Tidal Interactions with Local Topography Above a Sponge Reef
by
Jeannette Bedard BSc, Royal Roads Military College, 1994
A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
in the School of Earth and Ocean Science
Jeannette Bedard, 2011 University of Victoria
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Supervisory Committee
Tidal Interactions with Local Topography Above a Sponge Reef
by
Jeannette Bedard Bsc., Royal Roads Military College, 1994
Supervisory Committee
Dr. Eric Kunze (School of Earth and Ocean Science) Supervisor
Dr. Richard Dewey (School of Earth and Ocean Science) Co-Supervisor
Dr. Jody Klymak (School of Earth and Ocean Science) Departmental Member iii
Abstract
Supervisory Committee Dr. Eric Kunze (Department of Earth and Ocean Sciences) Supervisor Dr. Richard Dewey (Department of Earth and Ocean Sciences) Co-Supervisor Dr. Jody Klymak (Department of Earth and Ocean Sciences) Departmental Member
The interaction of tidal currents with Fraser Ridge in the Strait of Georgia, B.C., generates an internal lee-wave on each strong flood but, due to the ridge's asymmetry, not during ebbs. Just prior to lee-wave formation, a strong accelerated bottom jet forms with magnitudes up to 0.7 m s-1 forms during barotropic tidal flows reaching 0.2 m s-1. On the steepest slope, this jet forms directly above a rare glass sponge reef, and may prevent the sponges from being smothered in sediment by periodically resuspending and carrying it away. Both the accelerated jet and lee-wave remove tidal energy. At peak flood tide, the lee-wave has energy dissipation rates reaching 10-5 W kg-1 that removes energy at a rate of ~611 W m-1, while the bottom boundary layer at the time of the accelerated jet has energy dissipation rates reaching 10-4 W kg-1 that removes energy at a rate of ~525 W m-1. iv
Table of Contents Supervisory Committee...... ii
Abstract...... iii
Table of Contents...... iv
List of Figures...... vi
Acknowledgments...... vii
1. Introduction ...... 1 1.1 Glass Sponge Reefs...... 2 1.2 Study Location...... 3 2. Theory and Field Studies...... 6 2.1 Two-Dimensional Flow-Topography Interaction...... 7 2.2 Three-Dimensional Effects...... 9 2.3 Expectations at Fraser Ridge...... 10 3. Methods...... 12 3.1 16-27 November 2007 Field Program...... 12 3.2 June to August 2010 Mooring...... 13 4. Observations...... 16 4.1 General Flow Characteristics Around Fraser Ridge...... 16 4.1.1 Horizontal Flow Structure...... 16 4.1.2 Cross-Ridge Evolution of the Flow...... 20 4.1.2.1 Weak Flood Tide...... 20 4.1.2.2 Strong Ebb Tide...... 20 4.1.2.3 Strong Flood Tide...... 24 4.1.2.4 Weak Ebb Tide...... 27 4.1.3 Along-Ridge Evolution of the Flow...... 27 4.2 Flow Directly Above Sponge Reef ...... 30 4.2.1 Accelerated Jet...... 30 4.2.2 Bottom Turbulence and Mixing...... 34 4.3 Energy Budget...... 35 4.3.1 Local Energy Dissipation ...... 36 4.3.2 Time-Varying Term ...... 37 v 4.3.3 Bernoulli Drop ...... 39 4.3.4 Energy Budget Summary...... 41 5. Discussion...... 42 5.1 Ridge-Scale Flow...... 42 5.2 Flow at the Sponge-Reef Scale...... 43 6. Conclusions...... 48 7. Bibliography...... 50 vi
List of Figures 1. Map and Tides at Fraser Ridge...... 5
2. Parameter Definition Sketch...... 6
3. Fraser Ridge Topography and Transects...... 11
4. Energy Dissipation Rate Calculation Examples...... 15
5a. Depth and Time Average of Horizontal Velocity 0 – 25 m...... 18
5b. Depth and Time Average of Horizontal Velocity 25 – 100 m...... 19
5c. Depth and Time Average of Horizontal Velocity 100 m – bottom...... 19
6a. Time Series of Section B03 - B10...... 22
6b. Time Series of Section B10 - B19...... 23
7. Cross-Ridge Section B13...... 25
8. Cross-Ridge Section E06...... 25
9. Histograms of North Velocity for Tracks B13 and E06...... 27
10. Along-Ridge Track H...... 28
11. Two-Dimensional Histograms of Accelerated Jet, Energy Dissipation Rate and Barotropic Tides...... 31
12. Time Series From 12 August 2010...... 32
13. Zoomed In Velocities From Figure 12...... 33
14. Two-Dimensional Histograms of Frictional Velocity and Bottom Velocity...... 37
15. Hjulström Diagram...... 45 vii
Acknowledgments
I would like to thank my supervisors Eric Kunze and Richard Dewey for providing direction to my research and encouragement along the way. I'm particularly grateful to Eric Kunze for his expertise, endless patience, thoughtful comments and edits on multiple manuscript drafts, along with financial support for this research. Thanks to Richard Dewey for sharing his practical know-how on mooring deployment and matlab coding along with theoretical discussions. His office was always a valuable stop while improving my understanding of my thesis data. I also wish to thank Jody Klymak, my committee member, for asking difficult questions about my work and providing constructive criticism that ultimately improved this work. Thanks to Kevin Bartlett for answering my Matlab and Linux questions and for his practical help with data collection. Thanks to Sally Leys for giving me the opportunity to view Fraser Ridge in real time through an ROV and exposing me to glass sponges in person. Thanks to the team on the CCGS Vector for two weeks of data collection in 2007 and thanks to the team on R/V Strickland for the deployment and recovery of the 2010 mooring. I am grateful to Nortek, through their 2010 Student Equipment Grant, for the use of a Aqudopp Z-Cell Profiler and Vector Velocimeter for the 2010 mooring. Thanks to my fellow grad students, both past and present, for their friendship and support. Especially Mei Sato, Wendy Callender, Reyna Jenkins, and Shani Rousseau for our in office and field discussions. I would also like to acknowledge my friends and family. Thanks to my fiancé Gavin Hanke who was willing to listen to my rants about mathematics well outside his understanding and thanks to my friend, Alana Clarke for being willing to listen to my ideas and check my wording. I don't know what I would have done without the support of these two excellent people. 1. Introduction Ocean currents accelerate when they encounter topography resulting in turbulence and mixing. Internal lee waves often result from these interactions in stratified waters.
Observations show lee waves create regions of enhanced local mixing (Farmer and
Denton, 1985; Nash and Moum, 2001; Klymak and Gregg, 2001; Armi and Farmer,
2002; Inall et al., 2004; Dewey et al., 2005). The health of co-located biological communities often depend on these local flow patterns (Frechette et al., 1998; Genin et al., 2002; Monismith, 2007).
Lee waves are a complex phenomenon, efficiently extracting barotropic tidal energy through drag. When flow encounters higher pressure in the lee of an obstacle, it may separate into a lee wave, an effect potentially removing more energy than bottom friction
(Edwards et al., 2004). In Loch Etive fjord, form drag removes four times more energy from the barotropic tide than bottom friction (Inall et al., 2004). Off the short width of the elongated Stonewall Bank, lee waves form from coastal current interactions, becoming an important source of mixing and drag on the mean flow (Nash and Moum, 2001).
Flow/topography interactions become complex for three-dimensional obstacles. The parameter space for these three-dimensional effects has been explored through lab experiments (Castro et al., 1983, Baines and Hoinka, 1985; Castro et al., 1990; Killworth,
1992; Castro and Snyder, 1993; and Baines, 1995). Field observations show similar flow patterns. For example, over Knight Inlet sill, a non-linear lee wave with turbulent energy dissipation rates up to 10-4 W kg-1 was observed in conjunction with horizontal recirculations carrying an equivalent amount of water as a quarter of the tidal flux
(Klymak and Gregg, 2001; Klymak and Gregg, 2004). 2 Fraser Ridge, located in eastern Georgia Strait, provides the setting for this study. It is a sub-surface three-dimensional obstacle perpendicular to the tidal flow and home to one of the few glass sponge reefs known to exist. These sponge reefs reach several meters in height, forming the base of an ecosystem consisting of rockfish, sharks, and other fishes, as well as a diverse invertebrate population. These modern glass sponge reefs represent an analogue of ancient habitats that once formed vast reefs in much of the world's oceans. Flow interaction with Fraser Ridge may play a role in sponge reef formation and continuing health.
This study examines Fraser Ridge's impact on tidal flow and the resulting flow phenomena. Flow structure will be broken into two scales, a larger ridge scale and a smaller scale directly over the sponge reef. Examining this flow will aid in understanding why sponge reefs form here, and provide a baseline for studies of other sponge reefs in the area.
1.1 Glass Sponge Reefs Hexactinellid sponges, also known as glass sponges because of their silica skeleton, include ~500 species worldwide, with the greatest diversity living at ocean depths of 300-
600 m (Leys et al., 2007). The earliest animals found in the fossil record are sponges
(Love et al., 2009). In general, glass sponges live in regions of high productivity (Leys et al., 2007) and their growth depends on the availability of space, suitable firm substrate and local water currents (Barnes, 1987). Suitable hard substrate for glass sponges includes glaciomarine sediments, glacial till, bedrock or dead sponge skeletons (Conway et al., 1991). 3 Glass sponges are stationary filter feeders that have evolved with a unique structure to exploit external flow conditions. Supported by a skeleton of silicon dioxide that accounts for 90% of their dry weight (Leys et al., 2007), these sponges grow upwards from the substrate in a variety of rigid shapes ranging from clusters of vase-like forms to elongated spindles. The unique symmetrical scaffold-like structure of their skeletons is robust and remains after soft tissue has decayed, often filling with sediment to form a firm substrate for future sponges (Leys et al., 2007). Sponges are considered primitive in an evolutionary sense because they have no tissues or organs. Instead, their bodies are a colony of cooperating cells that depends on internal water canals lined with flagella to pump water through the colony. This internal current allows the sponges to feed, exchange gases and remove waste (Barnes, 1987). If external conditions are not ideal for the sponge, for example, if there is excess flow or sedimentation, the internal current can be turned off (Leys et al., 2007). Marine detritus does not build up on the surface of sponges, suggesting they also have a mechanism to remove particles from their outer surface (Conway et al., 1991).
1.2 Study Location Fraser Ridge is located off the Fraser River Delta, west of Sturgeon Bank, in Georgia
Strait, British Columbia (figure 1a). Oriented northwest-southeast (along 323° T), Fraser
Ridge sits in a water depth of 177 m to the south and 265 m to the north (figure 1b). At the 160-m isobath, the ridge is 2-km long with a minimum width of 381 m at the center, broadening to 524 m to the southeast. At the southeast end of the ridge is the shallowest point at 144 m. Further along the crest of the ridge is a deeper point of 157 m before the ridge rises to the second shallow peak in the northwest of 147 m. The north slope is four 4 times steeper than the south slope. Fraser Ridge is oriented almost perpendicular to local tidal flow.
Tides drive most of the fluid motion in the water column above the ridge. The exception is a ~20-m layer of fresh water at the surface originating from the Fraser River which typically moves southward independent of the deeper flow. Flood tide flows mostly north and ebb mostly south, with only a weak zonal component (figure 1). Below the surface layer, a mean northward flow augments the floods and reduces the ebbs.
Barotropic tidal currents predicted from the Southern Vancouver Island Tidal Model
(SVI tides) (Foreman, 1993) reach speeds up to 0.26 m s-1. During the 2007 and 2010 measurements used in this study, tides are mixed.
An important factor influencing glass sponge reef formation is sedimentation rate.
The Fraser River discharges (1-3) x 1010 kg of sediment annually (Johannessen et al.,
2003). In the vicinity of Fraser Ridge, average sedimentation from the Fraser River can exceed 2 cm yr-1 (Conway et al., 2004). Sediment dispersal in the Strait of Georgia is influenced by dynamic processes at the mouth of the Fraser River (Hill et al., 2008).
Because of the strength of tidal currents on the delta slope and elsewhere in the strait, sediment is regularly resuspended and moved throughout the basin (Hill et al., 2008). The mean northward flow results in a predominant northward sediment drift along the delta slope (Meulé, 2005). Sediment does not accumulate on ridges like Fraser Ridge because ambient currents tend to accelerate across and around these obstacles, keeping them relatively silt-free (Hill et al., 2008). 5
Figure 1a: Map of Southern Vancouver Island and the Strait of Georgia. The location of Fraser Ridge is marked with a red dot. Inset is the surface tidal currents with zonal (blue) and meridional (red) in m s-1 from the Southern Vancouver Island Tidal Model (Foreman, 1993).
Figure 1b: Bathymetry at Fraser Ridge. Contours are spaced in 10 m intervals. 6
2. Theory and Field Studies
Figure 2: Stratified flow interactions with a three-dimensional sub-surface bump can be characterized by the following parameters: barotropic flow U, obstacle height h, half cross-ridge width A, half along-ridge width B. At Fraser Ridge, the buoyancy frequency N is 1.8 x 10-2 s-1, h is ~30 m, A varies between 200-600 m on the northeast side, and B is 1000 m.
How topography modifies tidal flow is influenced by several factors (figure 2).
Dramatic and well-studied internal lee-waves often form in response to flow-topography interactions (Baines, 1995). Phenomena such as eddies, blocked upstream flow, lee-side regions of stagnation and increased turbulent mixing are also expected.
A lee wave is a standing wave that develops on the lee of an obstacle, resulting from the interplay between upstream water velocity and fluid buoyancy. Called mountain waves in the atmosphere, lee waves were first discovered by glider pilots in the 1930s
(Kuettner 1939 a and b; and Manley, 1945) and have since been identified as a common 7 ocean feature. Since their discovery, lab studies and models have fully explored the parameter space relevant to lee-wave development (Castro et al., 1983; Baines and
Hoinka, 1985; Castro et al., 1990; Killworth, 1992; Castro and Snyder, 1993; Vosper et al., 1999; Sutherland, 2002; Cummins et al., 2003; Ambaum and Marshall, 2005).
Two-dimensional flows will be described first, since much of the phenomenology carries over to three-dimensional obstacles. In previous studies, the two-dimensional approximation has often been made. This study confirms the validity of this approximation.
2.1 Two-Dimensional Flow-Topography Interaction Obstacles alter ambient flow patterns. If stratified flow has enough momentum when encountering an obstacle, lower layers are pushed up the upstream slope causing a convergence of streamlines at the crest. The result is a near-bottom layer of accelerated flow and corresponding pressure decrease from the Bernoulli effect at the top of the obstacle. Pressure increases again on the downstream slope, making flow separation possible. A difference in density between the waters on either side can result in flow separation and suppress lee-wave growth (Klymak and Gregg, 2003).
How flow separates, and if a lee wave forms, depend on a number of factors (figure
2) which combine into the non-dimensional number Nh/U, where N is the buoyancy frequency, h the obstacle height and U the upstream water velocity (figure 2). Also of importance is the along-stream half-width A, which, when combined with h, gives the lee slope.
Nh/U provides a measure of how much the stratification versus the upstream water velocity drives the resulting phenomenon. When Nh/U is small and the slope steep, water 8 velocity dominates over buoyancy, causing the flow to separate off the top of the obstacle, a phenomenon called boundary-layer separation. In this case, a turbulent wake forms over the entire lee side extending some distance downstream. As Nh/U increases, stratification inhibits flow separation. Once the separation point drops below the crest, accelerated flow down the lee slope develops downward momentum and flow separates further down the lee slope, a phenomenon called post-wave separation. Ultimately, the separation point can occur at the bottom of the lee slope. Another way to differentiate between boundary-layer and post-wave separation is by using the non-dimensional number NA/U; when NA/U < π, boundary-layer separation occurs while, when NA/U > π, post-wave separation occurs (Baines, 1995).
In post-wave separation, an accelerated jet forms on the lee-slope and hugs the bottom; this accelerated jet is analogous to downslope windstorms found on the lee of mountains (Lilly and Klemp, 1979). At some point along the lee slope, flow separates from the obstacle and water rebounds to its original height as a lee wave. The resulting lee-wave shape depends on the lee slope (Castro et al., 1983). Steeper slopes generate sharper lee waves while, if the lee slope is sufficiently gentle, flow may not separate. The upstream slope is not important to the lee wave and any sensitivity to this slope is due to surface friction effects (Miller and Durran, 1991). Beneath the lee wave, a region of slower flow and turbulence develops (e.g. Nikurashin and Ferrari, 2010). When Nh/U >
1.5, a stagnant patch forms above the accelerated jet just upstream of the lee wave
(Baines and Hoinka, 1985).
Once Nh/U ~ 1.5, the lee waves steepen and start to break. This non-linear flow regime where the lee wave transitions to an hydraulic jump. Over a relatively short 9 horizontal scale, the flow switches from domination by kinetic (supercritical) to potential energy (subcritical).
2.2 Three-Dimensional Effects The three-dimensional case has much in common with the two-dimensional with the potential for the development of additional dynamical complexities. For example, at sites like Stonewall Bank, that is neither axisymmetric nor the oncoming flow always from exactly the same direction, it is expected that a better-understanding of the character of the hydraulic flow would be gained by considering the third dimension (Nash and Moum,
2001). However, depending on the obstacle's geometry and ambient flow, the two- dimensional approximations from the previous section can still be applied for a period of time.
In the three-dimensional case, Nh/U and the lee slope remain important with the relationship between lee slope and steepness of the resulting lee wave still holding. Peak wave slopes for an idealized three-dimensional object occur for 2.5 < Nh/U < 5 (Castro et al., 1983).
In addition to the above parameters, the cross-stream topography half-width, B
(figure 2) comes into play. The ridge's aspect ratio, B/A, provides a measure of the duration that the two-dimensional approximation holds. When B/A << 1, the obstacle is longer along the flow than perpendicular to it, resulting in three-dimensional flow patterns from the onset. When B/A >> 1, that is, the obstacle is much longer across than along the flow, flow is initially two-dimensional except at the ends so two-dimensional approximations hold for a time. The minimum length of time the two-dimensional approximation is valid can be obtained through B/U (Baines, 1995). This time-scale 10 approximates when flow from the end of the obstacle may start influencing the cross- ridge flow. The two-dimensional approximation may or may not become invalid at this time.
In coastal waters, the strongest flows over obstacles are tidal, adding an additional time-varying component. Lee-wave structures grow and decay with each tidal cycle. A parameter space where lee waves persist long enough to influence the flow structure on the next tide is possible. An example of time-varying flow phenomenon arising from tidal interactions occurs at an isolated sub-surface bump near Race Rocks, B.C., which includes periodic lee-wave formation and enhanced turbulence (Dewey et al., 2005).
2.3 Expectations at Fraser Ridge Here, the parameterization from the previous section will be applied to Fraser Ridge, which is longer in the northwest-southeast direction than in the northeast-southwest
(figure 2) with aspect ratio B/A = 4. At peak flood, barotropic U reaches a maximum of
0.2 m s-1, N is approximately 1.8 x 10-2 s-1 and h varies from 24 to 33 m so Nh/U reaches a maximum of 3.3, and the separation point is expected to be pushed down the lee slope before a lee wave forms (Baines, 1995). NA/U ranges between 64 and 25, much greater than π, falling within the post-wave separation regime (Baines, 1995). Over Fraser Ridge,
B/U ~80 min which provides a minimum time the flow can be considered two- dimensional.
The geometry of the ridge affects lee waves produced on flood tides. Specifically, varying lee slopes influence the resulting lee-wave shape. The lee slope on the flood tide, h/A, is 0.09 at cross-ridge transect E and 0.05 at cross-ridge transect B (figure 3). We 11 therefore expect steeper lee waves at E where the lee slope is steeper. Since Nh/U exceeds 1.5, the resulting lee wave is expected to be a non-linear hydraulic jump.
On ebb, NA/U exceeds 500 and Nh/U reaches 9 (flow opposite direction). Since the cross-flow ridge is asymmetrical, on ebb the lee slope h/A is less than 0.01. Due to the gentle slope and weaker ebb tides, flow should not separate and no lee wave observed to form.
Figure 3: Bathymetry of Fraser Ridge. Blue lines indicate ship tracks where ship-mounted ADCP profiles were collected over 16-26 November 2007. Each track was repeatedly sampled for at least 12 h. Transects have been assigned track letters as labeled. Microstructure and water property profile sections were collected along cross-ridge tracks B and E. The red-dashed oval indicates the rough location of the primary glass sponge reef and the cyan dot on track E the 2010 mooring location. 12
3. Methods
3.1 16-27 November 2007 Field Program The primary data collection tool for the 16 – 27 November 2007 field program was a vessel-mounted 150-kHz ADCP manufactured by RD Instruments. Two days of vertical microstructure measurements (VMP), using a Rockland Scientific tethered freefall vertical profiler, were also made to obtain density and kinetic energy dissipation rates.
The repeated ship tracks (figure 3) were designed to capture the semidiurnal three- dimensional velocity structure over Fraser Ridge.
Initially, the ADCP was programmed to capture 4-m vertical bins. However, on 17
November 2007, this was changed to 3-m vertical bins to remove an interference band originating from other instruments. The bottom 6% of all profiles was removed because of contamination by side-lobe reflections off the seafloor.
ADCP data were viewed in two ways. First, data were sorted into transects and assigned a track letter (figure 3), allowing vertical slices through the water column to be viewed. Second, the overall flow characteristics were examined by placing a 20 x 20 grid over the study area and sorting the ADCP profiles into the appropriate grid square. This allowed examination of data in planview with a 50 x 50 m resolution. Most grid squares contained data from all phases of the tide. A consequence of this assumption is that spring-neap and short-term (<2 h) variability is not resolved.
Energy dissipation rates were calculated from microstructure vertical shear measurements by the VMP assuming isotropic turbulence. Vertical microscale shear, uz,
2 and energy dissipation rate, ε, relate through: ε = (15/2)ν
Nasmyth (1970) (Dewey, 1987) turbulent model spectrum (Wesson and Gregg, 1994), resulting in energy dissipation rates in the range 10-10 < ε < 10-5 W kg-1 with a factor of two uncertainty.
Down- and upwelling may impact the dissipation rate because it could alter the rate the instrument falls. Energy dissipation rates calculated from this type of instrument has a fourth-power dependence on the instrument's vertical velocity through water (Klymak and Gregg, 2004). Only on one VMP cast on track B13 does the instrument fall through downwelling of 0.1 m s-1 for 50 m. Since the instrument fall rate was 0.7 m s-1, this translates to a small region where the dissipation rates are low by a factor of 2, which is insignificant to the overall calculations.
3.2 June to August 2010 Mooring To quantify flow directly above the sponge reef, a mooring was deployed on Fraser
Ridge (123º 23.094'W 49º 09.489'N) partway down the steep northwest slope where sponges reside (figure 3). The mooring remained in place between 22 June -19 August
2010, with the goal of capturing the accelerated bottom jet that forms on flood tides.
Three instruments were deployed: a Nortek Vector, which provided a high-frequency (8-
Hz) point velocity measurement from which dissipation could be calculated 1.2 mab
(meters above bottom); a Nortek Z-cell ADCP to measure flow in the bottom 10 m; and an RDI 300-kHz ADCP to capture flow throughout the water column.
The instruments were rigidly deployed on a 20º slope. The Vector was set to sample a 61-s (8 Hz sampling rate) burst of 512 data points every 7 min. The Z-cell collected 2- 14 min averages for each 0.5-m bin, while the RDI ADCP collected data every 5 s in 3-m bins.
After the instruments were recovered, the following corrections were applied: The
RDI velocities were rotated into a ENU (East North Up) coordinate system corrected for the slope (Ott, 2002). A rotation was also attempted on the Z-cell data; unfortunately, the data were found to be very noisy so it was only used to give a rough qualitative view. For every burst of Vector data, velocities were rotated into an along-slope coordinate system with a flow principal axis and two orthogonal off-axis flows, one of which was normal to the bottom. Since the Vector was situated 1.2 mab, the bottom-normal component (w) of the flow was used to calculate energy dissipation rate, ε.
The high-frequency burst measurements allowed calculation of dissipation rates in the bottom boundary layer, a method used recently to measure turbulence in nonlinear internal waves (Moum et al., 2007). We assumed the structure of the turbulence did not evolve dramatically as it was advected past the sensor (Taylor's Hypothesis) and that an inertial subrange existed. It was also assumed that the resulting 0.3 – 0.6 m turbulence scales was isotropic, homogeneous and stationary.
Three velocity spectra with 50% overlapping were created using 256 data points each, these spectra were then averaged. This velocity spectra was fitted to the Nasmith universal curve (Nasmith, 1970) in the inertial subrange in order to estimate dissipation rates, ε, by finding the minimum variance between the theoretical curve and actual spectra. This fit was applied for the wavenumber range 10 – 21 rad m-1 (corresponding to wavelengths in the 30 – 60 cm range) chosen to work for the entire time-series. Example spectra are shown for high and low dissipation rates in figure 4. These calculated 15 dissipation rates have an uncertainty of ±50%. Unfortunately, VMP data did not extend this close to the bottom for comparison purposes. However, both data sets reach high dissipation values of the same order of magnitude.
Figure 4: Example wavenumber spectra for high (left) and low (right) dissipation rate cases from the 2010 mooring data. Spectra are blue, the Nasmith curve black with wavelengths of 30 – 60 cm (wavenumbers of 10 – 21 rad m-1) where the data was fit in red. 16
4. Observations
4.1 General Flow Characteristics Around Fraser Ridge The 2007 ship-based data varied both spatially and temporally over Fraser Ridge.
These repeated ADCP surveys provide a three-dimensional picture of the flow structure over the ridge as a function of tidal phase. Flow over Fraser Ridge is dominated by meridional tidal fluctuations interacting with topography. To understand the flow characteristics, the flow structure at different tidal phases will be discussed, first in planview at different depths, next at cross-ridge sections, B and E (figure 3), and finally at the along-ridge structure (transect H). Other transects (figure 3) support the conclusions based on these three transects but are excluded from the discussion in the interest in brevity.
4.1.1 Horizontal Flow Structure In the upper 25 m, flow predominantly moves southward at an average velocity of
0.14 m s-1 containing south-moving Fraser River outflow. Because these data were collected in November, flow from the Fraser River is at a minimum. During the 2007 sampling period, there was no wind to influence the surface flow. Mean flow structure in this layer is shown in figure 5a. Upper-layer flow is strongest (up to 0.18 m s-1 southward) and thickest (at times exceeding 50 m) during ebb. During flood, flow is on average 0.02 m s-1 southward and less than 25-m thick. Southward flow disappeared briefly during the spring flood tide on 25 Nov 2007.
Mean flow structure between depths of 25 to 100 m is shown in figure 5b. Tidal- phase averages in this layer follow the phase of the modeled barotropic tidal currents from the Southern Vancouver Island Tidal Model (Foreman, 1993). Maximum observed 17 velocities reached on flood and ebb are asymmetrical due to a mean northward flow. On flood, a maximum northward component of 0.16 m s-1 is reached, while on ebb, the maximum southward flow is only 0.05 m s-1. Weak eastward flow persists over all phases, reaching a maximum of 0.05 m s-1.
Mean flow structure below 100 m is shown in figure 5c. In this layer, asymmetry between flood (max 0.24 m s-1) and ebb (max 0.03 m s-1) is more pronounced than in the layer above. For most of the tidal cycle, water flows northward, reversing for a few hours around peak ebb. The zonal component of flow in this layer is weaker and more variable,
±0.04 m s-1, than the layer above. Below the ridge crest, flow is extremely variable and some blocked flow is observed in the middle of the southwestern side of the ridge. It is expected that a component of the flow in this layer passes around the ridge. However, this lies in depths affected by side-lobe contamination so it is difficult to quantify. 18
Figure 5a: Depth-and-time-averaged horizontal flow based on a 20 x 20 (~50 m x ~50 m) grid of the study area. Surface layer (0-25 m) (a), middle layer (25-100 m) (b), and bottom layer (100 m to bottom) (c). The transparency of the arrow indicates the number of profiles within a grid square, darker arrows containing more profiles with a maximum number of profiles of 1313. Minimum plotted is 5. Darker arrows also indicate how well a grid square is averaged over tidal phases. A scale arrow is included at the bottom right. The red dot with each arrow indicates the centre of the grid square. 19
Figure 5b: Middle layer (25-100 m)
Figure 5c: Bottom layer (100 m to bottom) 20
4.1.2 Cross-Ridge Evolution of the Flow Transects B03-B19 provide an example of the tidal evolution of the cross-ridge flow
~500 m northwest of the southeastern end of the ridge (figure 3). General flow characteristics are similar on each strong/weak tide and at other cross-ridge transects (A,
C, F, J and E). A cycle through weak flood, strong ebb, strong flood and weak ebb is discussed below. Each transect took on average 45 minutes.
4.1.2.1 Weak Flood Tide On weak flood (B03-B05 in figure 6), the bottom two layers merge and the flow structure is better-approximated as two-layer flow with a zero-crossing and density interface near ~75 m. As previously noted, the top layer consists of river water flowing south during all phases of the tide. As tidal flow increases between B03 and B04, a 10-m rise of the isopycnals occurs downstream of the ridge. As the tide slackens in B05, these perturbed isopycnals shift upstream back onto the ridge. VMP energy dissipation rates are elevated at the flow zero-crossing (10-7 W kg-1) compared to background values (10-9
W kg-1).
4.1.2.2 Strong Ebb Tide During strong ebb (transects B06-B10, figure 6), isopycnals flatten and northward flow components are pushed south until there is barotropic southward flow. Early in the ebb (B06-B07), when flow is reversing, there is variability on the north, now upstream, slope, which is most evident close to the bottom. As maximum ebb approaches (B09), flow becomes uniform at mid-depth. In the bottom layer, flow that is unable to surmount the ridge goes around the ends. At peak ebb, little vertical structure occurs. However, 21 VMP casts do not extend far enough south to be certain no structure exists further downstream.
Higher energy dissipation rates were found around 75-m depth of the same strength and location found at the earlier weak flood interface. Flow reverses to northward very quickly after maximum ebb passes (B10-B11). 22
Figure 6: Time-series of sections B03-B19 north velocity, v, with the dissipation rates, ε, overlaid as vertical stripes of colour. Red indicates north flow (from left to right) and blue south (from right to left). Dark gray lines are isopycnals ranging from σ = 22 kg m-3 by 0.25 to σ = 25 kg m-3. B03-B05 is a weak flood with an interface at 75 m between southward river water and northward tide. B06-B10 is a strong ebb where the northward flow is ultimately replaced by barotropic southward flow. B11-B15 is a strong flood where a lee wave forms above the north slope. B16-B18 is a weak ebb that never reaches a barotropic southward flow but shows weak flow changing direction on short vertical scales. 23
Figure 6 continued 24
4.1.2.3 Strong Flood Tide The most extreme internal structures occur during strong floods. At these times, all cross-ridge transects develop multi-layer flows. At the centre of the ridge, a more two- layer flow forms while, towards the ends, the flow is best-approximated as three layers. A strong three-layer flood forms over the southeast end of the ridge in transects B11-B15
(figure 6).
As tidal flow increases, the bottom ~50 m of the water column accelerates as it pushes up the ridge, achieving a faster northward velocity than the predicted barotropic tides. Leeward below the ridge crest, accelerated flow develops downward momentum pushing the separation point deeper. This bottom-accelerated jet flows down the h/A =
0.04 lee slope at a maximum of ~0.6 m s-1 (B13, figure 7). The jet separates from the ridge 600 m downstream of the crest and a lee wave forms. The separation point slides further down the lee flank as the flood builds to its maximum. At peak flood, the lee wave is at its largest. As the tide slackens, the lee-wave separation point rides back up the lee slope. The same process occurs at the northwestern end, but this transect is much steeper with a slope of 0.1. Here, the accelerated jet reaches a maximum of 0.7 m s-1 and flow separates ~300 m downstream of the ridge crest (figure 8). 25
Figure 7: Cross-ridge section B13 toward southeast end of ridge (figure 3) taken just after peak flood. North and vertical velocities over plotted as vectors. East velocity is plotted on a colour scale, red is coming out of the page and blue going in. A scale arrow can be found below the bottom axis on the left. The vertical red line at the top of the ridge indicates the ridge center line (Track H). Near-bottom flow has intensified over the ridge crest and a lee wave has formed on the north slope.
Figure 8: As Figure 6, but for cross-ridge section E06. Sponge reef is located along the lee (north) slope as indicated by the dashed green oval. Interference from a towed instrument appears around 75 m. 26 Differing slopes along the ridge result in a stronger accelerated jet at the northwest end (transect E, figure 3). Histograms of flow following a percent of the water depth along each transect, show that, below z = 0.8H where H is the total water depth, each transect has two velocity peaks (figure 9). The low one corresponds to flow beneath the lee wave and the higher one to the accelerated bottom jet. At z = 0.8H, the high peak for transect E is centered around ~0.55 m s-1 while, for B, it peaks around ~0.4 m s-1, a difference of ~0.15 m s-1(38%). At z = 0.9H, both flows have slowed. Transect E flows now peak at ~0.45 m s-1, ~0.1 m s-1 (29%) faster than ~0.35 m s-1 at B. This trend continues to z = 0.94H which is the deepest valid ADCP data point above the side-lobe contamination. In the lower water column, there is a consistent 0.1 m s-1 difference between the two transects, with the steeper transect E having faster flows. Downstream of the lee wave, both transects develop strong vertical oscillations.
Density overturns form downstream, signaling turbulence production. Beneath the lee wave, the rate of energy converted to turbulence reaches a maximum dissipation rate of 10-5 W kg-1, four orders of magnitude higher than the ambient 10-9 W kg-1. As flow slackens (B14 in figure 6), the lee wave shifts upstream. Ultimately, the lee wave radiates out of the study area; its eventual fate is unknown. 27
Figure 9: Histograms of north velocity at a percent depth for tracks B13 and E06. Water depth is H, the top panel z=0.5H, second 0.8H, third 0.85H, fourth 0.9H, and the bottom panel 0.94H. The histograms become bi-modal below 0.8H because these depths cut through the lee wave.
4.1.2.4 Weak Ebb Tide A weak ebb follows the strong flood (tracks B16-B18, figure 6). This weak ebb never reaches a barotropic southward flow state like the strong ebb. Instead, lingering flood structure remains. Flow is multi-layer, multi-directional and very weak. Well before the end of the weak ebb predicted by modeled tides, northward flow has returned. By slack tide (track B19, figure 6), northward flow is already increasing.
4.1.3 Along-Ridge Evolution of the Flow A unique feature of the sampling was a repeat track along the apex of the ridge perpendicular to the tidal flow (track H, figure 3). Few attempts have been made to 28 measure along-ridge flow structure (e.g., Knight Inlet sill, Klymak and Gregg, 2001).
This along-ridge transect may be the first for a sub-surface bump and it demonstrates that the two-dimensional approximation applied over the ridge is generally valid. A strong flood is well-sampled with seven transects. The evolution of the weak flood and weak ebb are not well-captured and no transects captured a strong ebb.
On strong flood, an accelerated jet forms below 100-m depth along the whole ridge
(figure 10). This jet is ~50-m thick at the southeast end of the ridge and ~25-m thick at the northwest. As tidal flow increases, this jet thins and accelerates to 0.6 m s-1 northward. This layer has a strong downward flow component, corresponding to the ridge-crest portion of the bottom jet previously described in the cross-ridge transects
(figures 7 and 8). Thus, the jet is like a sheet flowing over the ridge, forming a lee wave along the whole ridge length.
Figure 10: Along-ridge track H (figure 3) during peak flood looking due south. In the top panel, red is north out of the page and blue south into the page. In the middle panel, red is east to the right and blue west to the left. In the bottom panel, vertical velocities are multiplied by five, red is up and blue down. Red vertical lines indicate where cross-ridge tracks (left to right) B and E (figure 3) intersect. Interference from a towed instrument has been blanked out at 70-m depth. The bottom 6% of the data has been removed due to sidelobe contamination. In the top panel, the accelerated jet has formed directly above the ridge crest and at a depth of ~100 m extending up ~50 m is a stagnant patch. 29 Where track B intersects track H, a 50-m thick layer of nearly stagnant water forms above the bottom jet that extends past the point where track E intersects (figure 10). At the southeast end, the stagnant layer is 100-mab. It drops to 50-mab towards the northwest end. This layer only exists where lee waves are known to form and may be an extension of the forward-face stagnation point (Baines and Hoinka, 1985). Although the stagnant layer persists through all tidal phases, it is most dramatic during strong flood.
Just before peak flood, there is weak southward flow in the center of the layer. Both the stagnant layer and accelerated jet remain thin as the flow weakens towards slack. On the weak flood, the near-bottom accelerated jet and lee wave are less strong.
On flood tides, off the northwest end of the ridge, is a region of still water that extends from the ridge slope upwards where it merges with the stagnant layer. This region may be the result of a bifurcation of flow on the upstream slope, where a portion of the flow passes over the ridge and the remainder flows around. Since, a lee-wave is known to form at track E ~ 500 m from the end of the ridge, there may be an area between track E and the ridge end where the flow become more three-dimensional. A similar region is not seen on the southeast end, possibly because the slope in this area is very gentle.
On the weak ebb, most of the water column below the river layer flows weakly (~
0.1 m s-1) southward. Near the bottom, a thin northward-flowing jet remains along the entire ridge. This jet is ~25-m thick at the southeast end and ~5-m thick just before the northwest end. By slack tide, the water column below the river water layer is all moving north. 30 4.2 Flow Directly Above Sponge Reef The above spatial description is complemented by additional temporal data from the
60-day summer 2010 mooring deployment that captured three spring-neap cycles (figure
3). This time-series permits a shift from examining the larger ridge-scale flows to smaller-scale flows and how they may directly impact the sponge reef. In general, the same characteristics are observed in this time-series as are in the ship-based data. On each flood tide, a bottom accelerated jet forms that lasts for several hours before dissipating. The bottom jet is strongest on the strong floods and has a hysteresis cycle
(figure 11).
Typically, the accelerated jet forms on the strong flood tides with some spring-neap variability. During spring tides, a bottom jet may also form on the weaker flood tide.
Bottom jets may not form at all during neaps.
4.2.1 Accelerated Jet The accelerated jet is related to the barotropic tides over the 2010 mooring time- series through a two-dimensional histogram (top panel, figure 11). Here, the accelerated jet is defined as the average of the bottom three bins of the RDI data which centers around 15 mab (meters above bottom). On flood, the accelerated jet speeds up much faster than the predicted surface tides, in fact, the jet's acceleration begins while the tide is still ebbing. After peak flood tide, the jet rapidly reverses while the predicted tide is still strongly flowing north. Towards slack tide, the bottom jet hold at ~0.1 m s-1. On the following ebb, bottom velocities do not reach the same magnitude in the reversed direction (southward) as the barotropic tides instead, they continue to hover around ~0.1 m s-1. After peak ebb, the bottom jet returns to northward flow almost immediately. This hysteresis is most pronounced on the strong flood where jet velocities reach 0.7 m s-1. Jet 31 velocities exceed the barotropic tides 12% of the time and exceed 0.43 m s-1, the velocity
required to re-suspend sediments, 3% of the time. On the weak flood, the jet velocities
follow the barotopic tides and do not display hysteresis.
Figure 11: Top left panel is a two-dimensional histogram of the north component of the accelerated jet and predicted barotropic tides with colour indicating the number of data points. The yellow line is at 0.43 m s-1. The black line is a single strong flood to strong ebb cycle while the gray line is a weak flood to weak ebb cycle. Top right panel shows the percent of the data that is at the different accelerated jet velocities. Bottom left panel is a two-dimensional histogram of the energy dissipation rate and predicted barotropic tide. Bottom left panel show the percent of the data that is at the different dissipation rates with colour indicating the number of data points. 32
Figure 12: Left panels depict two days of data centered around 12 August 2010; (a), the north flow from the bottom up 100 m; (b), the vertical flow multiplied by two; (c), energy dissipation rate ε on a logarithmic scale 1.2 m above the bottom; (d), modeled tides in red, principle flow axis at 1.2 m off the bottom in black, flow 10 m above the bottom in blue and flow 50 m off the bottom in green. (e) shows an example of an accelerated bottom jet. This panel contains the velocity profiles at the instant indicated by the thick blue line on the left panels. Red is east, blue north and green vertical. The dashed black line is water speed.
The strong flood that peaked at 1800 h PDT, 12 August 2010 (figure 12) is examined
in more detail as it is representative of all strong floods. Starting on a slack tide before the
strong flood, there is already a slight northward flow of ~ 0.05 m s-1 in the bottom 100 m.
Two hours before peak flood, flows of 0.2 m s-1 develop within the bottom 40 m. This jet
increases in magnitude while narrowing and deepening. An hour before the peak flood,
when surface tidal flow is 0.2 m s-1, the 20-m thick accelerated jet reaches a maximum of 33 0.4 m s-1 at 27 mab. A flow minimum occurs 70 mab. As tidal flow continues to increase,
the jet accelerates and compresses against the bottom even more.
At peak flood, modeled surface tides reach 0.23 m s-1 (1800 h, figure 12). The 10-m
thick jet's 0.6 m s-1 maximum is at 17 mab. A flow minimum occurs 50 mab with no flow
reversal. An hour later, the jet is weaker but remains clearly distinguishable from the
background flow. The jet's maximum is now in the lowest bin of the RDI data and could
extend deeper. The flow minimum drops to 43 mab and does not reverse. Two hours past
peak flood, the jet weakens to 0.5 m s-1 and the flow minimum drops to 33 mab, above
which weak flow reversal occurs. After this time, the jet becomes indistinguishable from
the background flow.
Figure 13: A zoomed in view of the peak flood shown in figure 12. Top panel is the north component, middle panel the east component and the bottom panel the vertical component. 34 At the peak flood, complex structure forms above the jet. Figure 13 shows a blow up of the jet at peak flood tide for 12 August 2010, covering 60 mab. Temporal oscillations with time scales (Δt) on the order of 10 minutes occur along the jet top which is roughly the same scale as the buoyancy period. Vertical structure often extends 40 m above the jet. Given flow speed, using Taylor's hypothesis, a possible horizontal length scale (L) can be inferred by L = uΔt, where u is the velocity. This length scale is roughly 360 m.
This structure forms on all the strong flood tides and could be the focus of a future study.
Over the mooring time-series, on peak flood with an accelerated deep jet, a stagnant point or flow minimum occurs 40-60 mab where the zonal velocity switches directions.
On a flood tide, there is eastward flow below this point and westward above it.
4.2.2 Bottom Turbulence and Mixing The energy dissipation rate, ε, ranges from 10-9 - 10-4 W kg-1 over each tidal cycle. If the barotropic tides were directly correlated to the energy dissipation rate, we would expect peak dissipations to occur at both the peak flood and peak ebb. However, peak dissipations only occur on flood tides. Corresponding to the accelerated jet, the highest energy dissipation rates, ε, occur on the flood tides (bottom panel, figure 11), exceeding
10-5 W kg-1 about 5% of the time. For the majority of the time, ε hovers around 10-7 W kg-1, dropping below 10-9 W kg-1 on ebb.
For the strong flood on 12 August 2010 (figure 12), dissipation rates increase sharply to 10-6 W kg-1 almost immediately after slack. Just after the peak of a strong flood, corresponding with accelerated jet formation, dissipation rates reach a peak of 10-4 W kg-1. Dissipation rates hover around this value for several hours, then drop sharply when the jet disappears. On the weaker floods without an accelerated jet, maximum dissipation 35 rates typically reach 10-6 W kg-1, two orders of magnitude lower. On a spring tide, ~6:00 h, 13 Aug 10 (figure 12), dissipation rates on the weak flood tide can approach those of the strong flood tide if a weak accelerated jet forms.
On both strong and weak ebbs, tidal flow is weaker and laminar. During ebbs, dissipation rates remain extremely low ( 10-9 – 10-7 W kg-1), indicating there is little turbulence and mixing during ebbs.
4.3 Energy Budget Considering the flow at Fraser Ridge (B13, figure 3) as three layers with interfaces at the 1022.5 and 1024.06 kg m-3 isopycnals allows for a rough calculation of the power lost. This method was used for two layers at Stonewall Bank (Nash and Moum, 2001) and five layers over the Knight Inlet sill (Klymak and Gregg, 2004). At Fraser Ridge, the top layer contains river water flowing south, opposite to the flood tide. The lower interface, which contains an isopycnal displacement of ~10 m, is interpreted here as a hydraulic jump.
The power lost can be roughly estimated from energy conservation with the divergence of the flux of the Bernoulli function on the right hand side (Baines, 1995)
dE dV dV = B u⋅d A , (1) V∭ V∭ dt A∮
2 where B = ½u + P/ρ + gz, u is velocity, P pressure, ρ density, g gravitational acceleration and z depth. To use the Bernoulli drop over Fraser Ridge, track B13 was assumed to occur instantaneously when in fact it took ~45 minutes to complete. 36 4.3.1 Local Energy Dissipation Energy is turbulently dissipated locally on the left-hand side of (1) from contributions (i) beneath the lee wave and (ii) in the bottom boundary layer. A rough calculation of the power lost under the lee-wave is made from the VMP measurements
P = dV dA using: wave V∭ which, for a transect, becomes A∬ where ρ =
1024.4 kg m-3 and the integration is over the area under the jump along transect B13 of
96,398 m2 but, not extrapolated along the ridge. Energy dissipations rates, ε, reach 10-5 W kg-1 at peak flood tide resulting in ~611 ± 300 W m-1 lost.
The other primary site of energy dissipation is the bottom boundary layer. No bottom measurements were available on track B13, so the bottom mooring data from track E will be used here. On strong floods, bottom-boundary-layer energy dissipation rate peaks of
10-4 W kg-1 can be translated into an approximate power loss by considering the frictional velocity.
Frictional velocity u* provides a characteristic velocity scale within the bottom boundary layer that can be interpreted as the magnitude for turbulent velocity fluctuations. Frictional velocities were calculated using u*3 = εκz (Dewey and Crawford,
1988), which assumes a local production-dissipation balance and independence of depth in the bottom stress layer, where ε is the calculated energy dissipation rate, κ ~ 0.41 von
Kármán's constant and z = 1.2 m the instrument height off the seafloor. At Fraser Ridge, frictional velocities range from 4.6 x 10-4 to 2.7 x 10-2 m s-1 depending on the bottom flow
(figure 14).
The bottom stress, τb, relates to the frictional velocity in the constant-stress layer by
*2 τb = ρu . Power loss in the bottom boundary layer can be computed using 37
-1 PBBL=∫ ub dx , where u = 0.7 m s is the accelerated jet speed, over a across-ridge
distance of 1000 m, corresponding to the length of the region of accelerated flow and
jump. This method results in a very rough estimate of the power lost in the bottom
boundary layer of ~525 ± 250 W m-1..
Figure 14: The left panel is a two-dimensional histogram of the frictional velocity vs bottom velocity at 1.2 mab where the color bar indicates the number of data points. The right panel shows the what percent of the data is at each value of the frictional velocity.
From the above calculations, roughly the same amount of power is dissipatively lost
from the bottom boundary layer as under the jump. This differs from other sites where
power loss in the bottom boundary layer is often significantly greater than the power loss
in the jump (e.g., Nash and Moum, 2001). In total, ~1.2 ± 0.6 kW m-1 of power is lost to
turbulence and bottom friction.
4.3.2 Time-Varying Term dE To determine the time-varying component, ∭ dV , total energy, E, will be V dt
broken into available potential energy (APE) and horizontal kinetic energy (HKE); 38 vertical kinetic energy is negligible. This calculation is confined to in the bottom layer containing the hydraulic jump, defined as the region below 1024.06 kg m-3
dE dAPE dHKE = dV dV . (2) V∭ dt V∭ dt V∭ dt
dAPE APE We will start by calculating ∭ dV = ∭ dV where APE is the V dt V t available potential energy in density perturbations from the background density field.
To calculate ΔAPE, VMP casts on transects B13 and B14 were used. B13 casts were linearly extrapolated to the same location as B14 casts and the change in APE,
APE= z− z z gdA A∬ B13 B14 , where ρ(z) is the density at depth z, g the acceleration due to gravity and the integration is over the transect area but not along the ridge. The resulting ΔAPE = (1.7 ± 0.6) x 106 J m-1. The error was determined by linearly extrapolating the B14 casts to the same location as the B13 casts and comparing the difference between the results. To evaluate ΔAPE/Δt, the time between mid-point of transect B13 and the mid-point of transect B14 was used, Δt = 2700 s. The resulting bottom layer ΔAPE/Δt = 630 ± 300 W m-1.
dHKE Next, dV will be simplified to the area along transect B excluding V∭ dt
HKE the along-ridge component becoming dA where ∆HKE = HKE - A∬ t B13
2 HKEB14 and HKE = ½ρu . The velocities, u, were taken from the north component of
ADCP bins corresponding to VMP density values. The same method of linear extrapolation as in the APE calculations was applied. As a result, ΔHKE = (1.6 ± 1.4) x 39 106 J m-1. The error of almost 90% comes from the changing velocities between the two transects. In the bottom layer, ΔHKE/Δt = 593 ± 250 W m-1.
Since the time-varying component and local energy dissipation rates both represent losses, they can be added together, resulting in a time-varying component of
dE dA = 1223 ± 550 W m-1. A∬ dt
4.3.3 Bernoulli Drop B u⋅d A The right-hand side of (1), A∮ , represents the Bernoulli drop. Steady- state assumptions have been applied successfully to Knight Inlet (Klymak and Gregg,
2004) and Stonewall Bank (Nash and Moum, 2001). However, at Fraser Ridge the time- varying component to the flow is important. To use the Bernoulli drop over Fraser Ridge, track B13 is assumed to occur instantaneously with a steady flow structure. Negligible mixing between layers is assumed by conserving volume-flux, unhn, within each layer.
Here, n is the layer, un average ADCP velocity in that layer and hn the layer thickness taken from VMP measurement.
Power lost between the two ends of transect B13 in layer 3, ΔPB, is the sum of the differences between the right-hand side of (1)
upstream downstream PB =u3 h3 B3 −B 3 (3) with an integration at each end of the transect of the form
−h3−h2−h1
PB= ∫ B 3u3 dz (4)
−h2−h1 where η is the surface displacement. 40 The hydrostatic approximation was used for the pressure calculations. Surface displacement and pressure differences between the two ends of the transect were estimated by assuming no energy was lost within the top layer and that the volume-flux u1h1 remains constant between the ends of B13. These assumptions result in a calculated
0.06-m surface drop between the two ends of B13. 0.06 m was added to the downstream surface end.
Results in the bottom layer are considered here. The Bernoulli function, B = ½u2 +
P/ρ + gz, where u is velocity, P pressure, ρ density, g gravitational acceleration and z depth, has three components. The kinetic energy component, ½u2, the pressure component, P/ρ , and the potential energy component, gz. The kinetic energy term is small compared (order 103) to the other two terms (both of order 107). However, the pressure and potential energy terms almost cancel each other out, allowing the kinetic energy term to impact the result. As a check on the accuracy of the results, density was broken into two components, a background density field, Δρ, and perturbations from the background, ρ'. Density becomes: ρ = Δρ + ρ'. When this decomposed density is substituted into the Bernoulli function, results remained the same.
Power loss between the top of the ridge and downstream of the lee-wave calculated from (3) at peak flood is 7 kW m-1 where shifting the interface by ±10 m results in an error of ± 5 kW m-1. Over the entire water column the power loss over transect B13 is 9 ±
5 kW m-1, confirming that most of the power is lost in the bottom layer. When (3) is executed over track B14, the power loss in the bottom layer is 6 ± 4 kW m-1. 41 4.3.4 Energy Budget Summary In summary, ~611 ± 300 W m-1 of power is lost in the area under lee wave and ~525
± 250 W m-1 in the bottom boundary layer. So, the energy lost to turbulence in these two regions are very similar in magnitude. In total ~1.2 ± 0.6 kW m-1 of power is lost to turbulence and bottom friction. This value may be low under the jump as the VMP profiler may not have passed through the highest regions of dissipation.
The time-varying component of the power loss is also ~1.2 ± 0.6 kW m-1, resulting in combined power losses on the left-hand side of equation (1) of ~2.4 ± 1.2 kW m-1. The right-hand side of (1) Bernoulli drop is 7 ± 5 kW m-1. Within the errors, the two sides of
(1) balance. Thus, to balance power losses at Fraser Ridge, a time-varying component to the flow is required which raises doubts about the assumptions used to estimate the
Bernoulli power drop. Other studies using this method, such as Knight Inlet (Klymak and
Gregg, 2004) and Stonewall Bank (Nash and Moum, 2001), did not require a time- varying component. 42
5. Discussion As with the observations, discussion of the flow is broken into two scales. First, overall ridge-scale flows are compared to similar sites both in non-dimensional parameter space and in absolute values. Next, a smaller-scale view of flow at the scale of the sponge reef will be considered, including, potential positive and negative impacts on the sponges themselves.
5.1 Ridge-Scale Flow Fraser Ridge shows features that place it between the long, gently sloping Stonewall
Bank (Nash and Moum, 2001) and shorter, abrupt sill at Knight Inlet (Klymak and
Gregg, 2001). Fraser Ridge slopes ~0.09-0.05 are steeper than Stonewall Bank slopes of
0.01, and gentler than Knight Inlet slopes ~0.1-0.2. As the stratification and tidal flows vary, Nh/U over Stonewall Bank ranges between 0.4 – 1.2 at maximum flow, while, over
Knight Inlet sill, maximum flows correspond to Nh/U between 10 - 20. At peak flood,
Fraser Ridge Nh/U is intermediate at 3. All three sites fit into the post-wave separation regime, and show characteristics of hydraulic control including accelerated jets and hydraulic jumps. Lee flow structures are similar with the only major differences occurring in their magnitudes. Knight Inlet has the fastest accelerated bottom jet because of the steeper lee slope, in excess of 1.2 m s-1, followed by Fraser Ridge with a jet reaching 0.7 m s-1, while the jet at Stonewall Bank only reaches 0.5 m s-1. The resulting
~100 m jump is most dramatic at Knight Inlet. Both Stonewall Bank and Fraser Ridge have less dramatic jumps of 30 and 10 m, respectively.
The resulting power loss at Fraser Ridge in within the lee wave and in the bottom boundary layer is ~1.2 kW m-1. Stonewall Bank dissipates ~ 0.2 - 1.8 kW m-1 of energy 43 within the same areas depending on the occurrence of hydraulic control (Nash and
Moum, 2001). In both sites, the amount of energy lost was roughly split equally between the loss under the lee wave and in the bottom boundary layer. Even though the geometry differs between Stonewall Bank and Fraser Ridge, the power lost over a cross-ridge transect is similar.
5.2 Flow at the Sponge-Reef Scale At the sponge-reef scale, 10's of metres and smaller, the near-bottom accelerated jet becomes the important part of the lee wave. The jet sets the stage for smaller-scale turbulent flows in the bottom boundary layer just as the geometry of the ridge creates the jet that is strongest and hugs to bottom most closely directly above the sponge reef.
Enhanced turbulence in a bottom layer associated with flow over sub-surface obstacles is common (e.g., Nash and Moum, 2001; Klymak and Gregg, 2003).
During ebb and weak flood tides, overall flow at Fraser Ridge is weak, providing a good environment for sponges to feed. However, this region is in the wake of the Fraser
River with high sedimentation rates threatening to bury the sponges. Since the sponge reef formed on the steepest slope exposed to the accelerated flood tide flow, on a strong flood, the accelerated bottom-hugging jet is directly above the sponges. The jet corresponds to a few hours of high energy dissipation and turbulence atop the sponge reef. As a result, the sponges experience both positive and negative impacts. The jet keeps the sponges clear of sediment, stirs up nutrients and removes waste. The roughness of the sponge reef itself potentially can impact bottom flows by increasing turbulence within the bottom boundary layer. At the smallest scales within the sponges themselves, internal flows may shut down during the accelerated jet (Leys et al, 2007). 44 The accelerated jet helps keeps the ridge and sponge reef clear of sediment. Fraser
Ridge sits in a region of excess sedimentation off the Fraser River delta. However, its north slope is fairly silt free because ambient currents accelerate across and around the ridge (Hill et al., 2008). Fraser River sediment is 35% sand (Thomas and Bendell-Young,
1999), where sand is defined on the Wentworth grain-size scale (Wentmorth, 1922) as having a diameter between 0.0625 - 2 mm, falling between gravel (>2 mm diameter) and mud (< 0.0625 mm diameter). Because of its size, gravel is deposited near the mouth of the river, while the smaller sediments (mud containing clay and silt) remain suspended throughout Georgia Strait. At Fraser Ridge, the majority of sediment is in the sand size range.
Lab experiments have determined whether a particle is transported, deposited or resuspended as a function of grain size and current velocity (Hjulström, 1935) (figure
15). When the flow is strong, larger sediments can remain suspended or be re-suspended into the water column. When the flow is weak, larger sediments settle out and only fine sediments remain suspended. In energetic conditions with periodically strong flows and turbulence, some settled sediments are resuspended and carried away. 45
Figure 15: A Hjulström (1935) diagram relating sediment grain size to flow speed. The red curves depict boundaries between regimes of erosion, transport and deposition of sediment. Yellow band depicts sediments classified as sand. The blue line shows the maximum size of sediment the barotropic tides can re-suspend (~0.4 mm). The red line shows the maximum size of sediment the accelerated jet can re-suspend (~3 mm).
Barotropic tides at Fraser Ridge (assuming average maximum of 0.15 m s-1) can
resuspend maximum particle size ~0.4 mm, while the accelerated jet (assuming average
maximum of 0.6 m s-1) can resuspend particles up to 3 mm. This size difference
demonstrates why the sponges remain clear of sediment. Smaller size-particles are
resuspended and swept away while larger size classes never reach Fraser Ridge. If we
consider the velocity required to resuspend all sizes of sand, it would be 0.43 m s-1. The
accelerated jet at Fraser Ridge is in excess of this critical velocity 3% of the time. 46 Another potential positive impact of the accelerated jet may be that it advects food onto the site. This process is augmented by turbulent mixing of bottom waters. The metabolism of coral reefs, and other filter-feeding benthic communities, are a function of the interplay between water motion and biological form (Baird and Atkinson, 1997).
Stationary filter feeders that live in large groups like coral reefs and mussel beds have been shown to influence the flow around them by increasing drag on the flow
(Monismith, 2007). The high topographic roughness of a coral reef enhances the local turbulence (Genin et al., 2002). A study of mussel beds in the St. Lawrence River
(Frechette et al., 1989) showed that roughness due to mussels enhanced the turbulent transport which increased the food supply at the bed. As sponges develop and grow, the roughness of sponge reefs could augment the periodic turbulence, allowing the sponge reef to thrive.
Roughness over coral reefs reaches 0.27 m, where this value was obtained from the
* law-of-the-wall (Schlichting and Gersten, 2000) U = u /κ ln(z/zo) using a bottom velocity profile (Baird and Atkinson, 1997), with U the water velocity, u* frictional velocity, z instrument height off the seafloor and zo roughness scale. Fraser Ridge roughness zo is comparable to the roughness of a coral reef (Baird and Atkinson, 1997) and significantly greater than the maximum roughness of 0.01 m inferred at Stonewall Bank (Nash and
Moum, 2001).
A potentially negative consequence of the periodic strong flows and resuspended sediments to the sponges is the impact on their internal flow. Sponges turn their internal flow off to prevent excessive sediment ingress at times when there are high suspended sediments (Tompkins-MacDonald and Leys, 2008). A recent study at Fraser Ridge found 47 no clear correspondence between sponges shutting down their internal pumping with either ambient flow or suspended sediment concentration (Leys et al., in press). Flows through the sponge osculum were 0.007 to 0.087 m s-1 which correlated to the external flow. An increase in the pumping rate during accelerated flood flows corresponds to increased feeding.
Other sponge reefs in the Strait of Georgia live in different flow regimes where flows interact with different-shaped obstacles, including multiple obstacles. All other sponge reefs sites are further from the mouth of the Fraser River and thus not subject to the same levels of sedimentation. A question for future research is whether a common factor in flow dynamics influences where sponge reefs form. 48
6. Conclusions This study was designed to examine three-dimensional flow patterns around Fraser
Ridge and to quantify bottom flow conditions above the co-located sponge reef. It was discovered that the dominant flow feature impacting the sponges was accelerated bottom- jet that formed upstream of the lee-wave on the strong flood tides. The resulting periodic accelerated flows in this region enhance bottom mixing and appear to create an environment for the sponge reef to thrive.
Many oceanographic studies have captured lee-wave formation (Farmer and Denton,
1985; Loder et al., 1992; Nash and Moum, 2001; Klymak and Gregg, 2001; Armi and
Farmer, 2002; Inall et al., 2005; Dewey et al., 2005). However, the dataset at Fraser
Ridge provides unique three-dimensional sampling by including along-ridge sections. A two-dimensional description of the flow, as is often assumed, proves to be reasonably accurate. On most strong flood tides, the parameter space over Fraser Ridge fits into the post-wave separation regime (Baines, 1995) and a ridge-length lee wave develops.
Lee-wave development follows the same path each time it forms. As flood tidal flow encounters the ridge, an accelerated jet forms above the bottom in the region directly above the sponge reef. This jet moves over the ridge like a sheet overlain by a stagnant layer. On the lee slope, the jet accelerates to a maximum of 0.7 m s-1, significantly higher than the barotropic tide maximum of 0.23 m s-1. Beneath this jet, elevated turbulence occurs. Further down the lee-slope, the jet separates from the bottom, forming a lee wave.
Since the northeast slope is steeper towards the northwest end, the lee wave is correspondingly steeper there. Even though Fraser Ridge is three-dimensional, the resulting lee wave is two-dimensional on tidal timescales, the lee wave forming along the 49 entire steep northeast slope. The ultimate fate of lee waves produced at Fraser Ridge remains unknown and could be the basis for a future study. The gentle slope on the southwest side of the ridge does not allow lee-wave formation on ebbs.
On the strongest flows at peak flood tide, Fraser Ridge removes ~1.2 kW m-1 of power. Simultaneously, there is a time-varying component to the power loss of ~ 1.2 kW m-1 which implies that a steady-state is never achieved. Other studies (Nash and Moum,
2001; Klymak and Gregg, 2004) have successfully assumed a steady-state to calculate the
Bernoulli drop, which is an assumption that does not apply at Fraser Ridge.
The local energy loss on the peak flood tide has a direct impact on the sponge reef. The sponge reef has formed beneath the strongest bottom-accelerated jet flows and strongest turbulence. This location may be ideal, allowing the sponges to take advantage of regular advection of nutrients and periodic re-suspension of deposited sediments. 50
7. Bibliography
[1] Ambaum, M.H.P., and D.P. Marshall, 2005: The effects of stratification on flow separation. Journal of the Atmospheric Sciences, 62, 2618-2625.
[2] Armi, L., and D. Farmer, 2002: Stratified flow over topography: bifurcation fronts and transition to the uncontrolled state. Proceedings of the Royal Society, A, 458, 513-538.
[3] Baines, P.G., 1995. Topographic Effects in Stratified Flows, 482 pp., Cambridge University Press, New York.
[4] Baines, P.G., and K.P. Hoinka, 1985: Stratified flow over two-dimensional topography in fluid of infinite depth: a laboratory simulation. Journal of the Atmospheric Sciences, 42, 1614-1630.
[5] Baird, M.E. and M.J. Atkinson, 1997: Measurement and prediction of mass transfer to experimental coral reef communities. Limnography and Oceanography, 42, 1685- 1693.
[6] Barnes, R.D., 1987: Invertebrate Zoology Fifth Edition, 893 pp., Saunders College Publishing, Philadelphia.
[7] Castro, I.P., and W.H. Snyder, 1993: Experiments on wave breaking in stratified flow over obstacles. Journal of Fluid Mechanics, 255, 195-211.
[8] Castro, I.P., W.H. Snyder and P.G. Baines, 1990: Obstacle drag in stratified flow. Proceedings of the Royal Society, A, 429, 119-140.
[9] Castro, I.P., W.H. Snyder and G.L. Marsh, 1983: Stratified flow over three- dimensional ridges. Journal of Fluid Mechanics, 135, 261-282.
[10] Conway, K.W., J.V. Barrie and M. Krautter, 2004: Modern siliceous sponge reefs in a turbid, siliciclastic setting: Fraser River Delta, British Columbia, Canada. Neues Jahrbuch fur Geologie und Palaontologie, 6, 335-350.
[11] Conway, K.W., J.V. Barrie, W.C. Austin and J.L. Luternauer, 1991: Holocene sponge bioherms on the western Canadian continental shelf. Continental Shelf Research, 11, 771-790.
[12] Cummins, P.F., S. Vagle, L. Armi and D.M. Farmer, 2003: Stratified flow over topography: upstream influence and generation of nonlinear waves. Proceedings of the Royal Society, A. 459, 2034, 1467-1487. 51 [13] Dewey, R.K., and W.R. Crawford, 1988: Bottom stress estimates from vertical dissipation rate profiles on the continental shelf. Journal of Physical Oceanography, 18, 1167-1177.
[14] Dewey, R.K., and C. Garrett, 2005: Stratified flow over a bump. Journal of Physical Oceanography, 35, 1911-1927.
[15] Dillon, T.M., 1982: Vertical overturns: a comparison of Thorpe and Ozmidov length scales. Journal of Geophysical Research, 87(C12), 9601-9613.
[16] Edwards, K.A., P. MacCready, J.N. Moum, G. Pawlak, J.M. Klymak and A. Perlin, 2004: Form drag and mixing due to tidal flow past a sharp point. Journal of Physical Oceanography, 34, 1297-1312.
[17] Farmer, D.M. and R.A. Denton, 1985: Hydraulic control of flow over the sill in Observatory Inlet. Journal of Geophysical Research, 90, 9051-9068.
[18] Frechette, M., C.A. Butman and W.R. Geyer, 1989: The importance of boundary- layer flows in supplying phytoplankton to the benthic suspension feeder, Mytilus edulis L. Limnography and Oceanography, 34, 19-36.
[19] Foreman, M. G. G., R. F. Henry, R. A. Walters, and V. A. Ballantyne, 1993: A finite element model for tides and resonance along the North Coast of British Columbia, Journal of Geophysical Research, 98(C2), 2509–2531, doi:10.1029/92JC02470.
[20] Genin, A., G. Yahel, M.A. Reidenback, S.G. Monismith, and J.R. Koseff, 2002: Intense benthic grazing on phytoplankton in coral reefs revealed using the control volume approach. Oceanography, 15, 90-96.
[21] Hill, P.R., K. Conway, D.G. Lintern, S. Meulé, K. Picard and J.V. Barrie, 2008: Sedimentary processes and sediment dispersal in the southern Strait of Georgia, BC, Canada. Marine Environmental Research, 66, S39-S48.
[22] Hjulström, F., 1935: Studies of the morphological activity of rivers as illustrated by the River Fyris. Bulletin of the Geological Institute, University of Uppsala.
[23] Inall, M., T. Rippeth, C. Griffiths and P. Wiles, 2005: Evolution and distribution of TKE production and dissipation within stratified flow over topography. Geophysical Research Letters, 32, 4pp, doi:10.1029/2004GL022289
[24] Inall, M., F. Cottier, C. Griffiths and T. Rippeth, 2004: Sill dynamics and energy transformation in a jet fjord. Ocean Dynamics, 54, 307-314.
[25] Johannessen, S.C., R.W. MacDonald, and D.W. Paton, 2003: A sediment and organic carbon budget for the greater Strait of Georgia. Estuarine, Coastal and Shelf Science, 56, 845-860. 52
[26] Killworth, P.D., 1992: On hydraulic control in a stratified fluid. Journal of Fluid Mechanics, 237, 605-626.
[27] Klymak, J.M. and M.C. Gregg, 2004: Tidally generated turbulence over the Knight Inlet Sill. Journal of Physical Oceanography, 34, 1135-1151.
[28] Klymak, J.M. and M.C. Gregg, 2003: The role of upstream waves and a downstream density pool in the growth of lee waves: glow over Knight Inlet Sill. Journal of Physical Oceanography, 33, 1446-1461.
[29] Klymak, J.M. and M.C. Gregg, 2001: Three-dimensional nature of flow near a sill. Journal of Geophysical Research, 106, 22,295-22,311.
[30] Kuettner, J., 1939a: Moazagotl and Föhnwelle. Beitraege zur Physik der Atmosphaere, 25, 79-114.
[31] Kuettner, J., 1939b: Zur Entstehung der Föhnwelle. Beitraege zur Physik der Atmosphaere, 25, 251-299.
[32] Leys, S.P. G.O. Mackie and H.M. Reiswig, 2007: The Biology of Glass Sponges. Advances in Marine Biology, 52, 1-145.
[33] Lilly, D.K., and J.B. Klemp, 1979: The effects of terrain shape on nonlinear hydrostatic mountain waves. Journal of Fluid Mechanics, 95, 241-261.
[34] Loder, J.W., D. Brickman and E.P.W. Horne, 1992: Detailed structure of currents and hydrography on the northern side of Georges Bank. Journal of Geophysical Research, 97, 14,331-14,351.
[35] Love, G.D., E. Grosjean, C. Stalvies, D.A. Fike, J.P. Grotzinger, A.S. Bradley, A.E. Kelly, M. Bhatia, W. Meredith, C.E. Snape, S.A. Bowring, D.J. Condon and R.E. Summons, 2009: Fossil steroids record the appearance of Demospongiae during the Cryogenian period. Nature, 457, 718-721.
[36] Manley, G., 1945: The Helm Wind of Crossfell, 1937-1939. Quarterly Journal of the Royal Meteorological Society, 71, 197-220.
[37] Meulé, S., 2005: Processus mis en jeu dans l'evolution morphodynamique de Roberts Bank (Delta du Fraser): observation et modelisation hydrodynamiques et sedimentaires. Ph.D. Thesis, Rimouski, Quebec, Universite du Quebec a Rimouski. p. 224.
[38] Miller, P.P., and D.R. Durran, 1991: On the sensitivity of downslope windstorms to the asymmetry of the mountain profile. Journal of the Atmospheric Sciences, 48, 1457-1473. 53
[39] Monismith, S.G., 2007: Hydrodynamics of Coral Reefs. Annual Review of Fluid Mechanics, 39, 37-55.
[40] Moum, J.N., J.M. Klymak, J.D. Nash, A. Perlin and W.D. Smyth, 2007. Energy transport by nonlinear internal waves. Journal of Physical Oceanography, 37, 1968- 1988.
[41] Nash, J.D. and J.N. Moum, 2001: Internal hydraulic flows on the continental shelf: high drag states over a small bank. Journal of Geophysical Research, 106, 4593- 4611.
[42] Nasmyth, P., 1970: Oceanic Turbulence. Ph.D. Thesis, University of British Columbia, 69pp.
[43] Nikurashin, M., and R. Ferrari, 2010: Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: theory. Journal of Physical Oceanography, 40, 1055-1074.
[44] Ott, M.W., 2002: An improvement in the calculation of ADCP velocities. Journal of Atmospheric and Oceanic Technology, 19, 1738-1741.
[45] Schlichting, H., and K. Gersten, 2000; Boundary Layer Theory 8th Edition. 799 pp, Springer.
[46]Stacey, M.W., S. Pond, P.H. LeBlond, H.J. Freeland and D.M. Farmer, 1987: An analysis of the low-frequency current fluctuations in the Strait of Georgia from June 1984 until January 1985. Journal of Physical Oceanography, 17, 326-342.
[47] Sutherland, B.R., 2002: Large-amplitude internal wave generation in the lee of step- shaped topography. Geophysical Research Letters, 29, DOI 10.1029/2002GL015321
[48] Thomas, C.A. and L.I. Bendell-Young, 1999: The Significance of Diagenesis versus Riverine Input in Contributing to the Sediment Geochemical Matrix of Iron and Manganese in an Intertidal Region. Estuarine, Coastal and Shelf Science, 46, 635- 647
[49] Tompkins-MacDonald, G.J., and S.P. Leys, 2008: Glass sponges arrest pumping in response to sediment: implications for the physiology of the hexactinellid conduction system. Marine Biology, 154, 973-984.
[50] Vosper, S.B., I.P. Castro, W.H. Snyder and S.D. Mobbs, 1999: Experimental studies of strongly stratified flow past three-dimensional orography. Journal of Fluid Mechanics, 390, 223-249. 54 [51] Wentworth, C.K., 1922: A scale of grade and class terms for clastic sediments. Journal of Geology, 30, 377-392.
[52] Wesson, J.C. and M.C. Gregg, 1994: Mixing at Camarinal Sill in the Strait of Gibraltar. Journal of Geophysical Research, 99, 9847-9878.