJ Fn(ki). (45) It can be seen from these that if E is proportional to k 5 / / 3 then F\i and F22 will also be proportional to k~5/3. Furthermore, These relations can be used in both verifying the inertial subrange assumption and then in making an estimate of the dissipation and thus energy transfer from the mean flow to turbulence. 4.3.2 Results from 7 May The theory outlined above was compared with data from the tow-yo on 7 May. Fig-ure 4.19 shows that the turbulence was most predominant in the region around the first hole and was then fairly weak downstream of this point. The velocity measurements were not instantaneous measurements of the spatial struc-ture as is the requirement for the spectral analysis in wave-number space as outlined above. Measurements of fluctuating quantities when drifting with the flow represented time fluctuations of a point in the flow rather than spatial fluctuations along or across the flow. The corresponding spectrum will be a frequency spectrum rather than a wave-number spectrum. However, if the measurement probe is moved rapidly enough through the water, the turbulent field may be thought of as being frozen, with the probe recording the spatial structure. This is known as "Taylor's hypothesis" or the "frozen turbulence approximation" and is the basis on which most turbulence spot measurements are made. Fii and Chapter 4. Results from the VH-97 CTD/'ADCP Survey 124 Cast no. -3001 1 ' 1 1 1 1 1 1— i i_ 50 100 150 200 250 300 350 400 450 500 Time (sec) Figure 4.19: The turbulent regions on 7 May: (a) tow-yo track (with individual "casts" marked) and (b) u (east-west) and v (north-south) S4 velocities. Two blocks of data, from cast 6 and casts 7-8 were used for dissipation estimates. Note that the horizontal axis in these plots measure time, not distance through the transect. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 125 If u'/U <C 1 then the substitution t = x/U can be made to give u(t) = u(x/U). Figure 4.19 suggests that the boat drifting with the surface flow moved around 1 m/s faster than the deep flow. At two blocks within the highly turbulent region, when the instrument was near the bottom of casts, the mean flow was bigger than the turbulent fluctuations, and Taylor's hypothesis may hold. The averaged spectra of u and v (using the substitution t = x/U with U = 100 cm/s) from these two blocks are shown in Figure 4.20. 1 0 " 3 1 C f 2 1 0 " ' log(k) (cm-1) Figure 4.20: Turbulent kinetic energy spectra from tow-yo on 7 May. The 95% confi-dence interval and a -5/3 slope are also shown. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 126 In the log-log plot, the spectra2 Fn and F 2 2 (corresponding to u' and v' respectively) both fall off with a slope near -5/3 up to a wave number of 10-2cm-1, corresponding to a wavelength around 6 meters. At higher wave numbers however, the spectrum flattens out. The S4 instrument is apparently unable to resolve finer scales due to white noise in the electronics, most likely a result of the resolution limit of the internal compass. In addition, the measurement of velocity by electromagnetic induction around an instrument of finite dimensions (a sphere of diameter around 50 cm) will by its nature average out scales smaller than a few meters. Although both spectra fall off at approximately -5/3 for smaller wave numbers, the fact that F 2 2 is nearly an order of magnitude bigger than Fn rather than 4/3 times bigger, suggests that the flow at these scales may not be isotropic. The possibility exists however that the instrument is misrepresenting the true orientation of fluctuations, either due to a higher sensitivity to one velocity component, or due to limitations in the high frequency response of the internal compass. Estimates of the dissipation rate e from the two separate spectra at k = 10_2cm_1 give Fn ~ 2 * 103 cm3 s~2 = — 1.7 e2/3 (IO-2 cm'1)'5/3, 55 e ~ 3 cm2 s - 3 and F 2 2 ~ 2 * 104 cm3 s"2 = ^ — 1.7 e2/3 (IO"2 cm"1)"5/3, e ~ 50 cm2 s-3. The difference between these estimates should be taken as a measure of the uncertainty. 2All velocity power spectra were computed using Welch's averaged periodogram method (e.g. Press et al. 1988: pp. 437-447). Chapter 4. Results from the VH-97 CTD/'ADCP Survey 127 4.3.3 Comparison with results from 1996 Turbulence measurements were also taken east of Stn-54, around the second hole, during a big flood on 16 March 1996. Using a small boat, two attempts were made at holding a fixed position while holding the S4 at a relatively constant depth to make a better attempt at meeting the requirements of Taylor's hypothesis. The instrument depth, east-west and north-south velocities and their spectra taken during the most energetic periods of the casts are shown in Figures 4.21 through 4.24. For big portions of both casts mean U velocities of around 1.5 m/s supports the use of Taylor's hypothesis. The spectra (with the substitution t = x/U where U = 1.5 m/s) show similar behaviour to those discussed above, in that their slopes are approximately -5/3 up to wave numbers around 10~2cm-1 (the spectra from one of the casts maintains this slope up to approximately k = 2 * 10-2cm-1 which corresponds to a wavelength of 3-4 m). In the first cast the turbulent energy in the v' component (transverse component) is much bigger than the u' component. During the second cast however, the two components are comparable. Estimates of e from these spectra at k — 10-2 cm -1 give First cast: Fh ~ 1 * 103 cm3 s"2 = ^ 1.7 e2/3 (1(T2 cm"1)-5/3, 55 e ~ 1 cm2 s - 3 and F22 ~ 1 * 104 cm3 s"2 = | i | 1.7 e2/3 (1(T2 cm"1)"5/3, 3 55 e ~ 2 * 102 cm2 s-3. Second cast: Fn ~ 2 * 103 cm3 s"2 = ^ 1.7 e2/3 (10"2 cm"1)-5/3, Chapter 4. Results from the VH-97 CTD/'ADCP Survey 128 Figure 4.21: The turbulent regions on 16 March 1996, first cast: (a) tow-yo track and (b) v (east-west) and v (north-south) S4 velocities. Data from 300-500 seconds were used for dissipation estimates. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 129 Figure 4.22: The turbulent regions on 16 March 1996, second cast: (a) tow-yo track and (b) u (east-west) and v (north-south) S4 velocities. Data from 225-340 seconds were used for dissipation estimates. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 130 log(k) (cm"1) Figure 4.23: Turbulent kinetic energy spectra from the first cast on 16 May 1996. The 95% confidence interval and a -5/3 slope are also shown. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 131 Figure 4.24: Turbulent kinetic energy spectra from the first cast on 16 May 1996. The 95% confidence interval and a -5/3 slope are also shown. Chapter 4. Results from the VH-97 CTD/'ADCP Survey 132 e ~ 3 cm2 s 3 and F22 ~ 2 * 103 cm3 s-2 = ^~ 1.7 e2/z (IO"2 cm"1)-5/3, o DO e ~ 2 cm2 s-3. These results combined suggest that the turbulent dissipation rate in the neighbour-hood of the holes downstream of Second Narrows may range between 1-50 cm2 s~3. Since the time scales of the tidal forcing is so much longer than those of the turbulence, production should approximately equal the dissipation and these numbers also give an indication on the rate of transfer of mean kinetic energy into turbulent kinetic energy. The low accuracy of these estimates, however, limits their usefulness. Although a sam-pling frequency of 2 Hz is sufficient to reach inertial scales, further studies must rely on different instrumentation, estimating e from a longer record. Grant et al. (1962) observed the turbulence in Discovery passage, B.C., with velocities in the range of 1 to 1.5 m/s and obtained dissipation rates up to 1 cm2 s~3. Discovery passage is downstream of Seymour Narrows which has peak currents of 5 m/s. The estimated values downstream of Second Narrows are at least as large as those observed by Grant et al. and the largest ever estimated in the ocean. Chapter 5 Conclusions 5.1 Summary of Results Both First and Second Narrows are certainly very energetic regions. In their study of the internal tide in Indian Arm, de Young and Pond (1987) estimated the power loss in Second Narrows from the phase change in tidal heights on either side to be about 5 MW. If a turbulent dissipation estimate e from the present study (Section 4.3) of about 1 cm2 s~3 is used with a turbulent region, V, of about 500 m x 2000 m x 20 m, the total power loss AP would be AP = p e V ~ 2 MW. The turbulent dissipation downstream of Second Narrows is likely a significant portion of the total energy loss. Although observational evidence is lacking from First Narrows, it is probably safe to assume that turbulent mixing downstream takes on similar dimensions there. The turbulence in the narrows themselves is strong near the bed where density is already nearly homogeneous so it may well be less important for mixing than the downstream turbulence where density differences are larger. In section 4.2 ADCP/CTD tow-yo data were studied and showed that the high tur-bulence intensity east of Second Narrows was associated with stratified flow behaviour over the complex topography. Second Narrows exerts internal hydraulic control on the tidal flow on big floods during springs. Such control may not be present during small floods during neaps. Due to limited sampling, the location where the flow goes from 133 Chapter 5. Conclusions 134 being sub-critical to super-critical, was not identified. However, one or two topographic features, holes or depressions in the bed a few hundred meters east of the narrowest part, were identified as locations where the flow may be returning to a sub-critical state with respect to the first baroclinic mode. Data indicated the presence of hydraulic jumps at these locations and associated intense mixing throughout the water column. Current meter data at the three locations in 1995 (Chapter 3) and CTD data through-out the harbour in 1997 (Section 4.1) showed that water properties in Vancouver Harbour are chiefly dependent on the nature of the mixing in First and Second Narrows. A study of the phase lag of the barotropic tide as it works against drag due to both barotropic and baroclinic effects, and a comparison with earlier studies, suggests that the mixing over the Indian Arm sill is less important. Many time scales are involved; daily, weekly, monthly and seasonal changes were observed. During spring tides, the mixing in the narrows is intense on big floods and much weaker on small floods. A correlation was seen between tidal range of individual floods and the density change at depth. This is in agreement with the observations of different hydraulic response at Second Narrows on big vs. small floods. During neap tides, baroclinic adjustments in the harbour appear to confine currents to the upper parts of the water column. There is indication that the stronger stratification from reduced mixing during neaps may cause the internal tide in the harbour to be in resonance for some days. Although this theory stems from CTD casts in the western portion of the harbour (between First and Second Narrows), the quiescent conditions at depth during neaps were more pronounced at the current meter in the eastern part (Stn-48). The dimensions of the eastern and western parts of the harbour, however, are similar. The lack of currents at depth during some neap tides in 1995 enabled a study of the background vertical turbulent mixing at Stn-48, and an estimate was made of the vertical eddy diffusivity. Chapter 5. Conclusions 135 5.2 Suggestions for Further Work The wide range of water properties in the harbour and flow behaviour in Second Narrows encourages further studies as many questions remain unsolved at the present. How does the flow develop in each of the narrows from a sub-critical response at early stages of a flood, through hydraulically controlled flow as currents are large, and then back again to a sub-critical response as the flow slackens? The mixing will introduce hysterises, or an asymetric evolution of the dentisy field between the early and late parts of a flood (or ebb). Similarly, integrated effects of mixing will result in asymetries between early and late parts of the spring-neap cycle. The key to the understanding of effects from mixing in the narrows on conditions in the harbour, and in Indian Arm, lies primarily in the understanding of effects from such feedback. Present theories on topographic effects in stratified flows rely heavily on assumptions such as two-layer or linearly-stratified flow, and on idealized (often two-dimensional) topography. The complex topography around Second Narrows in particular suggests that one should not spend a huge effort in the application of such theories directly to reproduce the detailed flow structure through the narrows. Second Narrows is probably not a proper location for gathering further observations with the intension of extending the theoretical fluid-dynamical framework. The two narrows however are essential to the understanding of the over-all circulation in the region, and they should receive additional attention for that reason. The current numerical model of the Burrard Inlet/Indian Arm circulation underesti-mates the intensity of mixing downstream of the narrows. Since the baroclinic mecha-nisms that are responsible for generating turbulence in the interiour are not reproduced, a completely revised modelling approach must be attempted, or the effect of these mech-anisms must be parameterized within the present model. This study has identified the Chapter 5. Conclusions 136 location of regions where turbulence is triggered and also to some degree the extent of the turbulence. An additional source term in the turbulent kinetic energy equation can be inserted at the appropriate grid points of the present model. A preliminary estimate of the dissipation rate e has also been made. Further observational studies may want to make better estimates of the spatial extent of the turbulent regions and of how e varies throughout such regions. Further effort may also be put into extending the type of study which was sketched out in Section 3.3, correlating dissipation rates to the available kinetic energy of each individual flood (and ebb) tide, but also to the position in the spring-neap cycle. An ideal future observational study would benefit both from the continuous time series of moored instruments and the extended spatial coverage by ship-mounted instrumen-tation. For continuity, S4 current meters should be placed at the same locations as in the IA-95 study, but they would be deployed only over one spring-neap cycle. The sampling frequency could then be correspondingly higher. A fast boat should be used to collect CTD measurements at various locations throughout the harbour over several floods and ebbs while another boat equipped with a broadband ADCP, preferably of higher frequency for increased resolution, would focus on detailed studies around each of the narrows. 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UNESCO 1981: Tenth Report on the Joint Panel on Oceanographic Tables and Stan-dards. Technical Papers in Marine Science 3 UNESCO. WALDICHUK, M. 1957: Physical oceanography of the Strait of Georgia, British Columbia. J. Fish. Res. Bd. Canada 14(3):321-486. WALDICHUK, M. 1965: Water exchange in Port Moody, British Columbia, and its effect on waste disposal. J. Fish. Res. Board Canada 22(3):801-822. BIBLIOGRAPHY 144 WILLIAMS, R . and L . ARMI, 1991: Two-layer hydraulics with comparable internal wave speeds. J. Fluid Mech. 230:667-691. W O N N A C O T T , T. H . and R . J . W O N N A C O T T , 1981: Regression: A Second Course in Statistics. Wiley series in probability and mathematical statistics. John Wiley & Sons, New York, 556 pp. W U R T E L E , M . G . , R . D . SHARMAN, and A. D A T T A , 1996: Atmospheric lee waves. Annual Rev. Fluid Mech. 28:429-476. Appendix A Monthly CTD Casts during IA-95 Study CTD casts were made at stations QB, Stn-66 and Stn-48 (as well as some other stations in Burrard Inlet and Indian Arm) on five occasions during the IA-95 mooring program: on 9 March, 5 April, 4 May, 2 June and 23 June. The density profiles are shown below. 145 Appendix A. Monthly CTD Casts during IA-95 Study 146 Figure A.l: Density profile at QB from CTD casts during the IA-95 mooring program. The bottom 20 m are enlarged in the lower panels. Appendix A. Monthly CTD Casts during IA-95 Study 147 9 Mar 5 Apr 4 May 2 Jun 23 Jun 22.5 22.6 22.7 22.2 22.4 22.6 22.2 22.4 22.6 21.8 22 22.2 22.5 22.6 22.7 o t (kg r r f3 ) Figure A.2: Density profile at Stn-66 from CTD casts during the IA-95 mooring pro-gram. The bottom 20 m are enlarged in the lower panels. Appendix A. Monthly CTD Casts during IA-95 Study 148 9 Mar 5 Apr 4 May 2 Jun 23 Jun 21.5 21.6 21.7 20.8 21 21.2 20 20.5 21 20 20.5 21 21 21.2 21.4 a, ( kg r r f 3 ) Figure A.3: Density profile at Stn-48 from CTD casts during the IA-95 mooring pro-gram. The bottom 20 m are enlarged in the lower panels. Appendix B Raw IA-95 Time Series The following pages show the 15-minute time series (despiked as described in Sec-tion from the IA-95 mooring program in 1995. Data were collected by S4 elec-tromagnetic current meters at two depths at each of the stations QB, Stn-66 and Stn-48 (20 and 30 m below tidal datum at QB and 50 and 60 m below datum at Stn-66 and Stn-48) starting on 6 March and ending on 28 June. Horizontal velocities (east-west and north-south), temperature, and conductivity were measured by each instrument, and in addition pressure was measured by the 60 m instruments at Stn-66 and Stn-48. Time series are shown here are of pressure (of the 60 m instruments at Stn-66 and Stn-48), east-west and north-south velocities, temperature and density (computed from temperature and conductivity). The densities plotted here have not been corrected for offsets and drift in the instruments over the deployment period. Note also that the pressure record for QB is that of the Stn-66 60 m instrument. Also note that velocity scales for QB instruments are different from those for Stn-66 and Stn-48 instruments. 149 Appendix B. Raw IA-95 Time Series 150 Figure B.l: QB 20 m Appendix B. Raw IA-95 Time Series 151 Appendix B. Raw IA-95 Time Series 152 Appendix B. Raw IA-95 Time Series 153 Appendix B. Raw IA-95 Time Series 154 Appendix B. Raw IA-95 Time Series 155 Appendix B. Raw IA-95 Time Series 156 Figure B.2: QB 30 m Appendix B. Raw IA-95 Time Series 157 Appendix B. Raw IA-95 Time Series 158 Appendix B. Raw IA-95 Time Series 160 Appendix B. Raw IA-95 Time Series 161 Appendix B. Raw IA-95 Time Series 162 Figure B.3: Stn-66 50 m Appendix B. Raw IA-95 Time Series 164 Appendix B. Raw IA-95 Time Series 166 Appendix B. Raw IA-95 Time Series 167 Appendix B. Raw IA-95 Time Series 168 Figure B.4: Stn-66 60 m Appendix B. Raw IA-95 Time Series 170 Appendix B. Raw IA-95 Time Series 172 Appendix B. Raw IA-95 Time Series 173 Appendix B. Raw IA-95 Time Series 174 Figure B.5: Stn-48 50 m Appendix B. Raw IA-95 Time Series 175 Appendix B. Raw IA-95 Time Series 176 Appendix B. Raw IA-95 Time Series 177 Appendix B. Raw IA-95 Time Series 178 Appendix B. Raw IA-95 Time Series 180 Figure B .6: Stn-48 60 m Appendix B. Raw IA-95 Time Series 181 Appendix B. Raw IA-95 Time Series 182 Appendix B. Raw IA-95 Time Series 183 Appendix B. Raw IA-95 Time Series 184 Appendix B. Raw IA-95 Time Series 185 


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