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Upwelling flow dynamics in long canyons at low Rossby number. Waterhouse, Amy F.; Allen, Susan E.; Bowie, Alexander W. 2009-05-31

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Upwelling flow dynamics in long canyons at low Rossby numberAmy F. Waterhouse,1,2Susan E. Allen,1and Alexander W. Bowie1Received 11 June 2008; revised 17 January 2009; accepted 16 February 2009; published 6 May 2009.[1] Submarine canyons, topographic features incising the continental slope, vary in bothshape and size. The dynamics of short canyons have been observed and described in thefield, in the laboratory, and with numerical simulations. Flow within long canyons, such asJuan de Fuca canyon, located between Vancouver Island and Washington State in thePacific Northwest, is less well understood. Physical models of both long and shortcanyons have been constructed to understand the upwelling dynamics in long canyons andhow upwelling changes, as compared with the dynamics of short canyons, at low Rossbynumber. Stratification and rotation, both important parameters in determining thedynamics in canyons, can be controlled and scaled accordingly for replication of oceanicconditions. The physical model is spun up to an initial rotation rate, and the flow isforced by increasing the rotation rate over the equivalent of several days. Flowvisualization is used to determine the strength and location of upwelling, the strength andmechanisms generating vorticity, as well as the differences between the flow within thelong and short canyons. The pattern of upwelling between the two canyons is significantlydifferent in the horizontal with upwelling occurring through the canyon head in theshort canyon and upwelling occurring close to the mouth along the downstream rim in thelong canyon. At high Rossby number, upwelling is similar in both the long and shortcanyon and is driven by advection. However, as Rossby number decreases, the flow in thelong canyon is more strongly affected by the strong convergence of the isobaths near thecanyon than by advection alone.Citation: Waterhouse, A. F., S. E. Allen, and A. W. Bowie (2009), Upwelling flow dynamics in long canyons at low Rossby number,J. Geophys. Res., 114, C05004, doi:10.1029/2008JC004956.1. Introduction[2] Submarine canyons are topographic coastal featuresthat incise the continental shelf and are regions of locallyenhanced coastal upwelling (B. M. Hickey, Coastal subma-rine canyons, paper presented at Aha Huliko’a HawaiianWinter Workshop on Topographic Effects in the Ocean,University of Hawai’i at Manoa, Honolulu, Hawai’i, 1995).The unique flow dynamics and upwelling due to thesetopographic features have resulted in the observation ofhigh concentrations of zooplankton around canyon heads[Macquart-Moulin and Patriti, 1996; Allen et al., 2001]indicating that canyons are an important mechanism forcoastal upwelling. Canyons vary in both shape and size.Short canyons, such as Astoria and Barkley Canyons,feature a canyon head that reaches the depth of the conti-nental shelf well before the coast [Hickey, 1997; Allen,2000]. Long canyons, such as Juan de Fuca, Mackenzie andMonterrey Canyons, feature a canyon head that does notreach the continental shelf depth before the coastline, andextend far into the coastal region, where the head often endsin estuaries [Carmack and Kulikov,1998;Allen,2000;Kunze et al., 2002; Hickey, presented paper, 1995].[3] Flow dynamics in short canyons have been wellstudied and documented. As geostrophic currents pass overshort canyons, water is driven up the canyon because of anunbalanced pressure gradient caused by the constrictions inthe topography [Freeland and Denman, 1982]. This effectenhances upwelling and mixing (Hickey, presented paper,1995). As water columns on the shelf, originating up-stream of the canyon, flow over top of the canyon, theystretch as a result of an increase in bottom depth down-stream of the canyon rim. The water column stretching,due to conservation of potential vorticity, creates cyclonicvorticity in the flow [Hickey, 1997; Allen et al., 2003]. Thegeneration of cyclonic vorticity inside the canyon has alsobeen linked to flow separation at the canyon mouth, whichadvects into the canyon [Pe´renne et al., 2001a]. The flowthen turns toward the head of the canyon and is advectedup onto the shelf. A cyclonic eddy, formed because of thisvortex stretching, is observed in the canyon from the shelfbreak depth down to the deep layers inside the canyonmouth [She and Klinck, 2000]. The near surface flow(<100 m) is only weakly affected by the canyon [Hickey,1997; Allen et al., 2003]. Most upwelling processes inJOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, C05004, doi:10.1029/2008JC004956, 2009ClickHereforFullArticle1Department of Earth and Ocean Sciences, University of BritishColumbia, Vancouver, British Columbia, Canada.2Now at Department of Civil and Coastal Engineering, University ofFlorida, Gainesville, Florida, USA.Copyright 2009 by the American Geophysical Union.0148-0227/09/2008JC004956$09.00C05004 1of18short canyons occur during upwelling favorable windevents which generate a geostrophic incident flow [Kinsellaet al., 1987; Hickey, 1997]. Allen [2000] showed that in ashort canyon, higher-order effects generate the flow insidethe canyon and no upwelling occurs for strictly geostrophicflow.[4] The dynamics of long canyons are less well under-stood. Over long canyons it is possible for upwelling tooccur with geostrophic flow in all regions (except at specificsingular points [Allen, 2000]). Despite several field experi-ments studying both the wind-response in long canyons[Carmack and Kulikov, 1998] as well as various interactionsdriving upwelling [Freeland and Denman,1982;Vindeirinho,1998], the flow in long canyons and the difference in theflow to that of its shorter counterpart remain relativelyunknown.[5] Our study, based on a laboratory model, will focus onflow in long canyons and how it compares to its shortcanyon counterpart as well as how changes in velocity andstratification affect the flow dynamics. Thus far, severallaboratory experiments involving short canyons have beendone [Pe´renne et al., 1997, 2001a, 2001b; Allen et al., 2003;Mirshak and Allen, 2005] but no laboratory experiments oflong canyons have been performed. Understanding anddescribing the flow dynamics will not only help build onthe current understanding of the physics in long canyons butalso describe how local flow patterns and biology will beaffected by these unique topographic features, in particular,in the regions surrounding Juan de Fuca Canyon.[6] In this paper, the flow dynamics in long canyonsunder low Rossby number flow will be evaluated. Theexperimental methods, including scaling and flow visuali-zation, will be described in the next section. Following thissection, the observed flow in the long canyon will bedescribed including a discussion on vorticity generation.Next, a comparison to the observed flow in a short canyonunder similar low Rossby number conditions will be made.Last, the results obtained from both the long and shortcanyon experiments will be classified by considering threepossible upwelling mechanisms.2. Methods[7] The tank used in this experiment is a circular tankwhich has a 10-fold vertical exaggeration compared to thedepth scale of the ocean. The tank has a gently sloping shelfat 5C176 (22.5 cm horizontal length from the edge of the tank)followed by a sharply sloping continental shelf of 47C176 and a20.5 cm flat abyssal region for a total tank radius of 50 cm.The depth of the tank, when filled, is 10 cm from the surfaceto the bottom at the tank center with the shelf break depth at2.2 cm from the surface. Further details of the tanktopography can be found in papers by Allen et al. [2003]and Mirshak and Allen [2005].[8] Two canyon topographies, a long canyon and a shortcanyon, are used in this experiment and are built into a 22C176slice from the tank topography. The long canyon is ashortened, straightened version of the Juan de Fuca canyonwhich is rectangular in shape (‘‘u-shaped’’), featuring a longseparation between the slope of the canyon mouth and theslope of the canyon head. Although the model long canyondoes not completely interact with the coast (tank edge), thedepth of the continental slope beyond the canyon head isshallow. Results where the depth at the head of the canyonwas shallower than in the experiments presented here(approximately 4 mm, 40 m in the real world) werequalitatively similar [Waterhouse, 2005]. The short canyon,a smoothed version of Astoria canyon, is more triangular(‘‘v-shaped’’) with a uniformly sloping region from thecanyon mouth to the head with no separation between theslope at the mouth and head [Mirshak and Allen, 2005].The width of Juan de Fuca canyon and model canyons islarge in comparison to the radius of deformation (7.7 kmfor Juan de Fuca canyon and 3 cm for the model canyons)indicating that these canyons are wide [Klinck, 1989; Sheand Klinck, 2000]. The bathymetric contours of bothcanyons are shown in Figure 1.Figure 1. Geometry of the laboratory (a) long and (b) short canyons. Figures 1a and 1b are to thesame scale. The short canyon geometry is measured from the physical canyon; the long canyon was builtto the plans in Figure 1. Isobaths are 1 cm apart, except the shallowest on the left, which is at 0.5 cm.Lines a, b, c, d, and e denote the position of the cross-sectional light sheet used in conjunction withhorizontal layers of fluorescence dye. The distance from the edge of the tank (thick line) to the shelf breakis 22.5 cm.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS2of18C05004[9] To obtain a realistic density structure in the tank, theOster [1965] two-bucket method is used to fill the tank overa 90-min interval while the tank is rotating [Mirshak andAllen, 2005]. The density profile (Figure 2), measured usinga microconductivity probe in the nonrotating case, shows ashift of the theoretical and measured density curves. Twopossible reasons for this are diffusion, and water columnmixing due to the movement of the conductivity probe.Despite the shift of the density profiles in relation to thetheoretical curves, the dynamically important variable forappropriate tank scaling is the buoyancy frequency, N,which agrees between experimental and theoretical resultswithin measurement error.2.1. Scaling[10] To scale the laboratory model such that it is compa-rable to the ocean, the following nondimensional numbersare used: (1) the Rossby number (Ro = U/(fR)), where U isthe velocity, f is the Coriolis parameter (where f =2W,where W is the rotation rate of the tank), and R is the radiusof curvature of the isobaths upstream of the canyon [Allen etal., 2003; Mirshak and Allen, 2005]; (2) the Froude number(Fr = U/(NHs)), where N is the buoyancy frequency (N2=C0g/r Dr/Dz), where g is the gravitational constant, z is thevertical coordinate, r is the density, Hsis the depth of theshelf break; and (3) the Burger number (Bu = NHs/(fLc)),where Lcis the length of the canyon.[11] The Coriolis parameter, the buoyancy frequency, andthe incident velocity are the parameters that will be varied inthe lab experiments and therefore will be calculated suchthat the nondimensional numbers match between Juan deFuca Canyon and the long canyon–scale version. Table 1displays the values known for Juan de Fuca Canyon and thecorresponding values for the two physical models. Since itis difficult to observe quantifiable changes in the flow atlow velocities, f is chosen to be high such that the forcingvelocities are high and the Rossby number is low.2.2. Initiating the Flow[12] The experimental apparatus rotates at a fixed speedduring spin-up, which takes approximately 2 h before solidbody rotation is achieved [Mirshak and Allen, 2005]. Toobtain the required incident velocity, the tank speed ischanged from f = 1.475 sC01to f = 1.5 sC01over 27.3 s.The time period over which the change in rotation takesplace is equal to several inertial periods, which are chosen toresemble a mean, geostrophic flow in the tank slowlychanging over several days. To investigate the change inFigure 2. (a) The tank density profile showing the predicted profile as a solid line and the measuredprofile (crosses and circles). The crosses represent the average values from three separate conductivityprobes on the upward profile, while the circles are from the downward profile. (b) The buoyancyfrequency in the tank from theory (solid line) and the measured buoyancy frequency (crosses and circles).For purposes of this experiment, the buoyancy frequency at the shelf break level is used in the scalinganalysis.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS3of18C05004dynamics with velocity and stratification, several experi-ments are conducted. The corresponding nondimensionalnumbers and frequencies used are summarized in Table 2.[13] Initial investigations into the incident flow in thetank show that the flow over the shelf break, in thisparticular tank, does not follow u = DWr where r is theradius of the tank. The velocity decreases because of theincreased friction over the shelf [Pe´renne et al., 2001b;Mirshak and Allen, 2005]. Therefore, flow just offshore ofthe shelf will be stronger and faster than flow onshore(along the shelf), each following nearly separate linearrelationships (Figure 3).[14] Because of the nature of the incident flow, thevelocity offshore of the shelf break is calculated at 30 and60 s to verify how the incident offshore velocity changesover the specified time interval. The difference in velocitybetween the two time intervals (0.002 cm sC01) was wellbelow the measurement error (±0.06 cm sC01). Therefore, thevelocity off the shelf does not change significantly overtime.2.3. Flow Visualization[15] To record the changes in the flow, two basic geom-etries for the laboratory configuration of the camera andslide projector are used. The first has a video cameracentered over the canyon giving a plan view of the canyonarea [Mirshak and Allen, 2005]. A thin sheet of light isemitted from the slide projector (above the center of thetank) which projects onto a mirror placed in the center of thetank. The reflection from the mirror produces a thinly lithorizontal cross-sectional area inside the canyon betweenthe shelf break depth and less than 1 cm above the shelfbreak depth. Given that near surface flow is only weaklyaffected by the canyon [Hickey, 1997; Allen et al., 2003],the observation depth from the horizontal light sheet (1.2 to2.2 cm for the long canyon and 1.9 to 2.2 cm for the shortcanyon) is sufficient for observing upwelling from thecanyon. The second geometry requires switching the posi-tion of the video camera and projector giving a verticalcross-sectional view of the canyon from the reflectingmirror positioned in the center of the tank.[16] Three different flow visualization methods are usedin this experiment. The first uses neutrally buoyant particlesmade from wax and titanium dioxide powder illuminated byhorizontal light sheets, either white or multicolored. Theparticles are mixed with a surfactant and added to the tankapproximately 5 min before data collection begins and afterspin-up of the tank is complete.[17] The second visualization method involves the use offluorescein dye with a vertical plane of light. For theseexperiments, three common depths for the marked layers arechosen at 5 cm, 7 cm and 8.5 cm, as measured from thesurface. As the tank fills, 1 ml of dye solution is injectedinto the filling hose at the particular depths creating ahorizontal layer of dye at each of the prescribed depths.The vertical light sheet is moved farther toward the head ofthe canyon with each experimental run (lines a through e inFigure 1) to obtain a three-dimensional representation of theflow. Although diffusion occurs between the time of thedye injection and the end of spin-up (resulting in dye layers0.5 cm thick), the amount of diffusion occurring while theexperiment is being run (over 60 s) is negligible com-pared with other data acquisition and processing errors[Waterhouse, 2005].[18] The third visualization technique involves placingdye-filled syringes directly into the water (both on andbelow the shelf break) and releasing the dye a set periodof time after the initial change in rotations rate (30 s) using ahorizontal sheet of light to illuminate the area of interest.This technique is used to observe the effect of upwellingTable 1. Complete Physical Variables and Nondimensional Numbers for Juan de Fuca Canyon and the Physical Laboratory ModelPhysical Variables andNondimensional Numbers Symbol Juan de FucaModel LongCanyonModel ShortCanyonShelf break depth Hs180 m 2.2 cm 2.2 cmShelf length Ls68.6 km 22.5 cm 22.5 cmCanyon length Lc45 km 16.5 cm 8.0 cmCanyon width (average) W 12 km 5.8 cm 3.0 cmCanyon width (shelf break) Wsb23 km 6.5 cm 6.0 cmRadius of curvature of HsR 7.7 km 1.4 cm 1.4 cmCoriolis parameter f 1.08 C2 10C04sC011.5 sC011.5 sC01Buoyancy frequency at HsN 4.6 C2 10C03sC01a2.0 sC012.0 sC01Incident velocity U 10.0 cm sC01b0.3 cm sC010.3 cm sC01Rossby number Ro 0.12 0.14 0.14Froude number Fr 0.12 0.07 0.07Burger number Bu 0.17 0.18 0.37Width ratio W/Wsb0.52 0.89 0.5Width-length ratio W/Lc0.26 0.35 0.38Length-length ratio Ls/Lc1.52 1.36 2.81aConductivity-temperature-depth data available from Institute of Ocean Sciences, Station LW7, located at 48C1760.05’N, 125C17621.97’W from 7 September 2001.bData from Freeland and Denman [1982].Table 2. Nondimensional Numbers for Various Chosen VelocitiesU (cm sC01) N (sC01) DfRo0.16 2 0.0125 0.080.30 2 0.025 0.140.47 0 0.0375 0.240.47 1 0.0375 0.240.47 2 0.0375 0.240.47 3 0.0375 0.240.47 3.75 0.0375 0.240.60 2 0.048 0.291.50 2 0.12 0.71C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS4of18C05004from below the canyon rim and whether or not upwelling isoriginating from rim depth or below the rim depth.2.4. Data Acquisition and Image Analysis[19] All of the data is collected using a mounted digitalvideo camera recording images at 30 frames per second.Images captured using the multicolored light sheet areprocessed by tracking individual particles and their respec-tive changes in color 30 s after the initial change in rotationrate. Using the known depths of the colored light sheets forthe long canyon (red between 1.2 and 2.2 cm, greenbetween 2.2 and 3.2 cm, and blue between 3.2 and4.2 cm) and the short canyon (red and white between 2.8to 2.2 cm and yellow, green and blue between 2.2 to 1.3 cm),vertical as well as horizontal displacements are observed.[20] Images captured using the white horizontal lightsheet are processed by creating particle streak images overa time interval ranging between 2 to 6 s depending on theincident velocity (shorter time interval for faster flowspeed). Using these streak images (included in AppendixA) in combination with the video recordings, interpretationsof the flow from the captured data are generated (Figure 4).Regions of the topography which do not contain particlesare not interpolated and left blank.[21] For the second visualization method, the images areadjusted to a threshold which allows for the isolation andidentification of the top and bottom layer of the dye. Thethird visualization technique requires no further processing.3. Results: Long Canyon[22] The first visualization technique results in verticaland horizontal particle displacements. Upwelling is ob-served in the multicolored light sheet experiments bydisplacements of particles from the lower layers to the shelfbreak depth while the white light sheet experiments givestreak pictures of the horizontal velocity field.[23] The streak images are used for determination of thehorizontal velocity field as fewer particles are availablefrom the multicolored light sheet experiments. The draw-back in using the streak images is that we cannot directlyobserve vertical ‘‘upwelling’’ velocities from these streakimages. However, for flow near the depth of the topography,flow across the isobaths (from deep to shallow) is expectedFigure 3. Velocity on the shelf when U = 0.5 cm sC01, N =2sC01far away from the long canyon 30 safter the initial change in rotation rate (solid dots) with fits to the off-shelf flow (dashed line with U =(0.07 ± 0.02) sC01r +(C01.1 ± 0.5) cm sC01) and shelf flow (solid line with U = (0.0007 ± 0.002) sC01r +(0.32 ± 0.03) cm sC01), upstream of the long canyon 30 s after the initial change in rotation rate (crosses)and the associated fit (dotted line with U =(C00.008 ± 0.07) sC01r +(0.3 ± 0.8) cm sC01), and far away fromthe long canyon 60 s after the initial change in rotation rate (circles) and the associated fit (dotted-dashedline with U = (0.004 ± 0.006) sC01r +(0.24 ± 0.06) cm sC01). The vertical line at 22.5 cm represents thelocation of the shelf break where 0 cm is the tank edge (corresponding with the coastline). Velocitymeasurements are taken from 0.5 to 2.2 cm depth using a white light sheet.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS5of18C05004to result in vertical displacements. Our other visualizationtechniques (multicolored particle tracking after 30 s) andprevious observations [Hickey, 1997] and models [Pe´renneet al., 2001b] show upward flow resulting from such cross-isobath flow. Particles used in the experiment are subject toa small amount of settling. By comparing moving particlesupstream of the canyon in the streak images between 30 and60 s (Figure A1), moving particles observed after 60 s arefound at depths deeper than 1.7 cm even though the lightsheet is illuminating between 1.2 and 2.2 cm. Therefore,after 60 s, particles that are observed crossing isobaths fromwithin the long canyon are assumed to have verticaldisplacements associated with this flow. In the short canyon,the flow is observed in a thinner horizontal light sheet (1.9to 2.2 cm) for the entire duration of the experiments. In thefollowing discussion, we will use the term upwelling whenwe observe flow from the canyon across the canyon rim, atnear rim depths.3.1. Flow Field at Low Rossby Number[24] From observations of particle tracks, the flow dy-namics at low Rossby number (Ro = 0.14) are characterizedfor two distinct stages of the flow. The two stages arechosen on the basis of the time after the initiation of theimpulsively generated flow and the flow at these times aresimilar within several seconds.[25] The first and initial stage of the flow, occurringbetween 30 and 40 s (equivalent to 3.5 to 4.8 days in thereal world) after the initial forcing, features the incidentvelocity acting like a jet along the slope on the upstreamside of the canyon (Figure 4c). This flow, between the shelfbreak and 1 cm above in the vertical, enters the canyon atthe mouth upstream of the shelf break and turns into thecanyon. When this inflow reaches the downstream wall ofthe canyon the flow continues toward the canyon head orexits the canyon in the downstream direction. Flow insidethe canyon is very slow and begins a slow cyclonic circula-tion inside the canyon with up-canyon flow along thedownstream wall. Cross-isobath flow is observed alongthe downstream rim of the canyon close to the mouth. Onthe shelf upstream of the canyon, particles are moving at adiminished speed in the incident flow direction. On the shelfdownstream of the canyon, particles are moving downstreamand toward the shelf break.[26] In the second stage of the flow (Figure 4d) when t >60 s (equivalent to 7 days after the initial forcing), the flowinside the canyon slows. Two well developed cycloniceddies are visible inside the canyon walls. The first eddyis found just within the canyon mouth (below the rim depth)(Figure 4d). The depth of this eddy goes well below themeasurement depths (4 cm or equivalent to 400 m in theoceanic scale). The second eddy is found at the head. Flowon the shelf upstream of the canyon is diminished as wasobserved at 30 s. Flow downstream of the canyon continuesto be directed toward the shelf break. Cross-isobath flow isobserved along the downstream rim of the canyon close tothe mouth. The summary of the flow at 30 s and 60 s afterthe initial change in rotation rate are presented in Figure 5.3.2. Steady State[27] In an effort to simulate a steady state situation in thelaboratory model, the effect of friction on the incidentvelocity was balanced thus creating a steady current. Thiswas done by continually increasing the rate of rotation ofthe tank after the initial change, at a new rate of change,DW3= DW2/Dt. The rate of change required to maintain thedesired velocity is achieved by increasing the rotation of thetank from f = 1.5 sC01to f = 1.6 sC01over 1000 s (27.3 s afterthe initial change in rotation rate from f = 1.4875 sC01to f =1.5 sC01). Syringes with fluorescein dye were placedupstream of the canyon along the shelf as well as belowthe shelf break depth on the slope. The light sheet ispositioned between 0 and 2.2 cm (i.e., shallower than theshelf break) for full coverage of the shelf break region.[28] In these steady state experiments, upwelling occurscontinuously in the laboratory long canyon for the geo-strophic case with Ro = 0.14 (Figure 6). Upwelling, from0.5 cm below the canyon rim depth, occurs on the down-stream rim of the canyon close to the mouth in a 4 cmsection. A cyclonic eddy is visible trapped inside the canyonmouth and cyclonic circulation is visible in the interior ofFigure 4. (a–j) Interpretation of the flow in the longcanyon for varying Rossby numbers 30 and 60 s after thechange in rotation rate of the tank. The shelf break and tankedge are represented by solid black lines, and the flowvectors are representative of the flow between 1.2 and2.2 cm in the vertical. Arrows are not to scale, but theoriginal data is presented in Appendix A for comparison.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS6of18C05004Figure 5. (a) Initial stage of the laboratory flow in the long canyon. Flow separation occurs at thecanyon mouth between flow entering the canyon and flow returning along the downstream wall belowthe shelf break. Flow travels in the offshore direction, below the shelf break depth, and along theupstream wall of the canyon. On the shelf, flow upstream of the canyon is diminished while flowdownstream of the canyon is directed toward the shelf break. The flow in the deeper outer layer and upperlayer well above the canyon is unaffected. Upwelling occurs close to the mouth along the downstreamrim (not shown). (b) Secondary quasi-steady stage of the laboratory flow in the long canyon. Slowcyclonic circulation occurs inside the canyon away from the mouth affecting flow between 2.2 and 4 cm.A small amount of cross-isobath flow (upwelling) occurs close to the canyon mouth (not shown). Flowupstream of the canyon on the shelf is diminished, and the flow in the deeper outer layer and upper layerwell above the canyon is unaffected. The shelf break depth is 2.2 cm in Figures 1a and 1b.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS7of18C05004the canyon up to the canyon head. Flow crosses isobathsalong the downstream rim of the canyon close to the mouth.By conservation of volume, as flow crosses isobaths asindicated by the dye (and particles from the previousdiscussion) moving from deep to shallow areas, upwelling(vertical movement) of water must be occurring to accountfor the net influx of volume into the system. A flowseparation feature is observed at the downstream mouth ofthe canyon where flow inside the canyon mouth is directedinto the canyon via the canyon mouth eddy where it remainsin circulation inthe eddyor upwells onto theshelf (Figure 6).3.3. Vorticity[29] Flow in the canyon contains a significant amount ofvorticity which is observed by the formation of a cycloniceddy at the canyon mouth. The presence of strong vorticityis expected because of the large vertical displacementsobserved in the water column along the upstream wall ofthe canyon.[30] Two possible mechanisms of vorticity generationhave been proposed in previous submarine canyon studies:flow separation and vortex stretching [Pe´renne et al.,2001b]. From the experiments conducted here, it is pro-posed that vortex stretching is the most dominant mecha-nism of in-canyon vorticity generation despite significantshear along the continental slope upstream of the canyon.To determine the influence of each mechanism, we willdiscuss the affect of stratification on the canyon eddy.[31] The first possible mechanism of vorticity generationis due to flow separation. As incident alongshore flow meetsthe downstream canyon wall, flow separation occurs whetherthe canyon is moderately stratified or highly stratified[Waterhouse, 2005]. This process occurs because of incidentflow traveling along the slope, which is affected by frictionagainst the slope and as a result, has a strong shear. Onceacross the canyon mouth, part of the flow detaches from theslope and part of the flow follows the radius of curvature ofthe tank. Vorticity due to the shear against the slope mayinitiate cyclonic motion in the flow as it encounters thecanyon. In general, there does not appear to be a differencein the relationship between velocity and distance away fromthe wall as stratification changes (Figure 7) [Waterhouse,2005]. To determine the strength of the vorticity generatedbecause of this shear, a best fit function is found for all ofthe stratification cases to determine an equation thatdescribes the velocity close to a wall.[32] The equation describing the velocity on a slopingwall [Pedlosky, 1987] as well as the velocity in solid bodyrotation is fitted to the velocity data using a nonlinear leastsquares fit and is of the formU ¼ Uinterior*Boundarylayercorrection ð1Þwhere U is the velocity of the flow defined byU ¼ DW r C0 xðÞ1 C0 eC0x=LC16C17ð2Þwhere r is the radius of the tank, and x is the variabledistance away from the wall. A fit to the experimental datagives DW = 0.013 ± 0.001 sC01and L = 0.4 ± 0.2 cm where Lis the length scale constant (Figure 7). The error for the fit iscalculated using a bootstrap method. As expected, thevorticity closest to the wall is the greatest. However,because of the fact that the velocity is slow very close to thecontinental slope, the vorticity due to the shear will likelynot affect the flow inside the canyon until a long time afterthe flow has been initiated given how quickly the vorticitydecreases away from the shelf slope (Figure 7b).[33] The second possible mechanism of vorticity genera-tion is due to vortex stretching. Water columns travelingalong the continental shelf, originating upstream of theFigure 6. (left) Original and (right) enlargement of the steady state flow at the canyon mouth 200 safter the initial change in rotation rate of the tank. Dye was released from four syringes placed on theshelf upstream of the canyon. The dye released is at the shelf break depth. In the enlargement, red, yellow,and blue indicate high, lower, and zero dye concentrations, respectively. The horizontal light sheet isreflected on the canyon topography, which appears as light blue to yellow. The black and white arrowsindicate the flow of the canyon mouth eddy that is observed below the canyon rim depth with the black,and white arrows indicate flow at shallower and deeper depths, respectively. Note the full size of the eddyat the canyon mouth (white arrows) is obscured by the dye above (black arrows).C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS8of18C05004canyon, will flow over top of the canyon. As the watercolumns encounter the canyon, they will stretch as a resultof an increase in bottom depth downstream of the upstreamcanyon rim. The water column stretching, due to conserva-tion of potential vorticity, creates cyclonic vorticity in theflow at the upstream side of the canyon [Hickey, 1997].When stratification is high (and the Burger number is large),stretching of water columns originating from the shelf ismore difficult as they fall into the canyon. In a highlystratified fluid, parcels from the shelf will maintain theirvertical level because of the large amount of energy requiredto drop into the canyon and stretch. When the water columndoes not stretch, there will be less generation of cyclonicvorticity in the canyon. Conversely, if the Burger number islower, a water parcel encountering the canyon will moreeasily drop into the canyon generating more cyclonicvorticity because of vortex stretching.[34] Changes in the thickness of the dye in the vicinity ofthe long canyon for low Rossby number (Ro = 0.14) werequantitatively measured by using the second visualizationmethod. The vertical light sheet was set up at fivedifferent locations (lines a–e in Figure 1). As an example,the evolution of the dye layer at position c is shown inFigure 8. Although upwelling is not observed in thedisplacement of the dye layer below the shelf break, thetilted nature of the dye corresponds with observations oftilted isopycnals below the canyon rim [Hickey, 1997]. Theresults of observed vertical displacements of the dye dividedby the initial thickness of the dye are expressed as stretching(positive value) or compression (negative value) in f-units(Table 3).[35] This analysis shows that the greatest amount ofstretching occurs on the upstream side of the canyon fromPositions c–e on the scale of 0.2–0.5f over 60 s. Thedifference in stretching between the upstream location andthe other locations varies from 5 to 12 times. Fromconservation of potential vorticity, the large amount ofstretching at the upstream side of the canyon will induce acyclonic vorticity. Stretching increases along the upstreamwall of the canyon as the measurement location movescloser to the canyon head (from a to d in Table 3). There is asmaller amount of stretching midcanyon as well as along thedownstream canyon wall (except for at location d).[36] If isopycnal stretching were solely responsible forvorticity generation, the vorticity of the canyon mouth eddywill increase linearly with inverse stratification. Using (2),the vorticity due to shear generation between 0.5 to 2 cmaway from the wall ranges between 0.45 to 0 sC01which isFigure 7. (a) The upstream particle velocity (cm sC01) increases exponentially away from the wall.Results are plotted for various stratifications. There does not appear to be any difference in velocityprofile between the different stratifications. (b) The associated vorticity for the fit to the measuredvelocities from Figure 7a.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS9of18C05004not insignificant; however, vorticity follows a linear rela-tionship with inverse stratification such thatz ¼pNC0 q ð3Þwhere the coefficients p = (0.4 ± 0.2) sC02and q = (0.05 ±0.08) sC01and the error corresponds to the 95% confidenceinterval. The intercept is close to zero which indicates thatwhen stratification is infinite, no (or very little) vorticity willbe observed, within error of the fit (Figure 9). If sidewallfriction was significant to vorticity generation inside thecanyon, the intercept of the fit would be positive indicatingthat with no stretching, vorticity will still occur. Therefore,even through frictional shear is large far away from the shelfbreak, velocity close to the shelf slope is too small toaccount for the observed vorticity within the canyon.Vorticity in the canyon is, primarily, generated via vortexstretching since frictional shear will not have enough inertiato enter the canyon.4. Comparison: Long and Short Canyons[37] As Rossby number increases, flow features in thelong and short canyons show both similarities and differ-ences that are more easily compared using both the multi-colored and white light sheet experiments.[38] The trackedmulticoloredparticlesinthelongandshortcanyons show differing patterns of upwelling (Figure 10). Inthe long canyon, upwelling occurs very close to the canyonmouth after 30 s as only one particle is observed moving frombelow the shelf break (green) to above the shelf break depth(red in Figure 10a). Particles within the canyon are moving inthe cyclonic direction at the mouth as well as midway throughthe canyon as discussed in section 3.1. In the short canyon,upwelling occurs more predominantly along the entire down-stream rim for a similar forcing velocityas well as through thecanyon head with movement of four particles from below theshelf break (red and white) to above the shelf break depth(yellow, green and blue in Figure 10b). Only one particle isobserved moving offshore inside the canyon along the up-stream side.[39] The particle streak images also show differences inthe horizontal pattern of upwelling and flow dynamicsbetween the long and short canyons (Figures 4 and 11).The key flow features will be summarized below for eachRossby number and are separated into two separate cases:30 s and 60 s after the initial change in rotation rate.[40] At large Rossby number (Ro = 0.71), the longcanyon acts like a short canyon in that upwelling (cross-isobath flow) occurs in both canyons after 30 s along theentire downstream rim of the canyon as well as though thecanyon head. After 30 s, no canyon mouth eddy is observedin either long or short canyons. Flow on the shelf upstreamof the canyon is diminished by the long canyon (Figures 3and 4) but not affected by the short canyon. After 60 s, thecanyon mouth eddy exists in both long and short canyons.The interior canyon flow shows similar features between thelong and short canyons. The interior canyon flow at highRossby number has one large cyclonic eddy, an effectivecanyon mouth eddy in both cases, which encompasses theentire length and width of both long and short canyons. AFigure 8. Evolution of the horizontal layer of dye (verticallight sheet at position c) at (a) 0 s, (b) 30 s, and (c) 60 s afterthe initial change in rotation rate of the tank. The top andbottom bounds of the dye are indicated. Flow is directedfrom left to right, and view is toward the head of the canyonfrom the ocean (middle of the tank).C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS10 of 18C05004small amount of upwelling (cross-isobath flow) occurs alongthe downstream wall in the long canyon and the short canyon.[41] For Rossby numbers lower than 0.71, the flow in theinterior of the canyon after the first 30 s acts similarly inboth the long and short canyons in that flow is headingtoward the canyon head increasing in strength with increas-ing Rossby number and there is no observed canyon moutheddy. In the short canyon, the vertical shear is large atmedium Rossby number (0.24), with a much smaller shearobservedinthelongcanyon(visibleinrawdatainFigureA2).The difference in velocity shear between the two canyons,and a larger Hogg scale (fL/N) in the long canyon, indicatesthat the effects of the long canyon are more barotropic thanfor a short canyon in that forcing effects reach shallowerdepths [Hogg, 1973]. There is also an observed spilt betweenflow upwelling onto the shelf on the downstream canyon rimand flow that is traveling toward the canyon head in bothcanyons. A noticeable change in width of the incoming flowoccurs in both canyon lengths with the maximum entrancewidth occurring at a Rossby number of 0.24. Flow down-stream of the canyon is similar in both long and shortcanyons after both 30 and 60 s with flow being directedtoward the shelf break with increasing velocity as Rossbynumber increases.[42] Upwelling, in the short canyon, occurs in all casesthrough the canyon head at 30 s. At Ro = 0.08, flow istraveling onshore along the upstream rim of the canyon andoffshore along the downstream rim of the canyon while theflow in all other cases is traveling to the canyon head acrossthe width of the canyon. After 60 s, while upwellingcontinues to occur in the long canyon, upwelling onlyoccurs through the head and along the downstream rim ofthe canyon at Ro = 0.71 and only along the downstream rimclose to the mouth (not through the head) for Ro = 0.29.Upwelling may be occurring in the short canyon for lowerRossby number flow but because of a scarcity of particlesnear the head of the canyon after 60 s, cross-isobath flow isnot visible.Table 3. Stretching and Compression of the Horizontal DyeLayersaPosition Upstream Midcanyon Downstreama 0.01 ± 0.03 0.01 ± 0.02 0.00 ± 0.02b 0.11 ± 0.01 0.07 ± 0.01 0.03 ± 0.01c 0.21 ± 0.01 C00.02 ± 0.01 0.03 ± 0.01d 0.49 ± 0.03 C00.02 ± 0.02 C00.09 ± 0.01e 0.23 ± 0.01b0.12 ± 0.01 0.45 ± 0.01baExpressed in f-units, over 60 s of the time series. Upstream, midcanyon,downstream represent the position from the center of the canyon axis(C01.5 cm, 0 cm, and 1.5 cm, respectively) across the captured images fromthe dye experiments. Positions a–e represent the location of the light sheetas shown in Figure 1a.bResults calculated using the difference between the top and middle ofthe dye layer, not the top and bottom slopes as with the other cases. This isrequired as the dye in these two cases reaches the topography.Figure 9. Vorticity of canyon mouth eddy, z (sC01), increases with the inverse of buoyancy frequency(NC01(s)) which is indicated by the fit (z = 0.4 ± 0.2 sC02NC01– 0.04 ± 0.08 sC01, where the errors in the fitcorrespond to the 95% confidence intervals). The different symbols represent the radius away from thecenter of the eddy. The measurement error of the vorticity is 0.02 sC01, and the error of the radius is 0.1 cm.The vorticity increases toward the center of the eddy.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS11 of 18C05004[43] A special feature is observed, unique to the longcanyon, at both 30 and 60 s after the change in rotation rate.The flow on the shelf, upstream of the canyon, is reduced(in velocity) with the long canyon. This is not observed inthe short canyon experiments. At the lowest Rossby num-ber, the flow upstream of the canyon rim, close to the shelfbreak, is actually observed moving in the upstream direction(Figure 4a). As Rossby number increases, the flow at thislocation is moving in the downstream direction at a dimin-ished velocity compared to the shelf velocity downstream ofthe canyon (Figures 3 and 4). Comparing relative streaklengths within Figure A1 (or their representations inFigure 4), we see that velocities are slower on the shelfupstream of the canyon than downstream in all cases. At 60s, diminished flow on the shelf near the canyon rim isobserved, but because of a lack of data at higher Rossbynumbers (Ro = 0.29 and 0.71) conclusion can be madeonly at the three lowest Rossby numbers (Figure 4). In theshort canyon after 60 s, the flow upstream of the canyon isof a similar magnitude to the flow downstream of thecanyon except for the lowest except for the lowest Rossbynumber.5. Discussion[44] As described in the previous section, there are differ-ences in the flow dynamics between the laboratory long andshort canyons. The possible mechanisms driving upwellingin these different dynamical regimes: isobath convergence,advection and time dependence are described below and willbecharacterizedonthebasisoftheirstrengthascalculatedbythe respective Rossby number describing the flow.5.1. Isobath Convergence[45] Theoretical work has suggested that long canyons,which closely approach the coast, have strongly convergingisobaths and should thus exhibit upwelling at quite smallRossby number [Allen, 2000]. In particular, specifying thewidth of the group of converging isobaths as WT, a topo-graphic scale, gives that the flow cannot follow the topog-raphy ifC > RocðÞC00:5ð4Þwhere C is the ratio of the horizontal distance betweenisobaths far upstream of the canyon (dxu) to the distancebetween the isobaths of maximum convergence (dxc) andthe convergence Rossby number is defined by Roc= U/fWTwhere U is the shelf break flow speed. For the two canyonsconsidered here, the width of the canyon at the shelf break,Wsb, is a good measure of the total width of convergingisobaths.[46] It was expected that canyons would have significantupwelling at low Rossby Number in regions where isopyc-nals strongly converged. In the theoretical canyon [Allen,2000], this feature occurred at the head of the canyon, buthere, for the long canyon, it occurs from midway along thesides of the canyon (Figure 1). The isobath experiencingthe maximum convergence value is 1.7 cm depth, about2 cm coastward of the shelf break giving C = 24. This isthe region where upwelling over the rim is observed(Figure 12a). If the mechanism of Allen [2000] is at work,one would expect that upstream of the canyon, the flowalong the ‘‘converged’’ isobaths would be weak or‘‘blocked’’ as weak total flux for these isobaths is transmit-ted upstream from the canyon by shelf waves. Observationsshow that flow in this region just upstream of the canyon isabout 50% as strong as flow farther upstream at the samedepth (Figures 3 and 11).[47] Comparatively, there is no clear evidence of blockingupstream of the short canyon in that flow on the shelfupstream of the canyon, flows in the downstream directionat the same speed as flow farther upstream (Figures 11 andA2). Convergence of isobaths is considerably weaker in theshort canyon topography not only because of the fact it isshorter but also because of the more triangular shape.Maximum convergence occurs near the head at about1.5–2 cm depth giving C = 5. This convergence is belowFigure 10. Particle tracking from horizontal multicolored light sheet experiments for the (a) longcanyon and (b) short canyon at Ro = 0.24. In Figure 10a, the initial particle location is denoted with ablack circle, and red corresponds to above the shelf break (1.2–2.2 cm depth), while green and blue arebelow the shelf break (2.2–3.2 cm and 3.2–4.2 cm depth, respectively). The image dimensions are 25 C214 cm. In Figure 10b, the blue, green, and yellow particles are above the shelf break (1.3–1.6 cm, 1.6–1.9 cm, and 1.9–2.2 cm, respectively), while white and red particles are below the shelf break (2.2–2.5and 2.5–2.8 cm, respectively). The image dimensions are 19 C2 13 cm. The shelf break depth (2.2 cm) isdenoted by a thick solid black line in Figure 10a and 10b. The ambient flow is traveling toward the top ofFigure 10.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS12 of 18C05004the range of convergences expected to cause some upstream‘‘blocking.’’5.2. Advection[48] At larger Rossby numbers, flow is no longer geo-strophic in regions beyond those where isobaths converge.At these Rossby numbers, upwelling caused by flow cross-ing the canyon because of advection is expected to domi-nate. Results from the laboratory short canyon at the highestRossby number in the first stages of the flow show thisadvective upwelling regime which has been observed inboth field data [Hickey, 1997] and laboratory experiments[Allen et al., 2001; Pe´renne et al., 2001a, 2001b; Mirshakand Allen, 2005]. In this work, the criteria for determiningthe strength and importance of the advective regime indriving upwelling is through the advective Rossby number(Ro = U/fR). If the advective Rossby number is greater than0.2 (Tables 4 and 5), this mechanism is important and drivesflow characterized by upwelling at the canyon head with noblocking of the flow on the upstream side of the canyon(Figure 12b). Note, that actual velocities have been calcu-lated in Tables 4 and 5 to take into account the effect offriction described in Figure 3 and section 2.2. From thispoint on, the Rossby numbers calculated using the actualvelocities will be used.[49] Upwelling in the short canyon occurs (and is visible)between an advective Rossby number of 0.1 to 0.52 duringthe first 30 s by the advective mechanism. Both the time-dependent and isobath convergent criteria are low in com-parison (Table 4). After 60 s, upwelling through the head ofthe canyon is not visible in the short canyon except for anadvective Rossby number of 0.50 and again, time-depen-dent and isobath convergent criteria are low, in comparison(Table 5). At Ro = 0.20, upwelling is observed near themouth of the canyon and although it is not observed at thehead of the canyon, the advective Rossby number isFigure 11. (a–j) Interpretation of the flow in the shortcanyon for varying Rossby numbers 30 and 60 s after thechange in rotation rate of the tank. The shelf break and tankedge are represented by solid black lines, and the flowvectors are representative of the flow between 1.9 and2.2 cm in the vertical. Arrows are not to scale, but theoriginal data is presented in Appendix A for comparison.Figure 12. Flow schematic of three upwelling mechan-isms: (a) isobath convergence, (b) advection, and (c) timedependence of the flow.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS13 of 18C05004significant compared with the time-dependent and isobathconvergence criteria (Table 5). After a long period of timehas elapsed, upwelling in a short canyon may continue tooccur but will be difficult to visualize from observations inthe horizontal flow field as the flow is dominated by thecanyon mouth eddy [She and Klinck, 2000]. Therefore,although upwelling is not visible in the short canyon 60 safter the flow initialization for lower Rossby number,upwelling may be occurring (‘‘Not visible’’ in Table 5).[50] At the highest Rossby number, the flow in the longcanyon also acts in this advective regime at both 30 and 60 safter the flow initiation. As the advective Rossby numberdecreases, the dynamics in the long canyon are dominatedby the isobath convergence regime as the isobath conver-gence criteria remains high (Tables 4 and 5). This regimecontinues to show visible upwelling over a longer period oftime than the advective regime. Long canyon experimentscarried out at a steady state reveal the weak but continuingupwelling due to isobath convergence.5.3. Time Dependence[51] With the lowest incident velocity in the short canyon,the flow during the first 30 s shows onshore flow along theupstream side of the canyon and offshore flow along thedownstream side, as described above. Given this differencein flow structure, the mechanism responsible for driving thisflow and the associated upwelling is related to a timedependence of the flow (Figure 12c).[52] This third regime, not defined by either advective orisobath convergent processes, is related to the time-dependent changes in flow characteristics defined as thetime-dependent Rossby number, Rot=1/(ft) where t is thetime after the change in rotation rate of the tank [Boyer etal., 2004]. For time-dependent upwelling to be clearlyvisible we would expectRotLcWsbWaþ 2C18C19> 0:25 ð5ÞTable 5. Nondimensional Rossby Numbers (Time-Dependent (Rot), Advective (Ro), and Convergent (Roc)) for Long and ShortLaboratory CanyonsaForcing Velocity(cm sC01)Actual ShelfVelocity(cm sC01)Time-DependentAdvective(Ro = U/(fR);Criteria Ro > 0.2)Isobath ConvergenceUpwellingObservedDominantMechanismUpwelling FlowShown inRot=1/ftCriteria (5)>0.5Roc= U/(fWsb)Criteria From(4) RocC2>1Long Canyon0.16 0.11 0 0 0.05 0.01 6.6bYes IC Figure 12a0.3 0.21 0 0 0.10 0.02 12.4bYes IC Figure 12a0.47 0.33 0 0 0.16 0.03 19.5bYes IC Figure 12a0.6 0.42 0 0 0.20b0.04 24.9bYes IC Figure 12a1.5 1.05 0 0 0.50b0.11 62.2bYes AD Figure 12bShort Canyon0.16 0.11 0 0 0.05 0.01 0.3 Not visible - -0.3 0.21 0 0 0.10 0.02 0.6 Not visible - -0.47 0.33 0 0 0.16 0.04 0.9 Not visible - -0.6 0.42 0 0 0.20b0.05 1.2bYes AD Figure 12b1.5 1.05 0 0 0.50b0.12 2.9bYes AD Figure 12baRossby number-specific criteria for upwelling to occur given the flow regime 60 s after flow initialization. Actual shelf velocities are calculated usingresults from Figure 3 for shelf velocities measured far away from the canyon.bRossby numbers exceed the specified upwelling criteria.Table 4. Nondimensional Rossby Numbers (Time-Dependent (Rot), Advective (Ro), and Convergent (Roc)) for Long and ShortLaboratory CanyonsaForcing Velocity(cm sC01)Actual ShelfVelocity(cm sC01)Time-DependentAdvective(Ro = U/(fR);Criteria Ro > 0.2)Isobath ConvergenceUpwellingObservedDominantMechanismUpwelling FlowShown inRot=1/ftCriteria (5)> 0.25 Roc= U/(fWsb)Criteria From(4) RocC2>1Long Canyon0.16 0.12 0.02 0.22 0.06 0.01 6.8bYes IC Figure 12a0.3 0.22 0.02 0.22 0.1 0.02 12.8bYes IC Figure 12a0.47 0.34 0.02 0.22 0.16 0.03 20.1bYes IC Figure 12a0.6 0.43 0.02 0.22 0.21b0.04 25.6bYes IC Figure 12a1.5 1.09 0.02 0.22 0.52b0.11 64.1bYes AD Figure 12bShort Canyon0.16 0.12 0.02 0.09 0.06 0.01 0.3 Yes TD Figure 12c0.3 0.22 0.02 0.09 0.1 0.02 0.6 Yes AD Figure 12b0.47 0.34 0.02 0.09 0.16 0.04 0.9 Yes AD Figure 12b0.6 0.43 0.02 0.09 0.21b0.05 1.2bYes AD Figure 12b1.5 1.09 0.02 0.09 0.52b0.12 2.9bYes AD Figure 12baRossby number–specific criteria for upwelling occur given the flow regime 30 s after flow initialization. Actual shelf velocities are calculated usingresults from Figure 3 for shelf velocities measured far away from the canyon. IC, isobath convergence; AD, advective; TD, time-dependent.bRossby numbers exceed the specified upwelling criteria.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS14 of 18C05004where Lcis the length of the canyon, W is the canyon widthmidway between the mouth and head and a is the Rossbyradius of deformation (relevant derivation in Appendix B).[53] For both long and short canyons, this value is weakcompared with advective and isobath-convergent criteriaexcept for the incident velocity of 0.15 cm sC01. For the shortcanyon, flow inside the canyon at this incident velocity ismoving toward the head of the canyon along the upstreamside during the first 30 s which is indicative of time-dependent flow [She and Klinck, 2000] (Tables 4 and 5).Given the small advective and isobath convergent Rossbynumber criteria (0.06 and 0.3 respectively), the time depen-dence of the flow, although small, is the dominant mecha-nism in determining the flow structure. In the long canyonat this small incident velocity, the stronger isobath conver-gence upwelling is dominating over the advective or time-dependent upwelling regimes, thus time-dependent upwell-ing may be occurring in the long canyon at this incidentvelocity but it is most likely masked by the more dominantisobath convergent mechanism.[54] In summary, the mechanisms driving upwelling inboth long and short canyons can be defined by three distinctprocesses: advection, time dependence of the flow and theeffect of isobath convergence. By specifying criteria todetermine the strength of each process, the dominantprocess is determined at both 30 s and 60 s after theinitiation of the flow. The long canyon is most stronglyaffected by the effects of its bathymetry and thus isobathconvergence is the most dominant mechanism drivingupwelling, with advection becoming important only withstrong incident velocities. Upwelling in the short canyonoccurs through advective and time-dependent processes.6. Summary[55] At low Rossby number, the flow dynamics in thelong canyon show two distinct stages of flow that arecharacterized by separate and distinct features due to therestrictions of isobath convergence within the canyon. Thefirst stage includes the generation of vorticity due toisopycnal stretching inside the canyon on the upstream side,upwelling occurring at the downstream rim at the mouth, aslow cyclonic flow within the canyon walls and a slowingof flow on the shelf upstream of the canyon. The secondstage of the flow is characterized by the formation of acanyon mouth eddy and the continuation of the slowcyclonic flow within the canyon walls and again, upwellingoccurring at the downstream rim at the mouth. The canyonmouth eddy is found to have a vorticity dependent onstratification while the upstream slope flow is not dependenton stratification. At moderate Rossby number, upwelling inthe steady state experiment occurs continuously along thedownstream rim of the long canyon driven by isobathconvergence processes.[56] The pattern of upwelling, between the long and shortcanyons, is different for moderate Rossby number flow withupwelling occurring at the mouth of the long canyon andthrough the head and downstream rim for the short canyon.At high Rossby number, the long canyon has similarfeatures as the flow in the short canyon in an advectiveregime with upwelling occurring at the canyon heads inboth cases (Figure 12b). In the short canyon, as the Rossbynumber decreases, upwelling occurs during the first stage ofthe flow but is not visible during the second stage. Flow(and upwelling) within the short canyon at the lowestRossby number is likely dominated by the time dependenceof the flow (Figure 12c).[57] In short canyons, upwelling is observed duringstrengthening flows and high Rossby number flows. Longcanyons, such as Juan de Fuca Canyon, however, will havesignificant upwelling even during quasi-steady, low Rossbynumber conditions because of isobath convergence.Appendix A[58] Figures 4 and 11 are interpretations of the flowobserved in the tank on the basis of streak imagesFigures A1 and A2 as discussed in section 2.3. The actualstreak images are presented here for determining the relativechanges in the flow speeds (scale) and particle density foreach experiment. Original video recordings were used toverify and add to all observations made from these streakimages.Appendix B[59] The criteria for determining when the temporalRossby number is of importance depends on the amountof upwelling flux occurring in the time-dependent sense. Wecan estimate the ratio of up-canyon velocity due to time-dependent effects to the incoming velocity by estimating theflux needed to create a pressure gradient strong enough toturn the incoming velocity around the canyon [Allen, 1996].From geostrophy, the higher pressure over the canyonneeded to turn the incoming flow, U,isfU ¼1r@p@x: ðB1ÞFrom the hydrostatic approximation,@p@z¼C0r0g ðB2Þwhich is approximately equal to@p@z¼ r0N2b ðB3Þwhere b is the vertical distance over which the isopycnalsneed to be lifted to turn the incoming flow. Using (B3) in(B1) and approximating dx as the Rossby radius ofdeformation, a =(NHS)/f, and dz as Hs, (B1) becomesb ¼fUaN2Hs: ðB4Þwhich also gives the rate of change of b to be@b@t¼faN2Hs@U@t: ðB5ÞC05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS15 of 18C05004[60] The isopycnals need to be raised through a surfacearea of the canyon at the shelf break defined by the width ofthe canyon plus a Rossby radius on either side (W+2a) andthe length of the canyon, Lc. This volume is supplied by theup-canyon velocity, multiplied by the width of the canyon atthe mouth (Wsb) and the prescribed depth of the incomingflow (HS), to give, approximatelyUupcanyonWsbHs¼faN2Hs@U@tW þ 2aðÞLcðB6Þwhich gives an estimate for the up-canyon flow ofUupcanyon¼LcfWsb@U@tWaþ 2C18C19: ðB7Þ[61] Comparing the temporal Rossby number andup-canyon velocity to the velocity of the incoming (cross-canyon) flow, described by @U/@tC1t where tis the time afterthe initial change in rotation rate of the tank, gives ameasure of the strength of the time-dependent flow throughthe canyon. If the up-canyon flow is at least 25% of thecross-canyon time-dependent flow, then time-dependentFigure A1. (a–j) Streak images of particle displacement in the long canyon for varying Rossbynumbers 30 and 60 s after the initial change in rotation rate of the tank. The shelf break is represented bya solid black line. Observed particles are between 1.2 and 2.2 cm in the vertical. Initial particle locationsare denoted by gray streaks, while the particle displacement is captured over 3 s for Figures A1 and A2.Interpretations of the streaks are in Figure 4. Figure A1 dimensions are 25 C2 15 cm.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS16 of 18C05004canyon upwelling should be visible. This gives the follow-ing criteria for the time dependence upwelling of the flowRotLcWsbWaþ 2C18C19> 0:25: ðB8Þ[62] Acknowledgments. The authors would like to acknowledgeHarald Schrempp, Ted Tedford, and Christian Reuten for their technicalassistance in the laboratory work and data analysis. The comments of JohnKlinck and an anonymous reviewer substantially improved the clarity of thepaper. This research was supported by an NSERC Discovery grant to thesecond author.ReferencesAllen, S. E. (1996), Topographically generated, subinertial flows within afinite length canyon, J. Phys. Oceanogr., 26, 1608–1632, doi:10.1175/1520-0485(1996)026<1608:TGSFWA>2.0.CO;2.Figure A2. (a–j) Streak images of particle displacement in the short canyon for varying Rossbynumbers 30 and 60 s after the initial change in rotation rate of the tank. Streaks are captured over 8 s inFigures A2a and A2b; 4 s in Figures A2c, A2d, A2e, and A2f; and 2 s in Figures A2g, A2h, A2i, and A2j.The canyon contours are represented by solid black lines. Interpretations of the streaks between 1.9 and2.2 cm depth are in Figure 11. Figure A2 dimensions are 19 C2 13 cm.C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS17 of 18C05004Allen, S. E. (2000), On subinertial flow in submarine canyons: Effect ofgeometry, J. Geophys. Res., 105, 1285–1297, doi:10.1029/1999JC900240.Allen, S. E., C. Vindeirinho, R. E. Thomson, M. G. G. Foreman, and D. L.Mackas (2001), Physical and biological processes over a submarine can-yon during an upwelling event, Can. J. Fish. Aquat. Sci., 58(4), 671–684, doi:10.1139/cjfas-58-4-671.Allen, S. E., M. S. Dinniman, J. M. Klinck, D. D. Gorby, A. J. Hewett, andB. M. Hickey (2003), On vertical advection truncation errors in terrain-following numerical models: Comparison to a laboratory model for up-welling over submarine canyons, J. Geophys. Res., 108(C1), 3003,doi:10.1029/2001JC000978.Boyer, D. L., D. B. Haidvogel, and N. Pe´renne (2004), Laboratory-numer-ical model comparisons of canyon flows: A parameter study, J. Phys.Oceanogr., 34, 1588–1609, doi:10.1175/1520-0485(2004)034<1588:LMCOCF>2.0.CO;2.Carmack, E. C., and E. A. Kulikov (1998), Wind-forced upwelling andinternal Kelvin wave generation in Mackenzie Canyon, Beaufort Sea,J. Geophys. Res., 103, 18,447–18,458.Freeland, H., and K. Denman (1982), A topographically controlled upwel-ling center off Vancouver Island, J. Mar. Res., 40, 1069–1093.Hickey, B. M. (1997), The response of a steep-sided narrow canyon to time-variable wind forcing, J. Phys. Oceanogr., 27, 697–726, doi:10.1175/1520-0485(1997)027<0697:TROASS>2.0.CO;2.Hogg, N. G. (1973), On the stratified Taylor column, J. Fluid Mech., 58(3),517–537, doi:10.1017/S0022112073002302.Kinsella, E. D., A. E. Hay, and W. W. Denner (1987), Wind and topo-graphic effects on the Labrador Current at Carson Canyon, J. Geophys.Res., 92, 10,853–10,869, doi:10.1029/JC092iC10p10853.Klinck, J. M. (1989), Geostrophic adjustment over submarine canyons,J. Geophys. Res., 94, 6133–6144.Kunze, E., L. K. Rosenfeld, G. S. Carter, and M. C. Gregg (2002), Internalwaves in Monterey submarine canyon, J. Phys. Oceanogr., 32, 1890–1913, doi:10.1175/1520-0485(2002)032<1890:IWIMSC>2.0.CO;2.Macquart-Moulin, C., and G. Patriti (1996), Accumulation of migratorymicronekton crustaceans over the upper slope and submarine canyonsof the Northwestern Mediterranean, Deep Sea Res., Part I, 43, 579–601, doi:10.1016/0967-0637(96)00039-8.Mirshak, R., and S. Allen (2005), Spin-up and the effects of a submarinecanyon: Applications to upwelling in Astoria Canyon, J. Geophys. Res.,110, C02013, doi:10.1029/2004JC002578.Oster, G. (1965), Density gradients, Sci. Am., 213, 70–76.Pedlosky, J. (1987), Geophysical Fluid Dynamics, 2nd ed., Springer, AnnArbor, Mich.Pe´renne, N. P., J. Verron, D. Renouard, D. L. Boyer, and X. Zhang (1997),Rectified barotropic flow over a submarine canyon, J. Phys. Oceanogr.,27, 1868–1893, doi:10.1175/1520-0485(1997)027<1868:RBFOAS>2.0.CO;2.Pe´renne, N. P., D. B. Haidvogel, and D. L. Boyer (2001a), Laboratory-numerical model comparisons of flow over a coastal canyon, J. Atmos.OceanicTechnol.,18,235–255,doi:10.1175/1520-0426(2001)018<0235:LNMCOF>2.0.CO;2.Pe´renne, N. P., J. W. Lavelle, and D. L. Boyer (2001b), Impulsively startedflow in a submarine canyon: Comparisons of results from laboratory andnumerical models, J. Atmos. Oceanic Technol., 18, 1698–1717,doi:10.1175/1520-0426(2001)018<1699:ISFIAS>2.0.CO;2.She, J., and J. M. Klinck (2000), Flow near submarine canyons driven byconstant winds, J. Geophys. Res., 105, 28,671–28,694, doi:10.1029/2000JC900126.Vindeirinho, C. (1998), Currents, water properties and zooplankton distri-bution over a submarine canyon under upwelling-favorable conditions,MS thesis, Univ. of B. C., Vancouver, B. C.Waterhouse, A. F. (2005), A physical study of upwelling flow dynamics inlong canyons, MS thesis, Univ. of B. C., Vancouver, B. C.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0S. E. Allen and A. W. Bowie, Department of Earth and Ocean Sciences,University of British Columbia, Vancouver, BC V6T 1Z4, Canada.A. F. Waterhouse (corresponding author), Department of Civil andCoastal Engineering, University of Florida, Gainesville, FL 32611, USA.(awaterhouse@ufl.edu)C05004 WATERHOUSE ET AL.: UPWELLING FLOW DYNAMICS IN LONG CANYONS18 of 18C05004


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