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Flow dynamics around downwelling submarine canyons Spurgin, Jessica Michelle 2014

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FLOW DYNAMICS AROUND DOWNWELLING SUBMARINE CANYONSbyJessica Michelle SpurginB.Sc., Texas A&M University - Galveston, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Oceanography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)March 2014c© Jessica Michelle Spurgin, 2014AbstractFlow dynamics around a downwelling submarine canyon were analyzed with the Massachusetts In-stitute of Technology general circulation model. Blanes Canyon (Northwest Mediterranean) was usedfor topographic and initial forcing conditions. Fourteen scenarios were modelled with varying forcingconditions. Rossby number and Burger number were used to determine the significance of Coriolis ac-celeration and stratification (respectively) and their impacts on flow dynamics. A new non-dimensionalparameter (χ) was introduced to determine the significance of vertical variations in stratification. Down-welling (downwards advection of density) occurs under all forcing conditions and is enhanced within thecanyon. High Burger numbers lead to negative vorticity and a trapped anticyclonic eddy within thecanyon, as well as an increased density anomaly. Low Burger numbers lead to positive vorticity, cycloniccirculation and weaker density anomalies. Vertical variations in stratification affect zonal jet placement.Under the same forcing conditions, the zonal jet is pushed offshore in more uniformly stratified domains.Offshore jet location generates upwards density advection away from the canyon, while onshore jets gen-erate downwards density advection everywhere within the model domain. Increasing Rossby values acrossthe canyon axis, as well as decreasing Burger values, increase negative vertical flux at shelf break depth(150 m). Increasing Rossby numbers lead to stronger downwards advection of a passive tracer (nitrate).Comparisons were made to previous studies to explain how variations in initial forcing conditions impactregional flow dynamics.iiPrefaceThis thesis describes experiments that used an open-source numerical model designed for the studyof atmosphere, ocean, and climate (MIT general circulation model; Marshall et al., 1997). Methodsfor experimental design, model set-up, and result analysis were conceived and executed by the author,Jessica Spurgin. This work was supervised by Susan Allen; she assisted with experimental approach,comprehension of results and thesis edits. This work is unpublished, but undergoing preparation forsubmission to a peer reviewed journal.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Importance of submarine canyons in the Mediterranean Sea . . . . . . . . . . . . . . . . . 11.2 Coastal/open ocean separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Flow around submarine canyons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Previous downwelling canyon studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Study region; northwest Mediterranean Sea . . . . . . . . . . . . . . . . . . . . . . . . . . 71.6 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Flow Dynamics of Downwelling Submarine Canyons . . . . . . . . . . . . . . . . . . . . 102.1 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.1 Domain and canyon bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.2 Parameter specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1.3 Model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.4 Result calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18iv2.2.1 Flow evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.2 Circulation in the canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.3 Comparison to previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.4 Vorticity in the canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.2.5 Upwelling in a downwelling canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.6 Nitrate anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.1 Upwelling in downwelling canyons . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.3.2 Parameter effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.3.3 Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.3.4 Summary: Circulation, flux, and advection for steady flow over downwelling canyons 492.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1.1 Determine if upwelling occurs in or around downwelling canyons. If so, where doesupwelling occur, and how intense is upwelling? . . . . . . . . . . . . . . . . . . . . 513.1.2 Determine what parameters affect flow dynamics. . . . . . . . . . . . . . . . . . . . 523.2 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.3 Application to real world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56A Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61B Model Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64C Advection Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65D Extended Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66E Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68F Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70vList of Tables1.1 Features seen in previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Constant geometric parameters for model simulations . . . . . . . . . . . . . . . . . . . . 112.2 Non-dimensional parameters for all model simulations . . . . . . . . . . . . . . . . . . . . 132.3 Forcing flow for all model simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Temporal variations in forcing for all model simulations . . . . . . . . . . . . . . . . . . . 162.5 Absolute vorticity and canyon circulation for all model simulations . . . . . . . . . . . . . 252.6 Positive density anomaly depth range for all model simulations . . . . . . . . . . . . . . . 322.7 Diffusive and advective flux of nitrate across 3 vertical planes . . . . . . . . . . . . . . . . 48viList of Figures1.1 Model canyon bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Location of Blanes Canyon, Northwest Mediterranean Sea . . . . . . . . . . . . . . . . . . 82.1 Planes used for transport calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Time series of horizontal and vertical flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Horizontal and vertical circulation during the time-dependent phase . . . . . . . . . . . . 212.4 Horizontal velocity vectors at shelf break depth . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Particle trajectories in an anticyclonic simulation . . . . . . . . . . . . . . . . . . . . . . . 232.6 Particle trajectories in a cyclonic simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 242.7 Vorticity cross-sections at mid-canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.8 Vertical velocity at shelf break depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.9 Times of net upwards across 3 vertical planes . . . . . . . . . . . . . . . . . . . . . . . . . 292.10 Particle trajectories for all depths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.11 Density anomaly at shelf break depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.12 Density difference anomaly at shelf break depth . . . . . . . . . . . . . . . . . . . . . . . . 332.13 Nitrate anomaly upstream and along the canyon axis . . . . . . . . . . . . . . . . . . . . . 342.14 Isopycnal cross-sections at mid-canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.15 Burger and incoming Rossby number effect on canyon vorticity . . . . . . . . . . . . . . . 392.16 Zonal jet location upstream of the canyon . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.17 Incoming Rossby and canyon Rossby number correlation . . . . . . . . . . . . . . . . . . . 412.18 Burger and canyon Rossby number effect on vertical flux . . . . . . . . . . . . . . . . . . . 432.19 Burger and incoming Rossby number effect on density anomaly . . . . . . . . . . . . . . . 452.20 Incoming Rossby number effect on nitrate anomaly . . . . . . . . . . . . . . . . . . . . . . 47A.1 Isopycnal cross-sections along the upstream and downstream boundaries . . . . . . . . . . 63viiD.1 Time series of horizontal and vertical flux over 20 model days . . . . . . . . . . . . . . . . 67E.1 Time series of horizontal and vertical flux with 3 hour model output . . . . . . . . . . . . 69F.1 Time series of horizontal and vertical flux for all model simulations . . . . . . . . . . . . . 70F.2 Horizontal velocity vectors at shelf break depth for all model simulations . . . . . . . . . . 73F.3 Vorticity cross-sections at mid-canyon for all model simulations . . . . . . . . . . . . . . . 75F.4 Vertical velocity at shelf break depth for all model simulations . . . . . . . . . . . . . . . 77F.5 Density anomaly at shelf break depth for all model simulations . . . . . . . . . . . . . . . 79F.6 Density difference anomaly at shelf break depth for all model simulations . . . . . . . . . 81F.7 Nitrate anomaly upstream and along the canyon axis for all model simulations . . . . . . 83viiiAcknowledgementsI would like to thank my supervisor, Dr. Susan Allen for her constant assistance and support through-out my thesis program. Thank you Susan for always having time for a quick (and sometimes not so quick)meeting and for giving me the opportunity to grow and learn in a field in which I previously had limitedexperience. Also, thank you for the wonderful opportunity to get away from a computer screen andexperience oceanography from an observational point of view.I also wish to thank my supervisory committee (Dr. William Hsieh and Dr. Neil Balmforth) for theirconstructive input throughout my project. Thank you to Dr. Richard Pawlowicz for agreeing to examinemy thesis, as well as all the useful suggestions during lab seminars.Thank you to everyone in the Waterhole for your continued support and countless cookie breaks. Youall were there to help keep my sanity in check, even when it seemed too late.Finally, many massive thanks to my wonderful mother and extended family for their continual supportand encouragement, no matter the miles between us. Mom, without your undying encouragement I neverwould have made it this far in my project or in my life. There is no one else I would want to take an 8day cross-country trip with (twice).ixDedicationFor my father who continues to watch over me and who gave me his love of all things science!xChapter 1Introduction1.1 Importance of submarine canyons in the Mediterranean SeaAlmost 518 large submarine canyons have been identified in the Mediterranean Sea [Harris and White-way, 2011]. Interest in these canyons was initially driven by economic reasons (e.g. exploration for fossilenergy resources and exploitation of ancient deposits), but recent interest has focused on submarinecanyons and their impact on exchanges between the deep ocean and continental shelf [Wurtz, 2012].Submarine canyons concentrate sediments rich in organics and contain denser deposits of phytodetri-tus [Garcia et al., 2008]; making canyons more favorable habitats for benthic consumers and suspensionfeeders. Complex topography within a canyon enhances habitat heterogeneity, creating a greater abun-dance and diversity of fish along margins where canyons are common [Marques et al., 2005; Morais et al.2007].Due to the presence of several submarine canyons (Cap de Creus, Palamoˆs, Blanes, Arenys andMerenguera Canyons), the Catalan continental margin supports an important commercial fishery [Com-pany et al., 2012]. The deep-sea red shrimp Aristeus antennatus (Risso, 1816) is a target species andhighly appreciated crustacean in this region [Company et al., 2012], making it an important resource tothe local economy.Hydrodynamics in these canyons depends upon forcing conditions such as bottom morphology, generalcirculation, and atmospheric regime [Company et al., 2012]. Such forcing conditions can vary betweencanyons and lead to different hydrodynamic responses. These hydrodynamic responses in turn affectparticulate matter retention and/or resuspension and coastal biological productivity. Submarine canyonscan be classified as upwelling or downwelling, depending on the incoming flow direction. Upwelling1canyons generally have incoming flow with the coast to the left, and downwelling canyons typically havea right-bounded flow (in the Northern Hemisphere).Forcing conditions in the Mediterranean Sea create downwelling canyons, which have previously beenfound to enhance coastal downwelling [Klinck, 1996; Skliris et al., 2001; 2002]. However, the higher thanaverage biological productivity of this region [Palomera, 1992; Sabates and Olivar 1996] helps sustain theimportant commercial fisheries.This study will model a downwelling canyon based on forcing conditions observed in the MediterraneanSea. Forcing conditions will then be varied to test their impacts on canyon hydrodynamics. Advection,horizontal and vertical circulation will be used to determine if downwelling is enhanced, or if upwellingoccurs in these canyons.1.2 Coastal/open ocean separationThe oceans cover approximately 71% of the Earth, with the coastal oceans covering only 7%. Theproximity to land and its nutrient sources, the interception of sinking organic matter by the shallowseafloor, and the propensity for coastal upwelling all result in highly productive coastal ecosystems [Sig-man and Hain, 2012]. A shallow feature, the shelf-break, occurs at the transition between the gentlysloping continental shelf and the steeper continental slope and separates the coastal and open ocean.Geostrophic flow occurs when the balance of forces in the horizontal is between pressure gradient forceand Coriolis force. Geostrophic flow is parallel to isobars with high pressure to the right of the flow (inthe Northern Hemisphere; left of the flow in the Southern Hemisphere). In homogeneous, geostrophicflow, fluid columns cannot change their area (due to no net horizontal flux into or out of them) andtherefore move as rigid columns of water [Taylor, 1923]. In this state, flow cannot change its depthand is constrained to follow isobaths. When flow is stratified, it is similarly constrained up to a depthwhere there is zero flow [Brink, 1998]. Therefore, a shelf-break current that extends from the surface todepth blocks stratified (and non-stratified) geostrophic flow from crossing isobaths. This causes a lack ofexchange and is illustrated by significant changes in water properties near the location of the shelf-break.There are various processes (e.g. bottom friction and strong flow) that can break these dynamicalconstraints. Small-scale topography, such as submarine canyons, can lower the dynamical length-scaleand allow cross-isobath flow. Numerical models have shown, based on incoming flow direction, submarinecanyons can enhance upwelling/downwelling in coastal regions [Klinck, 1996]. Thus, submarine canyonshave a significant impact on regional circulation and are therefore an important feature for coastal and2open ocean interaction.1.3 Flow around submarine canyonsSubmarine canyons are features typical of continental slopes and deeply incise the continental shelf.In coastal regions with submarine canyons, the characteristic length scale (L) is reduced from the scaleof the slope or shelf, to the scale of the canyon, which is often an order of magnitude smaller [Allen andDurrieu de Madron, 2009]. By reducing the length scale, the non-dimensional Rossby number (U/fL;where U = incoming velocity and f = Coriolis parameter) increases and effects due to advection ofmomentum become important.In a review of coastal submarine canyons, Hickey [1995] points out that, on a regional scale, physicalprocesses can be modified/enhanced due to the presence of a submarine canyon. Some of these processesinclude mixing, internal wave activity, upwelling and cross-shelf/slope exchange. These processes can inturn affect mass balance on regional and larger scales.Allen and Durrieu de Madron [2009] distinguished three phases of flow response during an upwellingor downwelling scenario due to realistic coastal winds:1) An initial time-dependent response (shelf flow increases). This response is strong and usually occurswithin an inertial period [Klinck, 1988; Ka¨mpf, 2006]. If alongshore-current continues to increase (i.e.because of steady winds) density advection within the canyon reduces time-dependent upwelling afterabout 5 days [She and Klinck, 2000].2) An advection dominated response (shelf break flow is reasonably steady). This response is stronglydependent on canyon topography and flow strength [Allen, 2004]. For weaker flows, it can be enhancedif convergent isobaths occur over the canyon [Allen, 2000; Waterhouse et al., 2009].This advection dominated phase is not friction controlled but friction influenced and the concept of”steady” advection driven flow is theoretical. In reality wind is continually changing, which drives smallchanges in the strength of zonal flow; if the flow stops, the flow slowly spins down. These small changesin zonal flow impact other dynamics within the system. During this quasi-steady state, even with steadyforcing, flow can exhibit oscillations over multi-day periods [She and Klinck, 2000].3) A relaxation phase (shelf break flow decreases). This phase sees strong, generally cyclonic flowwithin the canyon [Hickey, 1997].Consider a right bounded flow (in the same direction as Kelvin wave propagation). The current will bein geostrophic equilibrium with a cross-shore pressure gradient, where pressure is lower towards the open3ocean. Within the canyon, alongshore flow is restricted by canyon walls and the Coriolis force cannotbalance the cross-shore pressure gradient [Allen and Durrieu de Madron, 2009]. These right boundedflows are generally associated with net downwelling (downward flow and flow toward the ocean) [Klinck,1996].The shoreward end of a canyon is known as the canyon head, while the broader side opening towardsthe open ocean is referred to as the canyon mouth (Figure 1.1). The boundary between the continentalshelf and submarine canyon is known as the canyon rim. The term shelf break refers to the continentaledge, where slope gradients increase toward the deep ocean bottom. For the purposes of this study, theterm canyon wall will refer to the vertical rise between bottom topography and the canyon rim. Flowdirection is towards the downstream, so 61-120 km (in the alongshore) is referred to as upstream of thecanyon axis, and anything 0-59 km is downstream of the canyon axis.−1000−800−600−400−2000Alongshore (km)Cross−shore (km)10 20 30 40 50 60 70 80 90 100 1101020304050607080WallCanyon headDownstream UpstreamOuter shelfOffshoreInner shelfSlopeMid−canyonCanyon mouth Shelf breakRimLower CanyonFigure 1.1: Canyon bathymetry (gray lines) and reference terminology used in this thesis. Canyon rimindicates the boundary between the continental shelf and the canyon. Shelf break indicates change inslope gradient between the continental shelf and slope. Canyon mouth is the open region along the shelfbreak; canyon head is the shallowest onshore canyon region; mid-canyon is the region between the canyonhead and mouth; lower canyon is offshore of the canyon mouth. Canyon wall refers to canyon topographybetween shelf break and bottom depth. Zonal flow is in the alongshore, and meridional flow is in thecross-shore. Contour intervals are 100 m.41.4 Previous downwelling canyon studiesThe direction of alongshore flow is critical to the circulation over a canyon [Klinck, 1996]. For right-bounded coastal flows, the geostrophic pressure gradient is offshore. Under barotropic forcing, the flow atthe shelf break turns towards the coast and begins to slow and weaken, due to the large scale, cross-shorepressure gradient, which leads to a reduction in the Coriolis acceleration [Klinck, 1996]. This reductionallows water to be pushed down the topographic slope. Once water crosses the axis of the canyon, itis then accelerated by the large scale pressure gradient, and begins to rise due to the increased Coriolisacceleration. With weak dissipation, water returns almost to its original depth and continues alongshore[Klinck, 1996].With either a uniform incoming flow or a continental slope jet, antisymmetrical upwards (downwards)vertical velocity is seen in the downstream (upstream) region of a canyon, with upwards velocity being lessintense than downwards velocity [Klinck, 1996; Skliris et al., 2002, respectively]. In both cases, cycloniccirculation is seen in the canyon head, as well as negative density anomalies everywhere over the canyon(with positive anomalies both upstream and downstream of the canyon in the slope region).Stratification controls the magnitude of a forcing response and limits the influence of a canyon onoverlying flow, independent of the direction of alongshore flow [Klinck, 1996]. Increased stratificationreduces vertical and cross-shore transport, as well as depth range over which fluid parcels move in acircuit around a canyon [Klinck, 1996; Skliris et al., 2002].Aside from Klinck [1996] and Skliris [2001, 2002], there are several other studies of downwellingsubmarine canyons, mostly numerical models of canyons in the northwest Mediterranean Sea.Observational cruises near Palamo`s Canyon (northeastern edge of Spain) reveal that small-scale tem-poral variability in the onshore/offshore location of an incoming zonal jet has important impacts on flowdynamics [Alvarez et al., 1996]. Transient factors (such as river runoff and the climatology of the area)induce a series of modifications in the permanent front-current of the region; affecting both its verticalextension and offshore location [ibid.]. In areas where canyon width is narrow and depth variations arestrong (i.e. canyon head), vorticity adjustments and associated vertical velocities are induced as part ofageostrophic adjustment, and the core of the front-current is displaced offshore downstream of the canyon[Alvarez et al., 1996]. When incoming zonal jets are displaced onshore, flow is narrower and faster, andvertical velocities are greater (relative to an incoming zonal jet placed further offshore) [Jordi et al.,2005]. The ageostrophic component of the current is more significant when a coastal current interactswith the canyon head instead of the canyon mouth [Alvarez et al., 1996; Jordi et al. 2005]. In areas where5depth changes are not so strong and the canyon is wide (i.e. canyon mouth), flow adjustment is almostgeostrophic and vertical velocity allows flow to maintain a thermal wind balance [Alvarez et al., 1996].At high Rossby number, vorticity and vertical velocity are maximum where a coastal jet interacts witha canyon [Jordi et al., 2005].Under constant downwelling winds and at low Rossby number (Ro= 0.005), a strong anticyclone withina canyon (in the upper 200 m) and small net cross-shore exchanges are driven by vortex compression orfrictional coupling to alongshore flow [She and Klinck, 2000]. Along the canyon mouth and above shelfbreak depth (150 m), upstream onshore (into canyon) transport is stronger than downstream offshore(out of canyon) transport. Transports below shelf break depth are net offshore until the anticycloneforms, at which point net cross-shore transport becomes onshore. Vertical flux is downwards everywhereover the canyon at shelf break depth and stronger over the upstream rim.Observational cruises around Blanes Canyon (northwest Mediterranean Sea) use velocity (measuredwith Acoustic Doppler Current Profiler, ADCP) and hydrographic (measured with Conductivity, Tem-preature, Depth instrument, CTD) samples taken in the upper 400 m of 59 stations in and around thecanyon to study horizontal and vertical circulation [Flexas et al., 2008]. Velocity data shows that nearthe shelf break, flow follows isobaths along canyon walls, with weak circulation in the canyon head. Inthe upper 100 m, circulation is cyclonic along the canyon mouth, but anticyclonic within the canyon.Vertical velocity is estimated in 10 m depth layers, using conservation of volume and balancing verticalvolume flux and net horizontal flux in each layer. In the upper 100 m, vertical velocities are negative(maximum velocity = -6.9 ×10−4 m s−1). From 100-200 m, vertical velocities are positive (maximumvelocity = 3.1 ×10−4 m s−1). Density sections suggest local downwelling/upwelling occurs along theupstream/downstream canyon walls between 100 m to 200 m depth.Meandering of the Northern Current (NW Mediterranean Sea) has been found to enhance verticalmotions inside Blanes Canyon and impact local net upwelling/downwelling events [Ahumada-Sempoalet al., 2013]. Northern Current meanders produce an oscillation of the vertical flow characterized by netupwelling when the onshore meander is located over the upstream side of the canyon followed by netdownwelling as the meander moves downstream [ibid.]. Net vertical fluxes are approximately two ordersof magnitude higher in the presence of a meander than in its absence.61.5 Study region; northwest Mediterranean SeaAs previously stated, flow dynamics in submarine canyons depend on forcing conditions, which canvary between canyon systems and individual canyons. For the purpose of this study, canyon topographyis based on the bathymetry of Blanes Canyon. Blanes Canyon is one of the few submarine canyons inthe Mediterranean Sea for which there have been multiple observational and numerical studies. Forcingconditions measured in previous studies are used to create a basic downwelling scenario similar to thatobserved in Blanes Canyon. However, changes to individual forcing parameters are made to betterunderstand the impacts to flow dynamics on any downwelling submarine canyon.Circulation in the Mediterranean Sea is characterized by a large cyclonic gyre of incoming Atlanticwaters (Northern Current) [Wurtz, 2012]. This flow can generate anticyclonic eddies on the right side(onshore side) and cyclonic eddies on the left side (offshore side), strongly affecting current patterns withinthe continental shelf and pelagic domain, respectively. Bottom morphology, wind forcing, river runoffand changes in regional climatology can alter current patterns, thus the main feature of Mediterraneancirculation is a high time-volume variability. Because the Mediterranean Sea is a semi-enclosed basinwith a narrow inlet/outlet into the Atlantic (the Strait of Gibraltar), tides are very small (i.e. maximumtidal amplitudes, away from the Strait of Gibraltar, are less than 10 cm [Tsimplis et al., 1995]) and arethus neglected in canyon studies of the region.Blanes Canyon (BC) lies along the Catalan coast, in the northwest Mediterranean Sea (Figure 1.2).General circulation around BC includes a baroclinic current (Northern Current), the path of which isgenerally a cyclonic flow along the continental slope [Millot, 1999]. The Northern Current is 30 to 50km wide and is characterized by a velocity profile of about 30 to 50 cm s−1 at the surface, decreasingapproximately linearly with depth to speeds of a few centimeters per second at several hundred metersdepth [Lapouyade and de Madron, 2001]. In fall, the core of the Northern Current has been observed asnarrow, lying over the shelf break with velocities of about 20 cm s−1 [Flexas et al., 2008].1.6 Research objectivesOf the relatively few studies of downwelling submarine canyons, there does not appear to be a clearagreement on flow dynamics. Some numerical models find antisymmetrical upwelling and downwellingoccurring in canyons, with downwelling being slightly stronger and net warmer/denser water everywherewithin canyons [Klinck, 1996; Skliris et al., 2001; 2002]. One observational study [Flexas et al., 2008] andone numerical model [Ardhuin et al., 1999] show net upwelling of water parcels. Some models exhibit7   6oW    0o     6oE   12oE   18oE   33oN   36oN   39oN   42oN   45oN   48oN InsetSpainFranceItalyMorocco−2000−2000−1000−1000−1000−500−500−500−150−15000   2oE  30’    3oE  30’    4oE   41oN  20’  40’   42oN  20’  40’   BarcelonaBlanesCanyonFigure 1.2: Location of Blanes Canyon, Northwest Mediterranean Sea.cyclonic circulation everywhere over a canyon [Klinck, 1996; Skliris et al., 2001; 2002], and other modelsexhibit anticyclonic circulation at the shelf break depth [Ardhuin et al., 1999; She and Klinck, 2000].In order to create an encompassing explanation of flow dynamics in downwelling canyons, it is impor-tant that current simulations are able to reproduce results of previous work. Then, from these simulations,the parameters that drive flow dynamics can be inferred. This study attempts to better understand theseand other differences between previous studies, as well as resolve the parameters that drive general flowdynamics in downwelling submarine canyons. The objectives of this study are:1) Determine if upwelling occurs in or around downwelling canyons. If so, where does upwelling occur,and how intense is upwelling?2) Determine what parameters affect flow dynamics. Particularly, which parameters impact:(a) horizontal circulation(b) vertical transport(c) density advection(d) passive tracer advectionThe core simulation is a model of Blanes Canyon, which replicates observations of Flexas et al. [2008].Simulations of Klinck [1996], She and Klinck [2000], and Skliris et al. [2001, 2002] are also replicated.8The key features this study attempts to reproduce are summarized in Table 1.1.The current model simulations have varying coastal jet placement. However, none of the simulationsinclude time-varying onshore/offshore jet displacements or meandering of the shelf break current, such asthose found in the studies performed by Alvarez et al. [1996], Jordi et al. [2005], and Ahumada-Sempoalet al. [2013]. While these studies have found time-varying current displacement to have significantimpacts on flow dynamics, this specification adds a level of complexity to the model that is beyond thescope of the current study. One goal of this study is to identify the parameters that impact flow dynamicsin a general, semi-steady state scenario. After these primary features are understood, future models canbuild upon the basic understanding and increase the complexity in simulations.Table 1.1: Features seen in previous studiesStudy Vorticity Vertical Velocity Temporal densitychangeKlinck [1996] Positive everywhere Net downwards (anti-symmetrical)Negative everywhere incanyon; positive on ei-ther side of the canyonShe and Klinck [2000] Negative over thecanyon, cyclonic at300 mNet downwards ——————Skliris et al. [2001,2002]Positive everywhere Net downwards (anti-symmetrical)Negative everywhere incanyon; positive on ei-ther side of the canyonFlexas et al. [2008] Negative over canyon Net upwards ——————9Chapter 2Flow Dynamics of DownwellingSubmarine Canyons2.1 Model descriptionSimulations were run with the Massachusetts Institute of Technology general circulation model (MIT-gcm) [Adcroft et al., 2004]. The model is rooted in incompressible Navier-Stokes equations; non-hydrostatic terms were used for all simulations.2.1.1 Domain and canyon bathymetryThe model domain is 120 km in the alongshore (x-direction), 90 km in the cross-shore (y-direction),and 1200 m in the vertical (z-direction) (Figure 1.1). Positive x points upstream (eastward), positive ypoints onshore (northward), and positive z points upwards.Minimum ocean depth is 20 m and stretches for ∼ 20 km in the cross-shore (hereafter referred to asthe inner shelf). Between the inner shelf and shelf break lies the outer shelf; in this region depth drops to150 m over 20 km. The slope extends from the shelf break (150 m) to an abyssal depth of 1200 m, andextends over 25 km in the cross-shore. The canyon topography was based on Blanes Canyon bathymetryshown by Flexas et al., [2008]. Geometric parameters were kept nearly constant in all model simulations(Table 2.1).10Table 2.1: Constant geometric parameters for model simulationsVariable Symbol ValueDepth at shelf break Hs [m] 150Depth at canyon head* Hh [m] 30Depth drop across canyon Hc [m] 950Depth of basin d [m] 1200Canyon length L [m] 16180Width at shelf break Wsb [m] 13005Width at mid-canyon W [m] 7660*Value is different for Klinck-like simulation(KL), which used a flat shelf; Hh = 150 m.2.1.2 Parameter specificationsTemperature, salinity, and nitrate stratification in the model were based on data from the NationalVirtual Ocean Data System (NVODS, http://ferret.pmel.noaa.gov/NVODS/UI.vm). Measured values atvarious depths of temperature and salinity were collected from the World Ocean Atlas 2005 1x1 degreeMonthly Means at approximately 40.5oN, 2.5oE. Values for nitrate were collected from annual means ofthe same data set at the same position. For high vertical resolution runs, values between data pointswere linearly interpolated. A linear equation of state was applied, with a thermal expansion coefficientof 2.0× 10−4 (oC−1) and a haline contraction coefficient of 7.4× 10−4.Horizontal resolution varies in alongshore and cross-shore directions, grid spacing is ∼ 1 km along eachboundary and decreases linearly to 200 m over the canyon. Overall, there is 200 m horizontal spacingbetween 33 km to 87 km in the alongshore, and 20 km to 80 km in the cross-shore. Ninety verticallayers are concentrated around the top of the domain, and vertical spacing ranges from 5 m (in the upper200 m) to 20 m (everywhere below 200 m).The Coriolis parameter was assumed constant (f = 1.0×10−4 s−1). Bottom friction was parameterizedwith a quadratic drag coefficient of 2.0×10−3. A vertical eddy viscosity of 1.0×10−2 m2s−1 was applied.The model used non-hydrostatic equation sets, with a time step of 40 seconds for all runs. Viscous (i.e.no-slip) conditions were applied at the sides and bottom of the domain, and an implicit free surface wasused. Heat and salt were laterally and vertically diffused with a Laplacian diffusivity of 1× 10−7 m2 s−1.A Smagorinsky harmonic viscosity factor [Smagorinsky, 1963] of 2.2 was applied (as recommended inGriffies and Hallberg [2000]. ) All tracers (i.e. temperature, salinity, and nitrate) were advected in timeusing a 3rd order direct space-time with flux limiting scheme.All model scenarios had a closed (no-slip) boundary along the coastal boundary. The offshore bound-11ary was open with an Orlanski [1976] radiation condition applied. All but 2 simulations used periodicalongshore conditions; these two simulations will be explained further in the next section.2.1.3 Model simulationsAll modelled scenarios were forced by applying a wind stress and/or body force over the domain.A body force was applied as an additional forcing to the momentum equations [Dawe and Allen, 2010].Fourteen scenarios were modelled based on minor changes in either forcing or domain stratification (Table2.2, Table 2.3). Two non-dimensional parameters were calculated to highlight incoming velocity (Rossbynumber, Ro):Ro = UfLand stratification (Burger number, Bu):Bu =NsbHsbfW .Dynamic parameters are incoming velocity, U , the Coriolis parameter, f , and stratification characterizedby the buoyancy frequency at shelf break depth (150 m), Nsb. Geometric parameters are length of thecanyon, L, depth at the shelf break, Hsb, and width across mid-canyon, W .To better understand the impact changes in stratification have on flow dynamics, a third parameter,a non-dimensional measure of vertical stratification, χ, was introduced. This new parameter measureduniformity of stratification and was calculated as the change in buoyancy frequency (N) divided by theaverage frequency near shelf break depth:χ = ∆N(z)[N¯(z)]−1,where N(z) is measured over a lengthscale of ± 75 m from the shelf break and N¯(z) is the averagestratification over the lengthscale. Negative χ values indicate stronger stratification in the shallowerlayers.In addition, placement of incoming coastal jets varied, vertically and horizontally, in previous studies(Table 2.3). These were recreated to ensure the dynamics of the original studies were reproduced.Core model simulations were based on the Flexas et al., [2008] observations. The first scenario(uniform wind, UW) consisted of a uniform wind stress (τ = -0.0626 N m−2) to drive a current alongthe surface, and a body forcing (applied near shelf break depth) to drive a current along the shelf break(similar to the Northern Current seen in the Mediterranean Sea). The current was accelerated over thefirst two model days, and then held at a steady state for the remainder of the simulation (steady stateindicates maximum flow velocity never varied more than 20%).12Table 2.2: Non-dimensional parameters for all model simulationsRossbynumber(Ro)Burgernumber(Bu)StratificationUniformity(χ)UW 0.22 0.46 -0.64OW 0.25 0.46 -0.64OBC 0.28 0.46 -0.64ST 0.25 0.46 -0.64KL 0.07 0.16 0SK 0.04 0.14 -0.46US 0.21 0.16 0HB 0.28 0.46 0She 0.04 0.28 -0.35SF 0.05 0.46 -0.64LRC 0.09 0.46 0SHR 0.15 0.14 -0.46BLRB 0.12 0.28 -0.63KHRB 0.22 0.46 0The second scenario (opposing wind, OW) consisted of two opposing wind stresses to drive surfaceflow, and a slightly stronger body forcing to drive the shelf break current. This setup was used toreproduce eastward flow seen over the continental shelf [Flexas et al., 2008]. To match the offshoredistance of the eastward flow, wind stresses were applied such that the offshore two-thirds of the domainhad a wind stress of τ = -0.0626 N m−2 and the nearshore one-third of the domain had a wind stress ofτ = +0.0376 N m−2. Again, the current was increased during the first two model days.Additional scenarios were modelled to either recreate flow dynamics seen in previous numerical studies(3 scenarios) or investigate other impacts to flow dynamics (9 scenarios).A Klinck-like (KL) scenario was modelled using a uniform stratification (N= 0.0016 s−1) and a flatshelf at 150 m (topography everywhere else in the domain remained the same) [Klinck, 1996]. A mostlyuniform flow was reproduced by removing all wind stress and y-dependence in the body forcing. However,flow over the flat shelf was weaker relative to flow along the continental shelf and over the open ocean.Speed of the body forcing was reduced to create a zonal velocity of about 10 cm s−1.A Skliris-like (SK) simulation has uniform stratification over three regions: 1) the upper 20 m (N =6.0 ×10−3 s−1); 2) from 20 m to 120 m (N = 1.5 ×10−3 s−1); 3) from 120 m to bottom depth (N=0.5×10−3 s−1) [Skliris et al., 2001]. Wind stress was removed, but y dependence on body forcing was kept.Body forcing was reduced to create a maximum zonal velocity of approximately 7 cm s−1.To simulate the She and Klinck [2000] study, a constant weak body forcing was applied over the upper13Table 2.3: Forcing flow for all model simulationsJet location Vertical shear Horizontal shearUW outer shelf surface intensified; negligible alongbottom topographyintensified over mid-outer shelf toshelf breakOW outer shelf surface intensified; negligible alongbottom topographyintensified over mid-outer shelf toshelf breakOBC outer shelf surface intensified; negligible alongbottom topography; secondary jetat shelf breakintensified over shelf breakST outer shelf surface intensified; negligible alongbottom topographyintensified over mid-outer shelf toshelf breakKL offshore uniform offshore uniform offshore of shelf break; weakflow over flat shelf (shelf break tocoast)SK shelf break intensified along bottom topography(150-600 m)intensified between shelf break and10 km offshoreUS offshore intensified at shelf break depth(150 m); negligible along continen-tal slopeintensified 5 km offshore of shelfbreakHB offshore intensified at shelf break depth(150 m); negligible along continen-tal slopeintensified 7 km offshore of shelfbreakShe coastal surface intensified intensified near inner shelfSF coastal surface intensified intensified near inner shelfLRC offshore intensified at shelf break depth(150 m); negligible along bottom to-pographyintensified 5 km offshore of shelfbreakSHR shelf break intensified along bottom topography(150-600 m)intensified between shelf break and10 km offshoreBLRB outer shelf surface intensified; negligible alongbottom topographyintensified over mid-outer shelf toshelf breakKHRB offshore uniform offshore; negligible alongcontinental slopeuniform 10 km offshore of shelfbreak; weak flow over outer shelf;negligible over inner shelf40 m, generating a maximum zonal speed of ∼13 cm s−1 (She). Stratification was varied over the entiredepth, based on the equation for density provided in the original study. Initial fields are temperature(T ):T (z, t = 0) = 10 - 0.5 exp( z110 )and salinity (S):S(z, t = 0) = 33 - 0.5 exp( z110 ),where z is depth below 0.To better understand the impact of open versus periodic boundary conditions, two scenarios withopen alongshore boundaries were modelled. In these simulations, Orlanski radiation conditions were14applied across both alongshore boundaries and the offshore boundary. The first scenario (open boundaryconditions, OBC) has the same geometry as the UW case, but both wind stress and body forcing wereincreased to recreate a similar zonal flow field as seen in the UW simulation. The second simulation(slanted topography, ST) used geometry that was similar to real world Blanes Canyon bathymetry (i.e.a slanted coastline and curvature within the canyon) (Figure F.4c). Forcing in this scenario was the sameas the OBC case.Two scenarios of constant surface forced (SF) flow were modelled, one forced by a wind stress andone forced with a surface body force applied to the upper 30 m. Results from these simulations were verysimilar, and will therefore be discussed as one example.A uniform stratification (US) scenario was modelled with the same geometry and forcing as the UWscenario, but stratification from the Klinck-like case was used (N=0.0016 s−1 everywhere). Similarly,a high Burger number (HB) scenario was modelled. This case is exactly the same as the uniformstratification scenario, but now with a uniform N value of 0.005 s−1.Four final scenarios were modelled using various parameter specifications from previous simulations.To generate a simulation with low Rossby and χ values (LRC), SK forcing was applied, but with thesame stratification as the HB case. The Skliris-like scenario was modelled again, but with a strongerforcing to generate a similar simulation but with a high Rossby number (SHR). Core case forcing andstratification was reduced to generate a simulation with low Rossby and Burger values (BLRB). Thebarotropic forcing was increased and run with core case stratification to produce high Rossby and Burgervalues (KHRB).For all simulations with a wind forcing, the wind stress was linearly ramped over the initial modelday, then held constant for model days 1-10 (wind magnitude, Table 2.4). All but one simulation with abody forcing (She) was linearly increased during the first model day. For these scenarios, a constant forcewas applied over model day 1-2 (body force magnitude; Table 2.4), followed by a linear decrease at thesame rate as the increase, down to a constant value which was maintained to the end of the simulation(Table 2.4). For the She simulation, a body force was linearly ramped over the initial model day, then aconstant body force was applied for model days 1-10.The two simulations with constant forcing (She and SF) are not steady in time and experience a largetime-dependence in their flow dynamics. However, none of the conclusions/trends discussed in this studyare dependent on the results from these two simulations.15Table 2.4: Temporal variations in forcing for all model simulationsWind magnitude(τ ; N m−2)Peak body forcemagnitude (m s−1)Constant body forcemagnitude (m s−1)UW 0.0626 0.315 0.047OW0.0626 (offshore)0.0376 (onshore)0.315 0.063OBC 0.13 0.53 0.133ST 0.13 0.53 0.133KL - 0.06 0.024SK - 0.09 0.029US 0.0626 0.315 0.079HB 0.0626 0.315 0.047She* - 0.18 -SF 0.0626 - -LRC - 0.09 0.032SHR - 0.3 0.105BLRB 0.0313 0.15 0.023KHRB - 0.18 0.0632.1.4 Result calculationsTransport calculations were used to estimate the volume of water exchanged vertically and horizontallyin the domain. An initial plane along the canyon axis divides the canyon into an upstream and downstreamhalf (Figure 2.1). Zonal flux was calculated across this plane from surface to shelf break depth, and fromthe canyon mouth to coastal boundary (U3). Meridional flux was calculated across two planes that liealong the canyon mouth; one in the upstream (V2) and one in the downstream (V3). Again, flux wascalculated from surface to shelf break depth. Finally, two planes were used to calculate vertical fluxat shelf break depth. These planes extend from the canyon head to canyon mouth and split across thecanyon axis (upstream = W1, downstream = W2). Net vertical flux was calculated by summing fluxacross these two planes. Flux across all planes was found by multiplying velocity of each grid cell by areaof each grid cell and summing over the entire plane.To better understand overall flow patterns, float particles were introduced at various positions inthe model domain. Particle trajectories were tracked from model days 2 through 10, with new particlepositions collected every six hours. The numerical model printed variable outputs twice a day, a fourth-order Runge-Kutta algorithm was then applied to interpolate particle movement more frequently [Daweand Allen, 2010].Relative vorticity in the basin can be expressed as:ζ = δVδx −δUδy ,1610 20 30 40 50 60 70 80 90 100 110−1200−1000−800−600−400−2000Across−shore (km)Depth (m)Transport Planes  V1 V4V1W2 W1V4   FlowPosition: shelf breakU7U5 U1U6V6 V5U4 U2U3W3W4V3 V2V8 V7Figure 2.1: Planes used for transport calculations.where ζ is the vertical component of vorticity, V is the meridional velocity, and U is zonal velocity.Absolute vorticity was measured as the relative vorticity divided by Coriolis parameter, f .Average zonal velocity across the canyon axis at shelf break depth (150 m) was used to calculate asecond Rossby number (RU¯can). This velocity is calculated as:U¯can =ΣU(y)∆yL ,where U is taken as the zonal velocity in each meridional grid point that lies along the canyon axis, and∆y is the horizontal distance the zonal velocity is applied. A canyon Rossby number was calculated as:RU¯can =U¯canfL .Density was calculated for all model simulations as average density in the canyon across the shelfbreak plane (W1 and W2). This value was averaged during the approximate advection dominated phase(averaged from model day 4-10). Average density was subtracted from initial density at shelf break depthto give an average density anomaly in the canyon.Changes in density difference within the canyon relative to away from the canyon were determined bycalculating a density difference anomaly. This anomaly was found by subtracting a background densitydifference (calculated as a 5 grid point average along the downstream boundary) from the difference atgrid points of similar isobaths:ρanom = ρdifference(xi, yi, z)− ρboundary(yi, z),where xi and yi are alongshore and cross-shore points (respectively) that are ± 5 m of the isobath usedto calculate the background density difference (ρboundary(yi, z)).17Nitrate concentration was used as a passive tracer in the model. An average nitrate concentrationwas also calculated as the average nitrate value in the canyon across the shelf break plane (W1 and W2)during the advection dominant phase (model days 4-10). The average nitrate concentration is subtractedfrom the initial nitrate concentration at shelf break depth to give an average nitrate anomaly in thecanyon.2.2 Results2.2.1 Flow evolutionAll model scenarios show an initial time-dependent response to model forcing, similar to that de-scribed by Allen and Durrieu de Madron [2009], which lasts approximately two to three days (Figure 2.2;Figure F.1). During this phase, zonal and vertical flux exhibit a negative ramping everywhere in thedomain. In all but two simulations, vertical flux across the downstream plane (W2; Figure 2.1) reversesat approximately day 1, and continues towards a maximum positive value by day 2-2.5. In these simu-lations, magnitude of meridional flux over the canyon gently increases across both planes, being positive(onshore) in the upstream (V2; Figure 2.1) and negative (offshore) in the downstream (V3; Figure 2.1)until reaching a maximum near the end of the time-dependent phase. In the simulations with a coastal jet(She and SF; Figure F.1h and F.1i, respectively), vertical flux is downwards across both the upstream anddownstream planes until day 1. After this, negative flux across the downstream plane weakens in time,while negative flux across the upstream plane continues to strengthen. For these scenarios, upstreamonshore flux and downstream offshore flux strengthen during the model simulation.The time-dependent phase is followed by an advection dominated phase. During this phase, zonalflux stays within approximately 2-17% of the maximum value reached during the time-dependent phasefor most simulations. Meridional flux also gently fluctuates, always being positive in the upstream andnegative in the downstream for all model scenarios. The two surface forced simulations (She and SF)show a zonal flux that continuously increases during the model simulation, with a final zonal flux thatis approximately 50% stronger than flux at the end of the time-dependent phase. This indicates neitherscenario may be reaching an advection dominated phase.Vertical flux time dependence varies between model simulations, with 3 primary patterns emerg-ing (Figure F.1). Firstly, vertical flux varies between positive and negative transport over both theupstream and downstream plane of the canyon, with flux values being roughly the same in the up-stream/downstream. This pattern is seen in the UW and OW simulations. Secondly, flux across the180 1 2 3 4 5 6 7 8 9 10−8−4048 x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesUW case  −9−4.504.59x 104Vertical Flux [m3 /s]U3V2V3W1W2Figure 2.2: Time series of horizontal and vertical flux directly over the canyon for core (UW) simulation.U3 indicates zonal flux across the canyon axis (from canyon head to canyon mouth). V2 and V3 aremeridional flux along the canyon mouth from the upstream rim to canyon axis, and from the canyonaxis to downstream rim, respectively. All horizontal fluxes are measured from surface to shelf breakdepth. W2 and W3 are vertical flux across the shelf break depth plane (150 m) everywhere within thecanyon, from the upstream rim to canyon axis and from the canyon axis to downstream rim, respectively.Negative U, V, and W values indicate westward, offshore, and downwards fluxes.upstream plane is mirrored across the downstream plane, i.e. as magnitude across one plane increases,magnitude across the other plane increases well. In 6 simulations (ST, KL, SK, US, HB, SHR) thispattern occurs with upstream transport always positive and downstream transport always negative. In4 runs (OBC, LRC, BLRB, KHRB) the above pattern occurs, but flux across the upstream/downstreamplanes does cross between positive and negative values during model days 4-6. Thirdly, simulations witha coastal jet (She and SF) exhibit strengthening negative flow across the upstream plane and weakeningnegative flow across the downstream plane. In the She case, flux across the downstream plane becomespositive around model day 4. In the SF case, flux over the upstream plane begins to weaken aroundmodel day 7.The core simulation was extended by 10 more model days to determine how steady flux is in time(Appendix D). Meridional and vertical fluxes (V2, V3, W1 and W2) were averaged from days 10-20 andvalues vary approximately 90% between the core (UW) and extended core simulations (zonal flux acrossthe U3 plane varied only 4% between the simulations). The steady zonal current developed an instabilityaround day 12, causing fluctuations in horizontal and vertical flux. To ensure aliasing is not occurring19with 12-hour model output, another 10-day UW simulation was run with model output written every3 hours (Appendix E). Small differences in flux estimates are seen during the time-dependent phase.Differences during the advection-dominant phase are less than 10%.2.2.2 Circulation in the canyonModel simulations exhibit three types of horizontal circulation: 1) formation of an anticyclonic eddywithin the canyon, 2) cyclonic circulation everywhere within the canyon and 3) weak circulation every-where within the canyon. The evolution of the first two horizontal flow patterns are discussed below.Firstly, the anticyclonic circulation is detailed, followed by a description of the cyclonic circulation.For high Burger number simulations (particularly, UW, OW, OBC, ST, HB, KHRB) horizontal flowduring the time-dependent phase is cyclonic over the canyon (Figure 2.3a, left). Towards the end of thisphase, flow along the downstream rim becomes stronger relative to the upstream rim (Figure 2.3b, left).After one more model day (by day 3), flow in the canyon head becomes anticyclonic and this patternpersists for the remainder of the model simulation (Figure 2.3c, left). Vertical velocity during the first dayof simulation is negative everywhere in the canyon, and strongest in the upstream. As the flow evolves,a region of positive vertical velocity appears in the downstream half of the canyon and moves toward thedownstream corner of the canyon mouth.During the time-dependent phase, flow becomes faster over the canyon axis and impinges on thedownstream wall. Thus, the shelf break jet splits as it reaches the downstream rim. Shoreward of the jet,an anticyclonic eddy forms in the canyon and persists during the advection dominated phase (Figure 2.4a).Approximately 20 particle drifters were used to trace circulation around the anticyclonic eddy, with5 particles used to highlight patterns in various regions (Figure 2.5). Particles flowing over the upstreamrim, near shelf break depth, interact with the anticyclonic eddy. After passing the upstream rim (between140-150 m depth), particles that fall to depths of 200 m or deeper are trapped in the eddy. Particles thatdrop to depths shallower than 200 m make one loop inside the eddy, then ascend over the downstreamrim. It takes all particles approximately 2.5 days to make one loop around the eddy. Particles initiatedfurther upstream of the canyon do not get caught in the eddy after dropping into the canyon. Instead,these particles make a slight descent into the canyon and move slightly onshore, then cross the canyonaxis and continue offshore, ascending along the downstream rim.For low Burger number simulations (particularly, KL, SK, US, SHR), the cyclonic circulation thatforms during the time-dependent phase strengthens as zonal flow accelerates and remains cyclonic (Fig-ure 2.3, right and 2.4b). Similar to the cases with anticyclonic circulation, vertical flow is negative20     Alongshore?Cross-shore?Anticyclonic case?Circulation? Time: day 1.5?     Alongshore?Cross-shore?Cyclonic case?Circulation? Time: day 1.5?(a) day 1.5 circulation     Alongshore?Cross-shore?Anticyclonic case?Circulation? Time: day 2.5?     Alongshore?Cross-shore?Cyclonic case?Circulation? Time: day 2.5?(b) day 2.5 circulation     Alongshore?Cross-shore?Anticyclonic case?Circulation? Time: day 3.5?     Alongshore?Cross-shore?Cyclonic case?Circulation? Time: day 3.5?(c) day 3.5 circulationFigure 2.3: Horizontal and vertical circulation at shelf break depth during the time-dependent phase on(a) day 1.5, (b) day 2.5, and (c) day 3.5. Pink shading indicates downwards velocity and teal shadingindicates upwards velocity. Circulation for a simulations with anticyclonic circulation (left) and cycloniccirculation (right) are shown.21Alongshore (km)Cross−shore (km)UW caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(a) Anticyclonic circulationAlongshore (km)Cross−shore (km)SHR caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(b) Cyclonic circulationFigure 2.4: Horizontal velocity vectors at shelf break depth (150 m) in (a) simulation with anticycloniccirculation (UW) and (b) simulation with cyclonic circulation (SHR). Vectors are averaged over a 3 modelday period during the advection phase (model day 5-8).22Figure 2.5: Trajectory for shelf break drifter particles released in a simulation with anticyclonic circula-tion; 5 (out of 20) sample particles are plotted. Trajectories are plotted for model days 2-10. Scale barand color of individual markers indicates vertical depth change from initial marker depth (first markerin the upstream). Initial particle depths: ? and red line = -150 m,  and purple line = -140 m,  andpink line = -150 m, / and blue line = -150 m, . and yellow line = -195 m.everywhere within the canyon and strongest in the upstream. However, as the flow evolves, positivevertical velocity begins to appear in the downstream half of the canyon where it remains (it does not getpushed offshore) (Figure 2.3a-c, left). For these cases, horizontal flow is strongest along the canyon wallsand weaker across the canyon axis.Twenty particle drifters in these simulations highlight the cyclonic circulation seen in the canyon(Figure 2.6). As particles cross the upstream rim, they descend and move onshore. This is followed byan ascent and offshore movement after crossing the canyon axis. Particles entering the canyon near thecanyon mouth, or offshore of the canyon mouth (at 130-200 m depth), experience a small (less than 20 m)ascent as they cross the upstream rim and then approximately 50 m before reaching the canyon axis.These particles slowly ascend after crossing the canyon axis.For the purposes of this study, results focus on flow dynamics during the advection dominant phase.Results in the following sections are time-averaged model output. Based on oscillations in the vertical23Figure 2.6: Trajectory for outer shelf drifter particles released in a simulation with cyclonic circulation;5 (out of 20) sample particles are plotted. Trajectories are plotted for model days 2-10. Scale bar andcolor of individual markers indicates vertical depth change from initial marker depth (first marker in theupstream). Initial particle depths: ? and red line = -77 m,  and purple line = -200 m,  and pink line= -150 m, / and blue line = -60 m, . and yellow line = -144 m.flux time series (Figure 2.2), results are averaged from model days 5-8.2.2.3 Comparison to previous studiesCurrent simulations reproduced canyon circulation features seen in previous studies (Table 1.1).Klinck [1996] was reproduced in the KL simulation. In this low Rossby number, low Burger numberand low |χ| simulation, the cyclonic circulation, antisymmetrical vertical velocity and and density changepattern (positive density anomaly outside the canyon mouth) seen in the original study was reproducedin the current model. Similarly, Skliris et al., [2001; 2002] was replicated in the SK simulation. Cycloniccirculation, antisymmetrical vertical velocity and positive density anomalies away from the canyon werereproduced in this low Rossby number, low Burger number, and intermediate |χ| simulation.She and Klinck [2000] was mostly reproduced in the She simulation. In this low Rossby number, inter-mediate Burger number and intermediate |χ| simulation, net downwards vertical velocity was reproduced.24However, a weak cyclonic circulation was seen at all depths in the canyon. This is different from theoriginal study, which saw anticyclonic circulation over the canyon and cyclonic circulation at 300 m andbelow. Multiple scenarios with varying Rossby, Burger, and |χ| values (UW, OW, OBC, ST, LRC, SHR)exhibit anticyclonic vorticity at shelf break depth and cyclonic vorticity deeper in the canyon, similar tothat seen in She and Klinck [2000]. Flexas et al., [2008] was reproduced in the UW and OW simulations.In these high Rossby number, high Burger number, and high |χ| simulations, the anticyclonic circulationand periods of net positive vertical velocity similar to that seen in the observations were replicated.2.2.4 Vorticity in the canyonAs previously discussed, all model scenarios either form an anticyclonic eddy in the canyon afterthe time-dependent phase (Figure 2.4a), or have cyclonic circulation in the canyon throughout modelsimulation (Figure 2.4b). Looking at shelf break depth circulation, 6 simulations exhibit an anticycloniceddy, 4 simulations show cyclonic circulation, and 4 other simulations show weak circulation at this depth.Table 2.5: Absolute vorticity and canyon circulation for all model simulationsAbsoluteVorticity (1/f)CanyonCirculationShelf breakcirculationUW -0.55 Anticyclonic (50-500 m) AnticyclonicOW -0.54 Anticyclonic (0-500 m) AnticyclonicOBC -0.50 Anticyclonic (75-400 m) AnticyclonicST -0.40 Anticyclonic (150-450 m) AnticyclonicKL 0.2 Cyclonic (0-400 m) CyclonicSK 0.34 Cyclonic (all depths) CyclonicUS 0.97 Cyclonic (all depths) CyclonicHB -0.26 Cyclonic (200-500 m) AnticyclonicShe 0.08 Cyclonic (all depths) WeakSF 0.07 Cyclonic (all depths) WeakLRC -0.09 Anticyclonic (100-350 m) WeakSHR 0.71 Cyclonic (all depths) CyclonicBLRB -0.1 Anticyclonic (100-350 m) WeakKHRB -0.14 Anticyclonic (100-300 m) Anticyclonic*Absolute vorticity is taken as maximum vorticity in the canyon head,away from canyon rims, at shelf break depth.Simulations with anticyclonic circulation display negative vorticity within the canyon, but opposingpositive vorticity along the canyon walls (Figure 2.7a). Simulations with cyclonic circulation have theopposite feature, positive vorticity within the canyon, but negative vorticity along canyon walls (Fig-ure 2.7b). This reversal of vorticity along bottom topography is due to friction between water parcelsand canyon walls. The simulation in which the anticyclonic eddy appears only at a depth below the shelf25(a) negative in canyon vorticity(b) positive in canyon vorticityFigure 2.7: Cross-section of vorticity at mid-canyon in (a) simulation exhibiting negative vorticity (UW)and (b) simulation exhibiting positive vorticity (SK).26break (HB) has negative vorticity at shelf break depth (Table 2.5).2.2.5 Upwelling in a downwelling canyonVertical velocityTwo main flow patterns are seen in plane views of vertical velocity. In the first pattern, enhanceddownwards (upwards) velocity is confined to the upstream (downstream) corner of the canyon mouth atshelf break depth (Figure 2.8a). This pattern occurs in simulations with weak or negative vorticity atshelf break depth (Table 2.5). One exception is the HB scenario, which exhibits varying positive andnegative vertical velocity patterns everywhere within the canyon.In the second vertical flow pattern, vertical velocity presents a more antisymmetric pattern, similarto that seen in previous studies [Klinck, 1996; Skliris et al., 2001; 2002]. In these simulations, regionsof positive and negative vertical velocity are split along the canyon axis from canyon head to canyonmouth, with negative velocity in the upstream and positive velocity in the downstream (Figure 2.8b).This pattern occurs in simulations with strong, cyclonic vorticity (Table 2.5).In all model scenarios, regions of enhanced upstream negative velocity are stronger than downstreamregions of positive velocity. All simulations also exhibit a background negative velocity in regions awayfrom the canyon.Using the 12-hourly flux time series, periods of positive vertical flux across 3 planes (100 m, 150 m,and 600 m) in the canyon (i.e. everywhere between canyon walls from the canyon head to mouth) werecalculated over the 10 day model period (Figure 2.9). Net upward flux does occur in various downwellingcanyon simulations. Note, only 4 scenarios do not see net upwelling at any time (She, SF, SHR, BLRB).Net upwards flux most commonly occurs across the 600 m plane, and least often across the 100 m plane.Periods of net upwards flux mostly occur during the advection dominated phase. The longest occurrenceof net upwards flux appears in the OBC simulation, there is a period of net upwards flux that lasts 2.5model days. Overall, the OBC scenario exhibits the most occurrences of net upwards flux across the150 m and 600 m planes.To understand the three-dimensional movement of flow in and around the canyon, particle drifterswere initiated upstream of the canyon at varying depths in one of the core simulations (UW case); 70particles were released near and slightly offshore of the canyon (Figure 2.10). Particles in the upper 20 mexperience relatively no change in depth as they cross over and downstream of the canyon. Particlesmoving over the canyon head descend over the upstream rim and ascend over the downstream with a27−1000−800−600−400−200Alongshore (km)Cross−shore (km)UW caseVertical Velocity [m/s]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−2.5−2−1.5−1−0.500.511.522.5x 10−3(a) enhanced vertical velocity along canyon mouth−1000−800−600−400−200Alongshore (km)Cross−shore (km)SHR caseVertical Velocity [m/s]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−6−4−20246x 10−3(b) antisymmetrical vertical velocity in canyonFigure 2.8: Vertical velocity at shelf break depth (150 m) in (a) simulation with enhanced vertical velocityalong canyon mouth (UW) and (b) antisymmetrical vertical velocity along canyon axis (SHR).280 1 2 3 4 5 6 7 8 9 10UWOWOBCSTKLSKUSHBSheSFLRCSHRBLRBKHRBTime (Days)Points of net upwelling  100 m150 m600 mFigure 2.9: Times of net upwards flux across 3 vertical planes for all model simulations. Net upwardsflux is plotted if larger than a minimum value of 1000 m3s−1.net offshore and downward movement from their original position. Over the outer shelf (depths between30-120 m), particles move fastest, descending along the upstream rim, lifting along the canyon axis, andmoving over the downstream rim. Upon exiting the canyon, these particles are further offshore and deeper.At these depths, particles move furthest downstream for all particles in the domain. Downstream andaway from the canyon, these particles continue to move slightly offshore and deeper with time. Particlesnear shelf break depth and below (120-250 m), that are not trapped in the anticyclonic eddy, move similarto those over the outer shelf, but slower. Around 250 m to bottom depth, particles descend over theupstream rim, ascend over the downstream rim, and continue moving downstream. Particles at thesedepths descend much deeper into the canyon relative to shallower particles, due to weaker stratificationat these depths.Particle trajectories are affected far offshore of the canyon (not shown). Trajectories curve shorewardwhen passing the upstream portion of the canyon and offshore along the downstream region. Curvatureof trajectory paths is seen in particles as far away as the offshore boundary. The degree of curvature andchange in depth decreases offshore of the canyon; particle velocity also decreases further offshore.29Figure 2.10: Particle trajectories for all depths in a basic simulation (UW). This is a 3-dimensional view ofthe model domain. The view is from the upstream boundary looking down at the canyon and towards thedownstream. The coast is to the right and open ocean to the left. Particles were initiated approximately5 km upstream of upstream canyon rim. Particles generally strongly descend and then weakly ascend asthey travel past the canyon (flow is into the page).Density anomalyDensity anomalies were calculated as density variations (averaged over days 5-8) relative to initialdensity profiles. Similar to vertical velocity, two distinct anomaly patterns appear. In the first pattern,density anomaly is negative everywhere in the canyon domain (Figure 2.11a). At all depths, anomalies arestrongest along bottom topography and weaken towards the offshore. This pattern is seen in simulationswith a coastal or outer shelf jet (UW, OW, OBC, ST, She, SF, BLRB; Table 2.6).In the second pattern, there are strong negative anomalies along bottom topography, but there arealso positive anomalies away from the canyon (Figure 2.11b). This pattern is seen in simulations witha shelf break or offshore jet (KL, SK, US, HB, LRC, SHR, KHRB); the depth range of positive densityanomalies varies (Table 2.6). For the majority of these simulations, positive anomalies do not extenddown to shelf break depth (SK, US, HB, SHR, KHRB), but in two simulations positive anomalies doextend down to shelf break depth and below (KL, LRC).30−1000−800−600−400−200Alongshore (km)Cross−shore (km)UW caseDensity Difference [psu]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−0.4−0.35−0.3−0.25−0.2−0.15−0.1−0.050(a) everywhere negative density anomalies−1000−800−600−400−200Alongshore (km)Cross−shore (km)KL caseDensity Difference [psu]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−12−10−8−6−4−2024x 10−3(b) positive density anomalies near canyonFigure 2.11: Density anomaly at shelf break depth (150 m) in (a) simulation with pattern 1: negativedensity anomalies at all depths (UW) and (b) simulation with pattern 2: positive density anomalies nearthe canyon (KL).31Table 2.6: Positive density anomaly depth range for all model simulations. Pattern 1 density anomalieshad no positive values. Pattern 2 density anomalies had positive values.Depth of positivedensity anomalyJet locationUW - outer shelfOW - outer shelfOBC - outer shelfST - outer shelfKL surface to 200 m offshoreSK surface to 120 m shelf breakUS surface to 100 m offshoreHB surface to 100 m offshoreShe - coastalSF - coastalLRC surface to 150 m offshoreSHR surface to 100 m shelf breakBLRB - outer shelfKHRB surface to 120 m offshoreDensity difference anomalyAs shown in vertical velocity and density difference, regions with downwelling canyons exhibit abackground downwelling flow, with both negative vertical velocity and negative density changes awayfrom the canyon region. To determine what extra effect a canyon has in a downwelling region, a densitydifference anomaly was calculated.Downwards density advection is enhanced in all canyon scenarios (Figure 2.12). Two patterns areseen, however, these patterns do not line up exactly with density anomaly patterns. In the first pattern,downwards density advection is strongest in the canyon head and along the canyon axis (Figure 2.12a);this pattern is seen in half (7) of the simulations (UW, OW, OBC, ST, HB, SF and LRC). In the secondpattern, downwards density advection is strongest along bottom topography (Figure 2.12b); this patternis seen in the other half of the simulations (KL, SK, US, She, SHR, BLRB and KHRB). Independentof density advection pattern, 8 simulations exhibit positive density difference anomalies away from thecanyon. In these cases, weaker downwelling (positive density difference anomalies) occurs along eitherthe upstream (OW) or downstream (SF, LRC and BLRB) corner of the canyon mouth, or along bothcorners of the canyon mouth (KL, US, She and SHR).32−1000−800−600−400−200Alongshore (km)Cross−shore (km)UW caseDensity Difference Anomaly [psu]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−0.3−0.25−0.2−0.15−0.1−0.050(a) Enhanced downwelling everywhere in canyon−1000−800−600−400−200Alongshore (km)Cross−shore (km)KL caseDensity Difference Anomaly [psu]  10 20 30 40 50 60 70 80 90 100 1101020304050607080−10−8−6−4−202x 10−3(b) Enhanced downwelling along canyon headFigure 2.12: Density difference anomaly at shelf break depth (150 m) in (a) simulation with pattern 1:enhanced density advection everywhere in the model domain (UW) and (b) simulation with pattern 2:enhanced downwelling within the canyon and weaker downwelling near the canyon mouth (KL).332.2.6 Nitrate anomalyAll model simulations included a passive tracer (nitrate concentration) that was initialized with thesame vertical variation for all runs. This provided one parameter that was the same in all simulations,allowing for better comparisons between model runs. Again, anomalies were calculated as changes betweenthe initial nitrate profile and the day 5-8 averaged model output nitrate profile.Similar to vertical velocity and density anomalies, two patterns appear. With the exception of 2cases (OBC and ST), simulations that exhibit the pattern 1 density anomaly exhibit the same patternfor nitrate anomaly; negative everywhere within the canyon and strongest along bottom topography(Figure 2.13a). Similarly, simulations that show pattern 2 density anomalies also exhibit negative nitrateanomalies along bottom topography and positive anomalies a few kilometers offshore (Figure 2.13b).The 2 simulations with open boundary conditions (OBC and ST) exhibit a pattern similar to pattern 2,however positive nitrate anomalies occur 5-20 km offshore (Figure F.7c-f).(a) negative nitrate anomalies(b) positive nitrate anomalies away from canyonFigure 2.13: Nitrate anomaly 10 km upstream of canyon axis (left) and along canyon axis (right) in (a)simulation with pattern 1: negative nitrate anomalies at all depths (UW) and (b) simulation with pattern2: positive nitrate anomalies near the canyon (KL).342.3 Discussion2.3.1 Upwelling in downwelling canyonsThere are various ways in which upwelling can be defined. Firstly, upwelling can be characterized asthe net upwards movement of water in a region. Secondly, upwelling can be described as the net onshoremovement of dense, cold (usually nutrient-rich) deep ocean water to the shallower coastal ocean. Coastalupwelling typically involves both processes working together, i.e. as surface waters are pushed offshore,deep ocean water is brought up from the depth to replenish surface waters along the coast. However,upwelling along the coast does not always occur following this same process.During two observational cruises around Blanes Canyon, Flexas et al., [2008] used velocity and hy-drographic samples to calculate vertical flux in the canyon. The authors estimated that at approximately100 m depth and shallower, vertical velocities were negative; below the thermocline (∼100-200 m depth),vertical velocities were positive. The authors concluded that upwelling did occur in Blanes Canyon, witha maximum near the shelf break depth and extending between 100-200 m. Ardhuin et al., [1999] modelledan upwelling cell beneath a trapped anticyclonic eddy. In this study, offshore deep waters from 300-500 mdepth were lifted at the canyon wall and pulled out to the open ocean in the 200-300 m layer.Plan view images of time-averaged vertical velocity in the current simulations do not directly revealnet upward movement of water in any canyon scenarios. All simulations do show regions of both upwardsand downwards vertical velocity, however, downwards motion appears to always be dominant. Results ofsnapshots of net vertical velocity across 3 planes indicate that net upwards displacement of water doesoccur in the majority of simulations (Figure 2.9). In most cases this upwards displacement is brief andcommonly occurs at depth. However, the OBC case shows an extended period of net upwards velocityacross the 150 m plane from model day 4-6, the beginning of the advection dominated phase. This periodof net upwards velocity at shelf break depth can be compared to observations in Flexas et al. [2008]. Inthe current study, a period of net upwelling may be occurring, but the time-mean flow of the advectionphase indicates an overall net downwelling.The prevalence of upwards displacement across the 600 m plane indicates a possible upwelling cellsimilar to Ardhuin et al., [1999], in which deep water is upwelled along canyon walls, but returns tothe offshore before crossing shelf break depth. Increased stratification has been found to reduce verticaltransport [Klinck, 1996]. For all current simulations, stratification is weaker with depth, which is likelythe reason vertical exchange shows more variation at depth. The irregular occurrences of net upwardsdisplacement across vertical planes, even under semi-steady circulation, indicates observational studies35may not be detecting the time-mean flow dynamics occurring in submarine canyons.Though vertical velocity reveals that upward displacement of water does occur in downwelling canyons,density and nitrate anomalies indicate there is downwards advection of physical properties. Both densityand nitrate exhibit regions of positive advection, however these regions occur away from the canyon andpositive advection is weaker than negative advection.Previous studies have found that submarine canyons in downwelling regions enhance coastal down-welling [Klinck, 1996; She and Klinck, 2000; Skliris et al., 2001; 2002]. Anomalies of density difference incurrent simulations show that downwelling is enhanced everywhere within the canyon and over the lowercanyon, with downwelling being strongest around the canyon axis. In the upper 100 m, relatively weakdownwelling occurs over the mid-canyon. This region of weaker downwelling appears as a relative liftingof isopycnals from the downstream to upstream canyon rim (Figure 2.14a). Lifting isopycnals is oftena characteristic of upwelling occurring in a region. However, these are instantaneous profiles of what isoccurring in the canyon. Using profiles of density difference and density difference anomaly it can be seenthat this relative lifting of isopycnals is actually a region of relatively weak downwelling. This is anotherindicator that some studies may not be observing all the time-mean flow dynamics.2.3.2 Parameter effectsStratification has been found to have significant impacts on vertical and cross-shore transport [Klinck,1996]. Previous studies have compared forcing responses between weakly and strongly stratified domains.However, these studies use either a uniformly stratified domain [Klinck, 1996], or a domain in whichstratification varied in only 3 regions [Skliris et al., 2001; 2002]. Other studies have varied stratificationin the canyon domain [Ardhuin et al., 1999; She and Klinck, 2000], but the effects of vertical variationin stratification have never before been studied. Thus, the non-dimensional parameter χ was introducedin this study to investigate the impacts vertical changes in stratification have on flow dynamics. Weak χvalues indicate stratification is more uniform in the domain. Negative χ values indicate there is strongerstratification variation at shallower depths.Rossby number and Burger number are non-dimensional parameters that are commonly used to mea-sure the regional significance of Coriolis accelerations and stratification, respectively. These parameterscan also be used to determine scales between observational, laboratory, and numerical models. In thissection, Rossby number, Burger number, χ values, and incoming jet location are used to determine whichregional parameters impact various flow dynamics.36(a) simulation with anticyclonic circulation(b) simulation with cyclonic circulationFigure 2.14: Isopycnal cross-sections at mid-canyon in (a) simulation with anticyclonic circulation (UW)and (b) simulation with cyclonic circulation (KL).37Circulation in the canyonPatterns in horizontal circulation reveal Burger number to be an important parameter in determiningvorticity within the canyon (Figure 2.15a). Four simulations with low Burger numbers (SHR, US, SK,KL) exhibit positive vorticity and cyclonic circulation at shelf break depth. Six simulations with highBurger numbers (UW, OW, OBC, ST, HB, KHRB) exhibit negative vorticity and anticyclonic circulationnear shelf break depth. Four simulations with varying Burger numbers (BLRB, She, SF, LRC) showweak vorticity and circulation. Rossby number also appears to have an impact on vorticity magnitude(Figure 2.15b). For the simulations with cyclonic circulation, as incoming Rossby number increasesvorticity magnitude also increases. This trend is not as apparent for the simulations with anticycloniccirculation.The importance of the Burger number and its impact on circulation within the canyon is highlightedin the US and HB cases. These two simulations have the same model set-up, with the only differencebeing their buoyancy frequency (N) value. The US simulation has a lower Burger number and cyclonicshelf break circulation, while the HB simulation has a higher Burger number and anticyclonic shelf breakcirculation.Anticyclonic circulation scenarios exhibit strong flow across the canyon axis and weaker flow alongcanyon walls and rims during the time-dependent phase, creating a negative shear in horizontal flow. Inthese simulations, flow is negligible along bottom topography (including the outer shelf) and flow turnsweakly into the canyon but does not follow canyon isobaths. This causes flow crossing the canyon axisto impinge on the downstream wall and a small portion moves onshore due to negative vorticity in thecanyon. This onshore flow, and compressing isopycnals, generates a trapped anticyclonic eddy within thecanyon (Figure 2.4a), which can persist to depths of 500 m.Cyclonic circulation scenarios have weakest horizontal flow across the canyon axis and strongest flowalong canyon walls and rims (Figure 2.4b). This creates a positive shear in horizontal flow and enhancesthe tendency for cyclonic circulation. In these simulations, flow across the canyon axis is relativelyweak and water parcels follow canyon isobaths, moving onshore in the upstream, and offshore in thedownstream (Figure 2.4b).Location of the incoming zonal jet is affected by stratification variations in the domain (Figure 2.16).Several model simulations use the same forcing conditions and different domain stratification, e.g. UW(SK) and US or HB (LRC) have the same forcing conditions with differences in χ values. The simulationswith uniformly stratified domains (lower χ; US, HB, LRC) have a zonal jet that is located further offshore38UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB Jet location  (a)UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB Shelf break vorticity  (b)Figure 2.15: Effect of (a) Burger number and (b) incoming Rossby number on canyon vorticity for allmodel simulations.39relative to their counterparts with high χ values (UW, SK). Simulations forced by wind stress have weakcoastal flows, regardless of domain stratification.UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB Jet location  Figure 2.16: Zonal jet location upstream of the canyon.As the body force is applied to model simulations, an onshore flow occurs and tilts isopycnals down-wards. This leads to surface intensification of the zonal jet. Baroclinicity increases with increasingstratification in the upper water column. However, downwelling tends to reduce stratification over theshelf, making the jet more barotropic. With weak near surface stratification (low χ), this leads to analmost barotropic jet which feels bottom friction fairly strongly and is therefore reduced in intensity. Insimulations with an offshore jet and low χ values, the zonal velocity is intensified at shelf break depthand negligible along continental slope topography (Table 2.3; KL, US, HB, LRC, KHRB). Strong nearsurface stratification (high χ) allows baroclinicity of the jet on the shelf, and thus less friction on it. Insimulations with an outer shelf jet and high χ values, zonal velocity is intensified near the surface andnegligible along bottom topography (Table 2.3; UW, OW, OBC, ST, BLRB).Until now, Rossby number has been based on incoming flow strength. However, a Rossby numberbased on flow across the canyon axis (RU¯can) may be more appropriate for looking at flow dynamicswithin the canyon. These values are compared to determine correlations between incoming and canyonaxis flow (Figure 2.17). Due to the more complex topography in the slanted canyon simulation (ST),it is suspected that RU¯can is overestimated for this scenario and is thus marked as a possible outlier insubsequent plots.For simulations with cyclonic circulation at shelf break depth, there is a relatively strong coupling40Shelf break vorticity  UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB (a) Incoming and canyon zonal flowFigure 2.17: Correlation between Rossby numbers based on incoming zonal flow and zonal flow integratedacross the canyon axis. Due to complex canyon topography, canyon Rossby number for ST is likelyoverestimated and ST is considered an outlier.between incoming and canyon axis flow speed. However, for anticyclonic circulation the coupling is weaker.The same incoming Rossby number results in a weaker canyon Rossby number. For the simulations withweak circulation, both Rossby numbers are small and not strongly correlated to each other.Flow patterns describe the stronger (weaker) coupling between incoming and canyon Rossby numbersin the cyclonic (anticyclonic) simulations. In the anticyclonic cases, the eddy is focused over the canyonaxis and flow in the canyon head is towards the upstream, while flow along the mid-canyon is towards thedownstream (flow between mid-canyon and canyon mouth is downstream and slightly stronger along thecanyon axis) (Figure 2.4a). This causes net zonal flow between the canyon head and mid-canyon to bealmost negligible and thus weaken overall flow strength across the canyon axis. For cyclonic simulations,zonal flow is weaker across the canyon axis but everywhere towards the downstream (Figure 2.4b).Therefore, strong incoming flow increases zonal flow everywhere within the canyon.For all simulations, Rossby number across the canyon is approximately one-third (or more) lower thanRossby number based on incoming flow. Incoming Rossby number is based on maximum zonal flow atshelf break depth upstream of the canyon, whereas Rossby number across the canyon is integrated fromthe canyon head to canyon mouth. Thus, incoming Rossby number is slightly overestimated relative to41canyon Rossby number.Downwelling submarine canyons have been observed to modify incoming coastal jets by deflecting thecurrent along canyon walls, with major modifications observed at shelf break depth [Flexas et al., 2008].Current simulations indicate two types of flow deflection occurring, dependent on Burger number. Witha high Burger number, strong flow impinges on the downstream wall and generates an anticyclonic eddy.With a low Burger number, flow follows canyon isobaths with strongest flow along bottom topography.Vertical fluxNet vertical flux was calculated for all model simulations as net flux in the canyon across the shelfbreak plane (150 m) averaged during the approximate advection dominated phase (averaged from modeldays 4-10). Initial errors in net vertical flux were calculated as the difference in flux values during twoaveraging periods, days 4-10 and days 3-9. However, 2 other sources of error were taken into consideration:1) error due to variations in zonal flux (which varied 2-17% for most cases and 50% for the She andSF simulations); 2) 12 hr model output provided an approximately 10% aliasing error (Appendix E).Therefore, error in all model simulations was taken as the maximum error in: 1) the sum of the minimum10% aliasing error plus error due to zonal flux variations or 2) errors in averaging period.Net vertical flux is directly proportional to Rossby number of flow across the canyon axis and inverselyproportional to Burger number (Figure 2.18). For example, US and SHR have the highest canyon Rossbynumber to Burger number ratios, and exhibit the greatest downward flux.Although previous studies have not specifically looked at changes in zonal flow strength, currentsimulations show that scenarios with stronger flow across the canyon axis lead to stronger downwardsflux. This is unsurprising since increasing Rossby number indicates increasing cross-canyon flow, andthus a stronger pressure gradient along the canyon.Increased stratification has been found to reduce vertical and cross-shore transport, as well as thedepth range which fluid parcels move in a circuit around a canyon [Klinck, 1996; Skliris et al., 2001;2002]. Current simulations show a similar pattern. For example, US and HB cases have the same forcingand variation in stratification, with the only difference being that HB has an increased buoyancy frequency(N). Net cross-shore transport (not shown) in the US (weaker stratification) case is 2x larger and netvertical transport is approximately 6x larger.Circulation and vertical velocity are instantaneous measurements that capture what is occurringduring the advection dominated phase, and both are influenced by Burger and Rossby number. Burgernumber drives circulation type and strength of vertical flux: simulations with a high Burger number420 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5−80000−70000−60000−50000−40000−30000−20000−100000Rossby number (canyon) / Burger numberVertical Flux (m3 s−1 )   Shelf break vorticity  UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB (a) Vertical fluxFigure 2.18: Burger and canyon Rossby number effect on vertical flux at shelf break depth (150 m).Bubble size is directly proportional to errors in flux estimates, based on percent differences. Due tocomplex canyon topography, canyon Rossby number for ST is likely overestimated and ST is consideredan outlier.exhibit a trapped anticyclonic eddy and weak vertical flux, simulations with a low Burger number exhibitcyclonic circulation and strong vertical flux. Rossby number drives strength of vertical flux: high Rossbynumbers generate strong vertical flux. Thus, Burger and Rossby numbers are important parametersduring the advection dominated phase.Zonal jet placement has an effect on the time dependence of vertical flux. Simulations with an outershelf jet show strong variations in flux across the shelf break plane (150 m depth). In the majority of thesesimulations, vertical flux across both the upstream and downstream planes oscillates between positiveand negative values. Simulations with an offshore jet have relatively steady vertical fluxes at this depth(Figure F.1). In the majority of these scenarios flux in the upstream is always downwards, while flux inthe downstream is always upwards. Previous studies have found that onshore/offshore displacement of azonal jet impacts flow dynamics in a canyon [Alvarez et al., 1996; Jordi et al., 2005; Ahumada-Sempoalet al., 2013]. Onshore displacement (towards the canyon head) has been found to generate a currentmeander which produces an enhancement of shelf-slope exchange and an oscillation in vertical flow [Jordiet al., 2005]. In present simulations, cross-shore transport is roughly the same in simulations with anoffshore or outer shelf jet (Figure F.1). It should be noted that differences exist between the current and43previous studies. Primarily, previous studies looked at time-varying displacement of the zonal jet, whichproduced a meander that drove vertical and cross-shore variations. Simulations presented here looked atflow that was semi-steady in time, and a meander is not produced.Density anomaliesPatterns in density anomalies indicate that Burger number (and subsequently vorticity) has the largestimpact on the magnitude of density anomalies (Figure 2.19a). All simulations show net downwardsadvection of density within the canyon. Simulations with lower Burger numbers (and cyclonic circulation)have weaker density anomalies at shelf break depth. Simulations with anticyclonic circulation exhibitstronger downwards density advection. Simulations with weak circulation also appear to be affected byBurger number.It is unsurprising that simulations with high Burger numbers have stronger density anomalies. Thesesimulations have stronger variations in initial density between vertical layers. Thus, a water parcel thatadvects the same vertical distance in a simulation with a high Burger number versus one with a lowBurger number will have a stronger density anomaly. To remove the effect of Burger number on densityadvection, density anomaly was divided by the squared buoyancy frequency (N2sb) to give a normalizeddensity value (Figure 2.19b). This value represents the vertical height change of a water parcel in eachsimulation. For this estimated vertical height change, there does not appear to be a pattern based on anyparameter. By normalizing the density anomaly, effects due to Burger number have been removed andthere appears to be no correlation in increasing/decreasing Rossby or Burger number and depth changeof an advected water parcel. However, it is likely that using normalized density anomaly to look for otherpatterns between model simulations does not work due to differences in initial density profiles. Curvatureof density profiles varies between simulations and vertical height change of a water parcel is estimateddifferently for each scenario.Location of incoming zonal jet does affect the occurrence of positive density anomalies in the modeldomain (Table 2.6). Simulations with the zonal jet located along the shallow coast or over the outershelf (directly above the upper canyon) exhibit negative density anomalies (downwards advection) at alldepths in the model domain (pattern 1). Simulations which show upwards density advection (positivedensity anomalies) during the day 5-8 averaged period have a zonal jet located either offshore or alongthe shelf break. The positive anomalies occur away from the canyon in the upstream and downstream(pattern 2). There is not a correlation between pattern 1/2 and average density anomaly.Forces can explain how jet location impacts the occurrence of positive density anomalies. For the44Shelf break vorticity  UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB (a) Density anomalyShelf break vorticity  UW SK She US HB OBC KL ST SF OW LRC SHR KHRB BLRB (b) Normalized density anomalyFigure 2.19: (a) Burger number effect on average density anomaly and (b) Burger and incoming Rossbynumber effect on normalized density anomaly in canyon for all simulations (averaged between model days4-10). Bubble size in (b) is directly proportional to relative magnitude of normalized density anomaly.45zonal jet to turn shoreward along the upstream canyon rim, it needs a centrifugal force. This is providedby a change in the pressure gradient: higher pressure offshore of the jet and lower pressure onshore. Thisweakens the Coriolis force and pressure gradient force balance, and allows flow to turn. In the simulationswith an offshore or shelf break jet, this pressure gradient change is provided by upwelling of denser wateroccurring offshore of the canyon and zonal jet (Figure 2.11b). For the simulations with a coastal or outershelf jet, this upwelling occurs over the outer shelf, where stronger downwelling is already occurring. Thisis seen as a reduction of downwelling rather than upwelling (Figure 2.11a).Previous studies have found that submarine canyons, in regions with a right-bounded jet, enhance thedownward advection of density properties [Klinck, 1996; She and Klinck, 2000; Skliris et al., 2001; 2002].Similar results are seen in plots of density difference anomalies (Figure 2.12). Downwards advection ofdensity is enhanced within the canyon for all simulations. The occurrence of positive density anomaliesaway from the canyon is affected by jet location. Simulations with on offshore or shelf break jet exhibitpositive anomalies away from the canyon, while simulations with a coastal or outer shelf jet exhibitnegative density anomalies everywhere in the domain.Nitrate anomaliesComparisons of non-dimensional parameters indicate incoming Rossby number has the greatest impacton vertical advection of nitrate (Figure 2.20). Simulations with higher Rossby numbers have greaterchanges in nitrate concentration. This indicates as more flow enters a canyon, advection of passivetracers strengthens. Patterns in incoming Rossby number show a stronger correlation than patternsbased on canyon Rossby number.Density and nitrate anomalies measure a combination of time-dependent and advection dominateddownwelling. Density and nitrate anomaly time series for the UW case (not shown) indicate averagedanomalies are approximately 85% time-dependent and 15% advection dominated. Allen [1996] finds ver-tical flux to be inversely proportional to the Burger number for time-dependent upwelling or downwelling.Thus, it would be expected that changes in nitrate advection would be inversely proportional to Burgernumber. However, this does not occur in current model simulations, e.g. UW and US cases have thesame Rossby number, different stratification, but similar nitrate anomalies. Comparing cross-sections ofnitrate anomalies (Figure 2.13a and F.7i, respectively), nitrate anomaly is weaker and broader in thestronger stratification scenario (UW) relative to the weaker stratification scenario (US). The region ofnegative anomalies upstream of the canyon is approximately 2.5-3x larger in the weaker stratification case(UW). Rossby radius of deformation is 3x larger in the UW case, so size of nitrate anomaly is proportional46UW SK She US HB OBC KL ST SF OW LRC SHR KHRB  BLRB Shelf break vorticity  Figure 2.20: Incoming Rossby number effect on nitrate anomaly for all simulations (averaged betweenmodel days 4-10).to Rossby radius (and stratification). Therefore, strength of nitrate anomaly is inversely proportionalto stratification, while size of nitrate anomaly is directly proportional to stratification. These have acancelling effect and only the Rossby number appears to have an influence on nitrate anomaly.Density and nitrate exhibit the same anomaly patterns in the same model scenarios: negative anoma-lies everywhere in the canyon domain (pattern 1) and positive anomalies away from the canyon (pattern2). This indicates jet location impacts the occurrence of nitrate anomalies following the same reasoningdescribed in the previous section. Therefore, the upwelling occurring away from the canyon includesdenser water and higher nitrate concentrations.Density and nitrate anomalies are integrated measurements and include a strong signal from the time-dependent phase. Anomaly patterns are influenced by jet location, which in turn is affected by verticalvariations in stratification. As previously discussed (vertical velocity section), zonal jet placement effectstime dependence of vertical flux. Offshore and shelf break jets generate upward velocity away from thecanyon and steadier vertical flux (relative to coastal/outer shelf jets). Thus, location of the zonal jet isimportant during time-dependent phases of flow.472.3.3 DiffusivityAverage diapycnal diffusivity in Ascension Canyon (west coast, North America) has been observed asapproximately 3.92×10−3 m2s−1 [Gregg et al., 2011]. Using this value, an estimate of flux due to mixingin the current canyon scenarios can be determined. Calculating diffusive flux as:Diffusive Flux = κp ×∆NO3∆z × area,where κp is average diapycnal diffusivity, changes in nitrate are taken from the initial nitrate profile, andarea is taken as area across three horizontal planes (100 m, 150 m, and 600 m).An advective flux was calculated by estimating the volume of water below the 100 m (150 m and600 m) plane with a nitrate concentration lower than the initial concentration at 100 m (150 m and600 m). This was done for each model grid cell below the respective plane (volumecell). This volume wasthen multiplied by depth of the grid cell below the 100 m plane (150 m and 600 m) (depthcell). Summingthese provided a measure of the volume of water advected below the 100 m (150 m and 600 m) plane andthe vertical extent of the advection (Vadv). This was calculated for each model simulation as:Vadv = Σ volumecell × depthcell.Vadv was measured for model days 4 and 10, and differences were calculated to isolate advection thatoccurred during the advection dominated phase. This value was divided by the timescale of the advectionphase (∆t) to give an advection speed. Finally, the advection speed was multiplied by the nitrate gradient(∆NO3∆z ) to give an overall advective flux for each model simulation:Advective Flux = ∆Vadv∆t ×∆NO3∆z .Nitrate gradient (∆NO3∆z ) was the same gradient used in the diffusive flux calculation. Diffusion in thecurrent model is small (10−7 m2 s−1), thus mixing has an insignificant impact on nitrate flux calcula-tions in the model simulations. Therefore, comparisons of estimated diffusive flux and model calculatedadvective flux are true comparisons of the separate processes (Table 2.7).Table 2.7: Diffusive and advective flux of nitrate across 3 vertical planesDiffusiveAdvective(maximum)Advective(mean)Advective(minimum)100 m 9.5×104 -5.2×105 -7.1×104 -7.6×103150 m 2.0×104 -2.0×105 -3.5×104 -1.5×103600 m 3.5×102 -3.9×103 -7.0×102 0Units are µM m3 s−1.Diffusive flux is likely overestimated for regions similar to the Mediterranean Sea, i.e. regions withlimited tides. However, these diffusive flux values provide a good estimate for nitrate diffusion in down-48welling canyons in other regions of the world. In the upper 100 m, diffusion of nitrate is stronger thanmean advection of nitrate. At 150 m and 600 m, mean downwards advection of nitrate is stronger thanupwards diffusion of nitrate. These positive diffusive flux estimates indicate that nitrate anomalies cal-culated in the previous section (Figure 2.20) are likely stronger that what would occur in a real worlddownwelling canyon scenario.Phytoplankton uptake nitrate as a nutrient in the surface photic zone, and as particulate matter sinksnitrate is lost from the photic zone to deeper water. Thus, nitrate concentration is low in the surfacelayers and high at depth, with strong variations between the surface and deep layers. In the currentmodel domain, nitrate variations are strongest between 50-200 m. Regions with strong nitrate variationsbetween vertical layers lead to stronger diffusive fluxes. This explains why diffusive flux becomes twoorders of magnitude smaller at 600 m depth.2.3.4 Summary: Circulation, flux, and advection for steady flow over down-welling canyonsAs present studies have shown, Burger number (stratification) has the largest impact on flow dynamicsin downwelling submarine canyons. Circulation in downwelling canyons can be broken down into 2 maincategories: 1) cyclonic circulation (positive vorticity), which occurs in canyons with low Burger numbers,and 2) anticyclonic circulation (negative vorticity), which occurs in canyons with high Burger numbers.We will ignore the 3rd category, weak circulation, which shows weak correlation between forcing conditionsand flow dynamics. Increasing flow strength increases the magnitude of vorticity for canyons with cycloniccirculation. In both canyon categories, stronger horizontal flow and weaker stratification allow for greatervertical flux at shelf break depth. Jet placement impacts the occurrence of positive density/nitrateanomalies away from the canyon. Offshore/shelf break jets lead to positive density anomalies away fromthe canyon.Flow dynamics seen in present studies have been found in previous literature using similar forcingconditions. Klinck [1996] and Skliris [2001; 2002] had offshore/shelf break zonal jets with small Rossbyand Burger numbers. This leads to a cyclonic flow pattern and small patches of weak upwelling awayfrom the canyon. Blanes Canyon has an outer-shelf jet with high Rossby and Burger numbers. Thehigh Burger number and jet placement lead to an anticyclonic flow pattern and everywhere downwardsdensity advection. The anticyclonic vorticity leads to a weak coupling between incoming flow strengthand flow strength across the canyon axis. Vertical flux is weak and density (nitrate) flux is strong due to49the high Burger (Rossby) number. She and Klinck’s [2000] jet was near the coast and weakly coupled tothe canyon, and thus vorticity, flux, density and nitrate advection were weak.2.4 ConclusionA numerical model (MITgcm) was used to study flow dynamics around downwelling submarinecanyons under various forcing conditions. Three non-dimensional parameters were used to determinehow regional dynamics impact flow dynamics. Although some simulations do see brief periods of up-wards displacement of water during the 10 day model period, the presence of the submarine canyon isfound to enhance downwards advection of density in all model scenarios. Stratification strongly affectscirculation and temporal density changes. Anticyclonic circulation and stronger downwards advection ofdensity occurs in simulations with higher Burger numbers, while cyclonic circulation and weaker densityadvection occur in simulations with a lower Burger number. For simulations with cyclonic circulation,stronger incoming flow (higher Rossby number) produces stronger vorticity magnitudes within the canyon.Simulations with cyclonic circulation have strong coupling between incoming and cross canyon Rossbynumbers, while anticyclonic simulations have a weaker coupling. Strong flow across the canyon axis (highcanyon Rossby number) and weak stratification (low Burger number) increase downwards vertical flux atshelf break depth (150 m), while increasing incoming Rossby number leads to stronger downwards advec-tion of nitrate. Patterns in advection phase nitrate anomalies differ from patterns of density anomalies,indicating that measurements of nitrate cannot be easily inferred from modelled density advection. Zonaljet location is influenced by vertical variations in stratification (χ). Uniformly stratified domains (low|χ|) exhibit offshore or shelf break jets, while non-uniformly stratified domains (high |χ|) exhibit outershelf or coastal jets. In turn, jet location impacts temporal density anomalies, with offshore or shelf breakjets generating positive density anomalies away from the canyon and outer shelf or coastal jets generatingnegative density anomalies everywhere in the model domain.50Chapter 3Conclusions3.1 Research objectivesFourteen numerical simulations of downwelling canyons were modelled based on various forcing condi-tions. Two simulations were modelled after coastal flow observed in Blanes Canyon [Flexas et al., 2008].Three more simulations were modelled after previous studies of various downwelling canyons [Klinck,1996; She and Klinck, 2000; Skliris et al., 2001; 2002]. Nine simulations include minor changes to variousparameters in the previous scenarios. These simulations were used to study flow dynamics in and arounddownwelling submarine canyons. Of particular interest was the degree to which upwelling occurs in theseregions, as well as how changes in forcing conditions impact flow dynamics in the canyon. Researchobjectives stated in Chapter 1 are used to summarize model results.3.1.1 Determine if upwelling occurs in or around downwelling canyons. If so,where does upwelling occur, and how intense is upwelling?Net upwards displacement does occur for some scenarios, but times of positive vertical flux in thecanyon is brief and irregular. Density and nitrate profiles show that net downwards advection of theseproperties occur in all model simulations. In none of the 14 modeled scenarios did upwelling of dense,cold deep water onto the shallow shelf occur.An observational study of Blanes Canyon [Flexas et al., 2008] found evidence of upwelling occurringnear shelf break depth inside the canyon (between 100-200 m depth), but upwelled water did not reachthe continental shelf. This was the first study with a right-bounded incoming jet which found upwelling51to occur near shelf break depth. Evidence for upwelling was based on volume flux estimates and isopycnalprofiles. Results from current model simulations show that periods of net upwelling do occur at shelfbreak depth in Blanes Canyon simulations (Figure 2.9; UW, OW, OBC). For the UW and OW cases,these periods are brief and do not last more than a day. However, the simulation with open boundaryconditions (OBC) did exhibit a 2 day period of net upwards velocity across the shelf break plane. In thecurrent study and the observational study, isopycnals along the downstream wall appear to lift relative totheir placement along the downstream wall (Figure 2.14), which is a characteristic of upwelling. However,plan views images of density difference reveal that downwards density advection occurs everywhere withinthe canyon (Figure 2.11a). Anomalies in density difference show that downwelling is enhanced everywherewithin the canyon (Figure 2.12a). For the Blanes Canyon simulation, downwards density advection alongthe upstream wall is stronger relative to the same position along the downstream wall.3.1.2 Determine what parameters affect flow dynamics.CirculationPlan view images of vorticity and horizontal velocity vector plots were used to determine absolutevorticity and canyon circulation. Three types of canyon circulation occur based on Burger number.Simulations with a high Burger number have negative vorticity at shelf break depth and generate atrapped anticyclonic eddy within the canyon. Simulations with a low Burger number have positivevorticity and cyclonic circulation at shelf break depth. Some simulations have very weak circulationregardless of Burger number. This is due to strength of incoming zonal flow (Rossby number). For thecyclonic simulations, increasing Rossby number creates stronger vorticity within the canyon.Vertical variations in stratification impact jet placement. Simulations with uniform stratification havejets located further offshore relative to simulations with the same forcing and less uniform stratification.Simulations with cyclonic circulation have a strong coupling between incoming and canyon axis flowstrength, while simulations with anticyclonic circulation (and a trapped eddy) exhibit weaker coupling.Scenarios with weak circulation have weak incoming and canyon Rossby numbers.Vertical fluxPlan views images were used to determine vertical flux patterns in model simulations; two patternsoccur. In simulations with weak or anticyclonic circulation, enhanced downwards (upwards) velocityis limited to the upstream (downstream) corner of the canyon mouth. In simulations with cyclonic52circulation, vertical velocity has an antisymmetrical pattern where positive and negative vertical velocityis split along the canyon axis. Negative velocity occurs in the upstream portion of the canyon, andpositive velocity occurred in the downstream portion of the canyon.An average net vertical flux was calculated as the average flux across each grid cell at shelf break depthwithin the canyon domain. Average net vertical flux during the advection dominant phase is negativefor all canyon scenarios. As canyon Rossby number increases, or Burger number decreases, vertical fluxwithin the canyon increases. This pattern is strongest for scenarios with cyclonic circulation.Density anomaliesAverage density within the canyon at shelf break depth was calculated during model day 5-8. Thisvalue was subtracted from initial density at shelf break depth to give a density anomaly. From this, abackground density anomaly was calculated along downstream isobaths. These values were subtractedfrom grid points of similar isobaths to give a density difference anomaly. The density difference anomalywas then used to determine how much the canyon enhanced or reduced the background downwelling inthe domain.Simulations with a zonal jet placed along the coast or over the outer shelf have negative densityanomalies everywhere within the model domain. Density difference anomaly revealed downwards advec-tion is enhanced everywhere within the canyon, and is strongest near the canyon head. Simulations witha shelf break or offshore jet have negative density anomalies within the canyon, but positive anomaliesaway from the canyon. For these simulations, downwards advection is enhanced within the canyon, beingstrongest along canyon walls and weaker towards the canyon axis.Average density anomalies were calculated during the advection dominant phase (model day 4-10).Burger number impacts the strength of density anomalies within the canyon. Simulations with a highBurger number (strong vertical variations in density) exhibit the greatest density anomalies, while sim-ulations with a low Burger number (weak vertical variations in density) exhibit relatively weak densityanomalies. However, none of the non-dimensional parameters appear to have an impact on verticaladvection (normalized density anomaly) of a water parcel.Nitrate anomaliesNitrate profiles act as a passive tracer and provide one input parameter that was the same for allmodel simulations. Cross-section images reveal downwards advection of nitrate within the canyon for allmodel simulations. However, simulations with an offshore or shelf break jet do show upwards advection53of nitrate away from the canyon over the outer shelf and shelf break.Nitrate anomalies within the canyon were used to calculate flux due to advection. An average nitratevalue within the canyon at shelf break depth was calculated. This average was subtracted from theinitial nitrate concentration at shelf break depth to give an estimate of nitrate anomaly in the canyon.Nitrate advection increases with increasing incoming Rossby number. This correlation is stronger withthe incoming Rossby number than the canyon Rossby number.3.2 Future researchThe aim of this study was to better understand basic forcing parameters and their impacts on flowdynamics in downwelling submarine canyons. But there are many real world forcing conditions that arenot included in this study. Future work could include addition of regional river input, as well as seasonalchanges in climate, which would both impact density structure and time-varying placement of coastalflow. Density structure is an important parameter in determining density advection and vertical flux,and a better understanding of seasonal changes would be important. Previous studies have suggestedthat onshore/offshore displacement of coastal jets has a significant impact on flow dynamics [Alvarez etal., 1996; Jordi et al., 2005; Ahumada-Sempoal et al., 2013]. Time-varying displacement of zonal jetsmay have different hydrodynamic responses depending on the canyon geometry and density structure.Future work could also include the addition of wind events. Studying a downwelling canyon with atrapped anticyclonic eddy, Ardhuin et al. [1999] found that a right-bounded 1 day wind event enhancedcoastal downwelling, but rebound upwelling occurred as the wind relaxed. In the same study, coastalwind blowing offshore initiated upwelling followed by rebound downwelling. However, the upwelling eventallowed renewal of waters trapped in the anticyclonic canyon eddy. Studying a downwelling canyon withcyclonic circulation, Skliris et al. [2001; 2002] similarly found a right-bounded wind event to enhancecoastal downwelling, while a left-bounded wind event led to a reversal of flow and strong coastal upwelling.Both studies found that during wind events, canyons enhanced cross-slope and vertical exchange. Windevents could be applied to simulations of the current study to develop an improved understanding of theimpacts these wind events have to various downwelling systems.Few laboratory studies have been performed for downwelling canyons, especially canyons with a strongshelf break jet. Laboratory experiments can isolate individual processes and aid in the development ofnumerical models [Boyer et al., 2004]. Important non-dimensional parameters found in this study couldbe used in a physical model to further test how these forces affect flow. Performance of the numerical54model can then be compared to laboratory results.3.3 Application to real worldForcing conditions can vary between submarine canyons along the same continental shelf. There aremany regional factors that impact forcing conditions, e.g. river runoff, wind events, bottom morphology,regional/seasonal climatology. Thusly, it would be naive to assume numerical models can incorporatethe many complex processes that occur in real world physical systems. Exact flow dynamics cannot bereproduced, but numerical models and knowledge of local dynamics can help to create an understandingof general circulation around downwelling canyons. It is hoped the results from this study can be used asthe foundational building blocks in the continuing pursuit of understanding canyon impacts on regionalcirculation.This project adds to the continuing study of flow dynamics in downwelling submarine canyons. 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Journal of Geophysical Research: Oceans,103(C1):1319–1341.Palomera, I. (1992). Spawning of anchovy Engraulis encrasicolus in the northwestern Mediterraneanrelative to hydrographic features in the region. Marine ecology progress series. Oldendorf, 79(3):215–223.Roed, L. and Cooper, C. (1987). A study of various open boundary conditions for wind-forced barotropicnumerical ocean models. In Nihoul, J. and Jamart, B., editors, Three-Dimensional Models of Marineand Estuarine Dynamics, volume 45 of Elsevier Oceanography Series, pages 305 – 335. Elsevier.Sabates, A. and Olivar, M. (1996). Variation of larval fish distributions associated with variability in thelocation of a shelf-slope front. Marine Ecology Progress Series, 135:11–20.She, J. and Klinck, J. M. (2000). Flow near submarine canyons driven by constant winds. Journal ofGeophysical Research: Oceans, 105(C12):28671–28694.Sigman, D. M. and Hain, M. P. (2012). The biological productivity of the ocean. Nature EducationKnowledge, 3.59Skliris, N., Goffart, A., Hecq, J. H., and Djenidi, S. (2001). Shelf-slope exchanges associated with asteep submarine canyon off Calvi (Corsica, NW Mediterranean Sea): A modeling approach. Journalof Geophysical Research: Oceans, 106(C9):19883–19901.Skliris, N., Hecq, J., and Djenidi, S. (2002). Water fluxes at an ocean margin in the presence of asubmarine canyon. Journal of Marine Systems, 32(13):239 – 251. ¡ce:title¿Exchange Processes at theOcean Margins¡/ce:title¿.Smagorinsky, J. (1963). General circulation experiments with the primitive equations. Monthly WeatherReview, 91(3):99–164.Taylor, G. I. (1923). Experiments on the motion of solid bodies in rotating fluids. Proc. Roy. Soc. A,104:213–218.Tsimplis, M. N., Proctor, R., and Flather, R. A. (1995). A two-dimensional tidal model for the Mediter-ranean Sea. Journal of Geophysical Research: Oceans, 100(C8):16223–16239.Waterhouse, A. F., Allen, S. E., and Bowie, A. W. (2009). Upwelling flow dynamics in long canyons atlow rossby number. Journal of Geophysical Research: Oceans, 114(C5):n/a–n/a.Wurtz, M. (2012). Submarine canyons and their role in the Meditteranean ecosystem. In Wurtz, M.,editor, Mediterranean Submarine Canyons: Ecology and Governance, pages 11–26, Gland, Switzerlandand Mlaga, Spain:. IUCN.60Appendix ABoundary ConditionsDue to limited computational capacity, it is impractical to model coastal circulation with enoughresolution around small topographic features (such as submarine canyons), and still have alongshoreboundaries placed beyond the decay distance of coastal trapped waves [Dinniman and Klinck, 2002]. Toget around this problem, numerical modellers use either open or periodic boundary conditions; however,open and periodic conditions each have their own problems. Disturbances in periodic domains are not ableto advect or propagate out of the model, leading to rapid accumulation of energy and model instability.Also, in periodic boundary conditions, the realism of the flow is limited because alongshore pressuregradients cannot be naturally created; they can only be externally imposed. Imposing open boundaryconditions on the hydrostatic primitive equations have shown that a small change in the boundarycondition can result in a large change in the interior solution [Oliger and Sundstrom, 1978; Bennett andKloeden 1978].Dinniman and Klinck [2002] ran numerical simulations of submarine canyons with upwelling anddownwelling winds to compare different boundary conditions. From their study, the authors found thatusing a modified Orlanski scheme (one which forces the phase speed to be either zero or the maximumlimit as defined by the model grid spacing and time step [Camerlengo and O’Brien, 1980]) producedan undercurrent that caused errors in the alongshore surface height gradient. Similar problems havebeen seen in other studies using the modified Orlanski scheme on barotropic coastal models [Roed andCooper, 1987]; [Palma and Matano, 1998]. Stability of the solution was the primary difference betweenopen and periodic boundary conditions in the case for upwelling winds. The presence of the canyoncreated a disturbance in the barotropic flow, for the periodic case this disturbance was not able to advector propagate out of the model. Waves in the surface height were visibly travelling with the coast on61their left and they grew well past the point where they were affecting the model flow. The same problemoccurred in the downwelling case, but to a lesser extent. Problems were also seen when trying to vary theCoriolis parameter (the β plane) in the periodic conditions. Beta effects are typically weak, especiallyfor small alongshore distances; however, some energy can be lost from the coast due to Rossby waves.Further investigation into these effects could only be studied using open model domains. Of the threeschemes used for open boundary conditions (modified Orlanski, Flather radiation scheme [Flather, 1976],and a flow relaxation scheme [Martinsen and Engedahl, 1987]), the Flather radiation scheme and flowrelaxation scheme were determined to be the most practical for their coastal ocean setup.For the current model, both open and periodic boundary conditions were tested. For all simulations,the onshore coast (i.e. northern boundary) was a closed boundary with no-slip conditions. The deepocean (southern boundary) was open with an Orlanski scheme applied [Orlanski, 1976]. Due to relativelyshort model run times, the majority of simulations were run with periodic alongshore boundaries (i.e.east and west boundaries); however, a few simulations use open alongshore boundaries, with an Orlanskischeme applied.62(a) upstream boundary(b) downstream boundaryFigure A.1: Isopycnal cross-sections along the (a) upstream and (b) downstream boundaries for the OBCsimulation.63Appendix BModel DiscretizationThe MITgcm is discretized using using a finite volume method as described by Adcroft et al. (2004).The governing equations are integrated over (space-filling) finite volumes that make up a discrete grid.By integrating over a finite volume and applying the Gauss-divergence theorem, the continuity equationbecomes:Aueastueast −Auwestuwest +Avnorthvnorth −Avsouthvsouth +Awupwup −Awdownwdown = 0 (B.1)A (the area of each cell) describes the geometry of a finite volume and the budget is written con-ceptually in terms of normal flow across the cell face. No normal flow at a rigid boundary translatesto setting the rigid boundary velocity to zero (i.e. a cell lying along bottom topography would haveAwdownwdown = 0). The components of velocity are staggered in the horizontal on an Arakawa C grid anda Lorenz grid is used on the vertical. The same finite volume treatment of the continuity equation (B.1)is applied to the tracer equations.The non-hydrostatic capability allows the model to simulate overturning and mixing processes. Thiscan be used in conjunction with the finite volume representation of topography to become a flexible toolfor studying mixing processes and dynamical interactions with steep topography.64Appendix CAdvection SchemeIn oceanography, advection is the transport of a property due to a fluid’s bulk motion; there can beactive and passive properties. Active properties (e.g. temperature and salinity) are advected due to thecurrents of a fluid. These properties affect density distribution, which in turn affects pressure field, andpressure field is used in the calculation of currents. Therefore, the accuracy in advection of active tracersis important to overall flow dynamics of a model.The MITgcm offers eight different advection schemes, each of which is optimum for different appli-cations. The eight schemes fall into 3 general categories: 1) linear schemes integrated with the Adams-Bashforth method (2nd, 3rd, and 4th ordered, 2) unlimited, but multi-dimensional schemes (2nd, 3rd, and4th order direct space-time), 3) flux limited (2nd and 3rd order). The MITgcm manual offers guidelinesfor finding the most suitable scheme, although use of trial and error is encouraged. It is recommendedthat if using a high resolution model, a higher order scheme will give a more accurate solution, butscale-selective diffusion might need to be employed. For solutions with shocks or propagating fronts, aflux limited scheme is highly recommended.65Appendix DExtended SimulationAn extended simulation of the UW case was modelled to determine how steady the flow is in time.The simulation was doubled to run for 20 model days. Flux time series indicates that flow oscillation inall 3 directions strengthens after day 12 (Figure D.1). Results averaged over model days 10-20 show flowstrengthens in the domain, which impacts magnitudes of variables such as velocity, density, and vorticity.Although zonal flux averaged from day 10-20 only varied 4% from day 4-10 averages, meridional andvertical fluxes were found to vary approximately 90% from the model day 4-10 averages. Although flux isstronger during the extended simulation, plots of individual averaged (day 10-20) parameters (not shown)indicate patterns in flow dynamics did not change.Flow oscillations seen in the flux time series indicate an instability may be occurring around modelday 12. Allen and Newberger [1998] modeled two-dimensional, time-dependent, wind-forced, stratifieddownwelling circulation along a continental shelf. The authors found that near-bottom offshore flowdeveloped time- and space-dependent fluctuations in the bottom boundary layer. Potential vorticity thatwas initially negative becomes positive in the regions of fluctuation.In the extended simulation, daily snapshots of zonal velocity show fluctuations in near zero velocityalong the continental shelf (not shown). Similarly, daily snapshots of vorticity show regions of weaklypositive and 0 vorticity along the continental shelf away from the canyon (not shown); regions whichhave everywhere negative vorticity during the advection averaged period. These are likely indicationsthat instabilities are occurring along the continental shelf after model day 12. Thus, model averages fromday 4-10 are good indicators of the dynamics occurring during the most steady period of flow, beforeinstabilities begin to appear and grow.660 5 10 15 20−8−4048x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesUW extended case  −9−4.504.59x 104Vertical Flux [m3 /s]U3V2V3W1W2Figure D.1: Time series of horizontal and vertical flux over the canyon for core simulation (UW), extendedfor 20 model days.67Appendix EAliasingTo determine if the 12 hour output of model data is not aliasing the results, a 10 day core case (UW)run was simulated with output collected every 3 hours. There are small differences in vertical flux valuesduring the first 2-3 days of simulation (Figure E.1). However, during the advection dominant phase thereappears to be minimal differences in trends across the vertical planes. Vertical flux estimates averagedfrom model day 4-10 were -9.39 × 103 m3 s−1 for the original (12 hour sampling) run and -8.52 × 103m3 s−1 for the 3 hour sampling run, therefore there is a 10% relative error.680 1 2 3 4 5 6 7 8 9 10−8−4048 x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesUW case  −9−4.504.59x 104Vertical Flux [m3 /s]U3V2V3W1W2(a) 12 hour model output0 2 4 6 8 10−8−4048x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesUW case (3 hour sampling)  −9−4.504.59x 104Vertical Flux [m3 /s]U3V2V3W1W2(b) 3 hour model outputFigure E.1: Horizontal and vertical flux time series in and around a canyon based on model output every(a) 12 hours and (b) 3 hours.69Appendix FAdditional Figures0 2 4 6 8 10−7−3.503.57x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesOW case  −9−4.504.59x 104Vertical Flux [m3 /s]U3V2V3W1W2(a) OW case0 2 4 6 8 10−1−0.500.51x 106Horizontal Flux [m3 /s]Time (days)Flux time seriesOBC case  −1.2−0.600.61.2x 105Vertical Flux [m3 /s]U3V2V3W1W2(b) OBC case0 2 4 6 8 10−1.5−0.7500.751.5x 106Horizontal Flux [m3 /s]Time (days)Flux time seriesST case  −1.2−0.600.61.2x 105Vertical Flux [m3 /s]U3V2V3W1W2(c) ST case0 2 4 6 8 10−3−1.501.53x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesKL case  −3−1.501.53x 104Vertical Flux [m3 /s]U3V2V3W1W2(d) KL caseFigure F.1: Time series of horizontal and vertical flux directly over the canyon. Same as Figure 2.2.700 2 4 6 8 10−2−1012x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesSK case  −5−2.502.55x 104Vertical Flux [m3 /s]U3V2V3W1W2(e) SK case0 2 4 6 8 10−6−3036x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesUS case  −3−1.501.53x 105Vertical Flux [m3 /s]U3V2V3W1W2(f) US case0 2 4 6 8 10−7−3.503.57x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesHB case  −1−0.500.51x 105Vertical Flux [m3 /s]U3V2V3W1W2(g) HB case0 2 4 6 8 10−3−1.501.5x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesShe case  −2.5−1.2501.25x 104Vertical Flux [m3 /s]U3V2V3W1W2(h) She case0 2 4 6 8 10−4−200.8x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesSF case  −10000−500002000Vertical Flux [m3 /s]U3V2V3W1W2(i) SF case0 2 4 6 8 10−1.6−0.800.81.6x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesLRC case  −1−0.500.51x 104Vertical Flux [m3 /s]U3V2V3W1W2(j) LRC caseFigure F.1: Continued.710 2 4 6 8 10−5−2.502.55x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesSHR case  −3−1.501.53x 105Vertical Flux [m3 /s]U3V2V3W1W2(k) SHR case0 2 4 6 8 10−3.5−1.7501.753.5x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesBLRB case  −4−2024x 104Vertical Flux [m3 /s]U3V2V3W1W2(l) BLRB case0 2 4 6 8 10−3.5−1.7501.753.5x 105Horizontal Flux [m3 /s]Time (days)Flux time seriesKHRB case  −3−1.501.53x 104Vertical Flux [m3 /s]U3V2V3W1W2(m) KHRB caseFigure F.1: Continued.72Alongshore (km)Cross−shore (km)OW caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(a) OW caseAlongshore (km)Cross−shore (km)OBC caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(b) OBC caseAlongshore (km)Cross−shore (km)ST caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(c) ST caseAlongshore (km)Cross−shore (km)KL caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(d) KL caseAlongshore (km)Cross−shore (km)SK caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(e) SK caseAlongshore (km)Cross−shore (km)US caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(f) US caseFigure F.2: Horizontal velocity vectors at shelf break depth (150 m). Same as Figure 2.4.73Alongshore (km)Cross−shore (km)HB caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(g) HB caseAlongshore (km)Cross−shore (km)She caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(h) She caseAlongshore (km)Cross−shore (km)SF caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(i) SF caseAlongshore (km)Cross−shore (km)LRC caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(j) LRC caseAlongshore (km)Cross−shore (km)BLRB caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(k) BLRB caseAlongshore (km)Cross−shore (km)KHRB caseHorizontal Velocity [m/s]45 50 55 60 65 70 754550556065700.2 m/s(l) KHRB caseFigure F.2: Continued.74(a) OW case (b) OBC case(c) ST case (d) KL case(e) US case (f) HB caseFigure F.3: Cross-section of vorticity at mid-canyon. Same as Figure 2.7.75(g) She case (h) SF case(i) LRC case (j) SHR case(k) BLRB case (l) KHRB caseFigure F.3: Continued.76−1000−800−600−400−200Alongshore (km)Cross−shore (km)OW caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−2−1.5−1−0.500.511.52x 10−3(a) OW case−1000−800−600−400−200Alongshore (km)Cross−shore (km)OBC caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−6−4−20246x 10−3(b) OBC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)ST caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−3−2−10123x 10−3(c) ST case−1000−800−600−400−200Alongshore (km)Cross−shore (km)KL caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−3−2−10123x 10−3(d) KL case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SK caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−1−0.500.51x 10−3(e) SK case−1000−800−600−400−200Alongshore (km)Cross−shore (km)US caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−0.01−0.00500.0050.01(f) US caseFigure F.4: Vertical velocity at shelf break depth (150 m). Same as Figure 2.8.77−1000−800−600−400−200Alongshore (km)Cross−shore (km)HB caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−4−3−2−101234x 10−3(g) HB case−1000−800−600−400−200Alongshore (km)Cross−shore (km)She caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−6−4−20246x 10−4(h) She case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SF caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−2−1012x 10−4(i) SF case−1000−800−600−400−200Alongshore (km)Cross−shore (km)LRC caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−6−4−20246x 10−4(j) LRC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)BLRB caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−1−0.500.51x 10−3(k) BLRB case−1000−800−600−400−200Alongshore (km)Cross−shore (km)KHRB caseVertical Velocity [m/s]  20 40 60 80 1001020304050607080−1.5−1−0.500.511.5x 10−3(l) KHRB caseFigure F.4: Continued.78−1000−800−600−400−200Alongshore (km)Cross−shore (km)OW caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.4−0.35−0.3−0.25−0.2−0.15−0.1−0.050(a) OW case−1000−800−600−400−200Alongshore (km)Cross−shore (km)OBC caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.35−0.3−0.25−0.2−0.15−0.1−0.050(b) OBC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)ST caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.3−0.25−0.2−0.15−0.1−0.050(c) ST case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SK caseDensity Difference [psu]  20 40 60 80 1001020304050607080−12−10−8−6−4−20x 10−3(d) SK case−1000−800−600−400−200Alongshore (km)Cross−shore (km)US caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.03−0.025−0.02−0.015−0.01−0.00500.0050.01(e) US case−1000−800−600−400−200Alongshore (km)Cross−shore (km)HB caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.3−0.25−0.2−0.15−0.1−0.050(f) HB caseFigure F.5: Density anomaly at shelf break depth (150 m). Same as Figure 2.11.79−1000−800−600−400−200Alongshore (km)Cross−shore (km)She caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.1−0.08−0.06−0.04−0.020(g) She case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SF caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.14−0.12−0.1−0.08−0.06−0.04−0.020(h) SF case−1000−800−600−400−200Alongshore (km)Cross−shore (km)LRC caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.08−0.07−0.06−0.05−0.04−0.03−0.02−0.0100.010.02(i) LRC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SHR caseDensity Difference [psu]  20 40 60 80 1001020304050607080−15−10−50x 10−3(j) SHR case−1000−800−600−400−200Alongshore (km)Cross−shore (km)BLRB caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.08−0.07−0.06−0.05−0.04−0.03−0.02−0.010(k) BLRB case−1000−800−600−400−200Alongshore (km)Cross−shore (km)KHRB caseDensity Difference [psu]  20 40 60 80 1001020304050607080−0.2−0.18−0.16−0.14−0.12−0.1−0.08−0.06−0.04−0.020(l) KHRB caseFigure F.5: Continued.80−1000−800−600−400−200Alongshore (km)Cross−shore (km)OW caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.3−0.25−0.2−0.15−0.1−0.0500.05(a) OW case−1000−800−600−400−200Alongshore (km)Cross−shore (km)OBC caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.3−0.25−0.2−0.15−0.1−0.050(b) OBC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)ST caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.25−0.2−0.15−0.1−0.050(c) ST case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SK caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−12−10−8−6−4−20x 10−3(d) SK case−1000−800−600−400−200Alongshore (km)Cross−shore (km)US caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.025−0.02−0.015−0.01−0.00500.0050.01(e) US case−1000−800−600−400−200Alongshore (km)Cross−shore (km)HB caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.25−0.2−0.15−0.1−0.050(f) HB caseFigure F.6: Density difference anomaly at shelf break depth (150 m). Same as Figure 2.12.81−1000−800−600−400−200Alongshore (km)Cross−shore (km)She caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.09−0.08−0.07−0.06−0.05−0.04−0.03−0.02−0.0100.01(g) She case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SF caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.1−0.08−0.06−0.04−0.0200.02(h) SF case−1000−800−600−400−200Alongshore (km)Cross−shore (km)LRC caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.08−0.06−0.04−0.0200.02(i) LRC case−1000−800−600−400−200Alongshore (km)Cross−shore (km)SHR caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−8−6−4−202468x 10−3(j) SHR case−1000−800−600−400−200Alongshore (km)Cross−shore (km)BLRB caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.08−0.06−0.04−0.0200.02(k) BLRB case−1000−800−600−400−200Alongshore (km)Cross−shore (km)KHRB caseDensity Difference Anomaly [psu]  20 40 60 80 1001020304050607080−0.2−0.18−0.16−0.14−0.12−0.1−0.08−0.06−0.04−0.020(l) KHRB caseFigure F.6: Continued.82(a) OW case, upstream (b) OW case, axial(c) OBC case, upstream (d) OBC case, axial(e) ST case, upstream (f) ST case, axialFigure F.7: Nitrate anomaly 10 km upstream (right) and along canyon axis (right). Same as Figure 2.13.83(g) SK case, upstream (h) SK case, axial(i) US case, upstream (j) US case, axial(k) HB case, upstream (l) HB case, axialFigure F.7: Continued.84(m) She case, upstream (n) She case, axial(o) SF case, upstream (p) SF case, axial(q) LRC case, upstream (r) LRC case, axialFigure F.7: Continued.85(s) SHR case, upstream (t) SHR case, axial(u) BLRB case, upstream (v) BLRB case, axial(w) KHRB case, upstream (x) KHRB case, axialFigure F.7: Continued.86

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