Coastal Wall Research Articles

Hydrodynamic performance of a periodic array of flap-type devices installed on the stepped bottom topography in the front of the coastal wall

Harnessing wave energy stands as a promising method to mitigate carbon dioxide emissions and address the global energy shortage. The strategic placement of wave energy converters (WECs) in offshore areas is contingent upon the distinctive features of the coastline and the topographical layout. This study is dedicated to scrutinizing the hydrodynamic characteristics and the wave energy absorption of a periodic array of flap-type WECs situated on a stepped bottom topography, strategically positioned in front of a straight coast. The coastline is modeled as a fully reflecting vertical wall. To analyze the oblique wave interaction with this system, we have developed a semi-analytical solution grounded in the linear potential flow theory. We evaluated key performance metrics, including hydrodynamic efficiency, reflection coefficient, wave excitation torque, added inertia torque, and radiation damping. Case studies were conducted to assess the impacts of varying parameters, such as the distance between the flap and the wall, the wave depth above the step, the incident angle, and the step length on the hydrodynamic performance of the current system. The results underscore the substantial influence of the distance between the flap and the coastal wall on wave power efficiency. The trigger condition's frequency downshift, indicative of the standing wave field between the flap and the coastal wall, is observed with a reduction in the wave depth above the step, in contrast to scenarios without the step. In addition, wave resonance above the stepped bottom topography amplifies wave power extraction, albeit with the caveat of a diminished hydrodynamic efficiency due to the presence of Rayleigh–Bloch waves.

Numerical investigation of the effect of using a combined design of coastal wall and coastal forest in the protection and beaches stability

Numerical investigation of the effect of using a combined design of coastal wall and coastal forest in the protection and beaches stability

Power performance of an asymmetric wave energy converter near a partial reflection wall

Wave power absorption of a heaving-body wave energy converter (HBWEC) can be improved by making the device highly asymmetric and deploying it near a coastal wall, harbour pier, or breakwater. However, the coupling between the geometric asymmetry of the HBWEC and the partial reflecting boundaries of the various walls and the consequential influence on the power performance of the HBWEC are unclear. This research aims to fill this gap. A semi-analytical model based on the linear potential flow theory is proposed to deal with an HBWEC with an arbitrary bottom shape and a partial reflection wall. The degree of asymmetry (DoA) of the HBWEC and the reflection rate of the wall are mathematically defined. Results show that the wall increases the power performance of an HBWEC by increasing the reflected wave energy through an increase in the reflection rate. Practically, an HBWEC should have a larger DoA to make it more immune to the change of the reflection rate and therefore more adaptable to different situations. These findings could offer recommendations for the design and deployment of an HBWEC according to the properties of the wall, improving wave power absorption efficiency and avoiding unnecessary costs due to improper design.

Beta-Plane Arrested Topographic Wave as a Linkage of Open Ocean Forcing and Mean Shelf Circulation

AbstractPressure anomaly set by the open ocean affects the dynamic topography and associated circulation over the continental shelf, which is explored here on a linearized β-plane arrested topographic wave framework that considers the variation in Coriolis parameter with latitude. It was found that on a meridional shelf, a nondimensional parameter Peβ, termed the β Péclet number, signifies the characteristics of open ocean–shelf interaction. The Peβ ≡ Dβ/α is determined by the ratio of long-wave-limit planetary to topographic Rossby wave speeds, i.e., the β drift Dβ, and the linear Ekman number α. On the western boundary shelf, due to the westward planetary Rossby wave, open ocean pressure propagates shoreward as Peβ > 1, and shelf circulation peaks where Peβ drops to 1. At this location, the planetary β effect is balanced by the bottom friction. The Peβ = 1 must occur either on the shelf or on the coastal wall when Peβ > 1 is observed at the shelf edge. On the eastern boundary shelf, however, Peβ < 0, the pressure anomaly is removed from the shelf, and hence the inductive circulation decays rapidly from the shelf edge. This β effect is robust on gently sloping meridional shelves. For zonal shelves, the planetary β increases the effective bottom slope on the northern boundary shelf but decreases it on the southern one, in a sense of potential vorticity conservation. However, this effect could be less significant in reality, given the complex dynamics involved. The above mechanism can explain the dynamics driving the Taiwan Warm Current in the East China Sea and its bifurcation around 28°N.

Demonstrating a High‐Resolution Gulf of Alaska Ocean Circulation Model Forced Across the Coastal Interface by High‐Resolution Terrestrial Hydrological Models

AbstractWe demonstrate a linking of moderately high resolution (1 km) terrestrial hydrological models to a 3‐D ocean circulation model having similar resolution in the northern Gulf of Alaska, where a distributed line source of freshwater runoff exerts strong influence over the shelf's hydrographic structure and flow dynamics. The model interfacing is accomplished via mass flux boundary conditions through the ocean model coastal wall at all land‐ocean adjoining grid cells. Despite the high runoff volume and lack of a coastal mixing estuary, the implementation maintains numerical stability by prescribing depth invariant and surface‐intensified inflows at fast and slow discharge grid cells, respectively. Based on comparisons against in situ hydrographic data, the coastal sidewall mass flux boundary condition results in more realistic hindcast surface salinity and salinity gradient fields than models that distribute coastal runoff in the form of spatially distributed precipitation. Correlations with observed thermal and haline monthly anomalies reveal statistically significant hindcast temporal variability during the freshet season when the signal‐to‐noise ratio is large. Comparisons of ocean models forced by high‐ and low‐resolution hydrological models reveal differences in salinity, surface elevation, and velocity fields, highlighting the value and importance of accurate coastal runoff fields. The model results improve our understanding of the regional influence of runoff on sea level elevations and the distribution and fate of fresh water. Our approach has potential applications to biogeochemical modeling in regions where distributed line source freshwater coastal discharges deliver heat, momentum, and chemical constituents that may influence the marine carbon pump.

The effect of the coastal reflection on the performance of a floating breakwater-WEC system

In this paper, the hydrodynamic performance of a floating breakwater-Wave Energy Converter (WEC) integrated system was investigated under the framework of the linear potential flow theory, with a focus on the effect of the coastal reflection. The reflection coefficient and capture width ratio were verified using the rule of wave energy flux conservation. The water wave resonances, including the piston- and sloshing-mode, between the device and the coastal wall, were excited. By comparing to the cases without the coastal wall, the presence of the coastal wall led to the significant modifications of the hydrodynamic characteristics, efficiency and wave attenuation performance of the system. Specifically, the occurrence of the piston- and sloshing-mode resonance accompanies the increment of the efficiency of the system. The null efficiency was found when the device was located at the node of standing waves, which was formed due to the presence of the coastal wall. The effect of the coastal wall in irregular waves was found to be relatively milder when compared to that in regular waves.

Utjecaj izgradnje obalnog zida na dinamiku valovanja ispred postojeće prirodne obale

U ovom radu opisan je utjecaj izgradnje obalnog zida na postojećoj prirodnoj stjenovitoj obali na dinamiku valovanja ispred obale, na primjeru projektiranja plaže Kostanj u Rijeci. Analize postojećeg i projektiranog stanja valovanja provedene su korištenjem numeričkog modela valovanja Simulating Waves Nearshore (SWAN) uz primjenu autorskih algoritama neophodnih za prikaz rezultata numeričkih simulacija. Predviđa se proširenje postojeće plaže prema zapadnom dijelu uvale nasipavanjem prirodne obale te izgradnjom armirano-betonskih zidova prema moru. Zbog izgradnje obalnih zidova doći će do povećanja koeficijenta refleksije valova u odnosu na postojeću stjenovitu obalu. Ispred projektiranog zida, značajne visine valova juga 50 godišnjeg povratnog perioda povećat će se sa 2,20 na 2,50 m. U radu su opisane konstrukcijske metode umanjenja nepovoljnog učinka izgradnje obalnog zida na postojećoj stjenovitoj obali. Kao primjer opisano je i simulirano djelovanje zaštitnog podmorskog praga na polje valovanja ispred obalnog zida. Izgradnjom zaštitnog podmorskog praga s dubinom uronjenosti krune -2,0 m n.m. simulirane značajne visine valova juga 50 godišnjeg povratnog perioda su 1,90 m ispred projektiranog obalnog zida.

Breaking wave impact on a floating body with air bubble effect

The hydrodynamic problem of a breaking wave impacting on a floating body with air bubble effect is modelled based on the incompressible velocity potential theory, which is solved using the boundary element method in the time domain. To avoid the numerical inaccuracies due to the sharp temporal and spatial variations of velocity and pressure at the initial stage of impact, a dual system is adopted. The simulation close to the impact zone is conducted in a stretched coordinate system, while away from the impact zone the deformation and propagation of incoming overturning wave is simulated in the physical coordinate system. The continuities of both pressure and velocity are enforced at the interface of two zones. When the impact zone is no longer small, the dual systems will be merged and the simulation will be undertaken in one single domain. The air bubble trapped between the breaking wave and the solid surface is taken into account based on the assumption that the trapped air undergoes an adiabatic process. An auxiliary function method is used to decouple the nonlinear mutual dependence of fluid loading, body motion and bubble deformation. Simulations are undertaken for cases related to breaking wave impact in various engineering problems, including a solid coastal wall, a freely floating ship cross section, a floating breakwater and a tension leg platform. Detailed results for pressure, free surface profile, bubble deformation and body motion are provided, and their physical implications are discussed.

Motion of a floating body in a harbour by domain decomposition method

A three-dimensional domain decomposition method is used to solve the problem of wave interaction with a ship floating inside a harbour with arbitrary shape. The linearized velocity potential theory is adopted. The total fluid domain is divided into two sub-ones: one for the harbour and the other for the external open sea. Boundary integral equations together with the free surface Green function are used in the both domains. Matching conditions are imposed on the interface of the two sub-domains to ensure the velocity and pressure continuity. The advantage of the domain decomposition method over the single domain method is that it removes the coastal surface from the boundary integral equation. This subsequently removes the need for elements on the coastal wall when the equation is discretized. The accuracy of the method is demonstrated through convergence study and through the comparison with the published data. Extensive results through the hydrodynamic coefficients, wave exciting forces and ship motions are provided. Highly oscillatory behaviour is observed and its mechanism is discussed. Finally, the effects of incident wave direction, ship location as well as the harbour topography are investigated in detail.

The role of periodically varying discharge on river plume structure and transport

We present results from laboratory experiments that simulate the effects of periodically varying discharge on buoyant coastal plumes. Freshwater is discharged into a two meter diameter tank filled with saltwater on a rotating table. The mean inflow rate, tank rotation period and density of the ambient salt water are varied to simulate a range of inflow Froude and Rossby numbers. The amplitude and the period of the inflow modulation are varied across a range that simulates variability due to tides and storms. Using the optical thickness method, we measure the width and depth of the plume, plume volume and freshwater retention rate in the plume. With constant discharge, freshwater is retained in a growing anticyclonic bulge circulation near the river mouth, as observed in previous studies. When the discharge is varied, the bulge geometry oscillates between a circular plume structure that extends mainly in the offshore direction, and a compressed plume structure that extends mainly in the alongshore direction. The oscillations result in periodic variations in the width and depth of the bulge and the incidence angle formed where the bulge flow re-attaches with the coastal wall. The oscillations are more pronounced for longer modulation periods, but are relatively insensitive to the modulation amplitude. A phase difference between the time varying transport within the bulge and bulge geometry determines the fraction of the bulge flow discharged into the coastal current. As a result, the modulation period determines the variations in amount of freshwater that returns to the bulge. Freshwater retention in the bulge is increased in longer modulation periods and more pronounced for larger modulation amplitudes.

The Columbia River plume as cross-shelf exporter and along-coast barrier

An intensive Lagrangian particle-tracking analysis of the July 2004 upwelling period was conducted in a hindcast model of the US Pacific Northwest coast, in order to determine the effect of the Columbia River plume on the fate of upwelled water. The model, implemented using Regional Ocean Modeling System (ROMS), includes variable wind and atmospheric forcing, variable Columbia river flow, realistic boundary conditions from Navy Coastal Ocean Model (NCOM), and 10 tidal constituents. Model skill has been demonstrated in detail elsewhere [MacCready, P., Banas, N.S., Hickey, B.M., Dever, E.P., Liu, Y., 2008. A model study of tide- and wind-induced mixing in the Columbia River estuary and plume. Continental Shelf Research, this issue, doi:10.1016/j.csr.2008.03.015]. Particles were released in the Columbia estuary, along the Washington coastal wall, and along the model's northern boundary at 48°N. Particles were tracked in three dimensions, using both velocities from ROMS and a vertical random displacement representing turbulent mixing. When 25 h of upwelling flow is looped and particles tracked for 12 d, their trajectories highlight a field of transient eddies and recirculations on scales from 5 to 50 km both north and south of the Columbia. Not all of these features are caused by plume dynamics, but the presence of the plume increases the entrainment of inner-shelf water into them. The cumulative effect of the plume's interaction with these transient features is to increase cross-shelf dispersion: 25% more water is transported laterally past the 100 m isobath when river and estuarine effects are included than when they are omitted. This cross-shelf dispersion also disrupts the southward transport of water along the inner shelf that occurs in the model when the Columbia River is omitted. This second effect—increased retention of upwelled water on the Washington shelf—may be partly responsible for the regional-scale alongcoast gradient in chlorophyll biomass, although variations in shelf width, the Juan de Fuca Eddy to the north, and the intermittency of upwelling-favorable winds are likely also to play important roles.

Estimating tidal current amplitudes outside estuaries and characterizing the zone of estuarine tidal influence

Tidal currents within many estuaries are stronger than on the adjacent continental shelf. Estuarine tidal influence extends onto the shelf elevating tidal amplitudes above ambient shelf levels over a region outside the estuary. In this paper, a kinematic theory that describes tidal flow in these estuary–shelf tidal interaction zones is derived and tested. Using these results, tidal current amplitudes outside estuaries are estimated and the range and intensity of estuarine tidal influence is characterized. The estimates for the tidal current amplitudes ( u tide) of the dominant constituent are appropriate for linear or weakly nonlinear systems with predominantly barotropic tides; the ratio of tidal height to water depth is small ( η/ h≪1) in linear or weakly nonlinear regimes. Within tidal interaction zones, the tidal current amplitude is composed of an ambient shelf part ( u a) and an estuary-induced part ( u e). The characteristic shelf amplitude far from the estuary is used to set u a. Continuity arguments indicate that u e (averaged over a control volume arc centered on the mouth with radius r and a swath angle of γπ) approximately equals the ratio of the tidal volume flux through the mouth ( V m) and the cross-sectional area of any control volume arc ( u e ≈ V m / γ π r h ¯ ) . This approximation holds where the squared product of the tidal wave number and radial distance is small: ( kr) 2≪1. For a shelf with constant slope α and small coastal wall depth, the arc-averaged depth is h ¯ ≈ sr (where s=2 α/ pi for γ=1). For this shelf bathymetry, u e decays with squared radial distance from the estuary mouth. Theoretical predictions are consistent with observed tidal current amplitudes outside the Delaware Bay and Block Island Sound. In both test cases, the estimated and observed amplitudes exhibit an r −2 dependence and decay over a similar distance. The relative importance of estuarine tidal influence is assessed with the tidal interaction index ( T i= u e/ u a). The intensity of estuarine influence is characterized by the value of T i at the mouth ( T im). The extent of an estuary–shelf tidal interaction zone is measured by the interaction radius r i (where T i=1) and by r ∞ (where T i=0.1). These metrics are used to compare the tidal interaction zone characteristics for the Delaware Bay, Block Island Sound, several other major estuaries, and a small tidal inlet. The kinematic theory can be applied outside other estuaries where only limited tidal information is available or used to interpret observed patterns in tidal amplitudes and characterize the degree of estuarine influence.

Observations of near‐inertial current variability on the New England shelf

Observations from the Coastal Mixing and Optics (CMO) moored array (deployed from August 1996 through June 1997) and supplemental moored observations are used to describe near‐inertial current variability over the New England shelf. Near‐inertial band current variance comprises 10–20% of the total observed current variance, and has episodic peak speeds exceeding 30 cm s−1. Near‐inertial current variability during CMO is characterized by a first baroclinic mode vertical structure with one zero‐crossing between 15 and 50 m. The zero‐crossing is shallower during periods of stronger stratification. Laterally, near‐inertial variability is coherent over the extent of the CMO moored array, and cross‐shelf decorrelation scales for near‐inertial currents are about 100 km, approximately the entire shelf width. The magnitude of near‐surface near‐inertial variability is stronger in the summer and weaker in the winter, following the seasonal variation in stratification and opposite the seasonal cycle in wind stress variance. During CMO, near‐surface near‐inertial kinetic energy is inversely related to surface mixed layer depth. Near‐inertial variance decreases onshore, matching approximately the cross‐shelf decrease in near‐inertial energy predicted by a two‐dimensional, linear, flat‐bottom, two‐layer, coastal wall model. In this model, the nullifying effects of a baroclinic wave emanating from the coastal wall play a dominant role in controlling the onshore decrease. Finally, strong persistent anticyclonic relative vorticity shifts near‐inertial variability on the New England shelf to subinertial frequencies.

Local and remote forcing of currents and temperature in the central Southern California Bight

A comprehensive study of the central Southern California Bight shows that subtidal currents are dominated by relatively long time scales (10–25 days), large alongshore scales, and significant offshore and upward phase propagation. A one‐dimensional model shows that observed fluctuating, poleward propagating (speeds 140–260 cm s−1) alongshore pressure gradient disturbances account for a much larger fraction of the alongshore velocity variance than local wind stress (at least 40% in both seasons) and have the longer periods of the dominant currents. With the addition of local wind stress, about half the velocity variance can be accounted for, and overall, about 5% more variance in spring than in summer. Results are consistent with generation of disturbances by remote wind stress several hundred kilometers equatorward of the bight and alongcoast propagation as low‐mode coastally trapped waves. The large‐scale remote forcing is also responsible for much of the velocity variance on the adjacent shelf, the semienclosed Santa Monica Bay. A nonlinear, three‐dimensional model shows that water is pushed into the bay initially as part of a throughflow, later becoming an eddy that gradually fills the bay, producing counterflow on its shoreward side. On the shelf, local alongshore wind stress accounts for only 25% of the velocity variance in spring and none in summer. The large‐scale disturbances also produce significant temperature fluctuations throughout the region, via lateral advection of the mean alongshore temperature gradient. Local wind‐driven coastal upwelling is responsible for temperature fluctuations on the inner shelf during several 2–4 day events in spring, but only very near the coastal wall.

One-Dimensional Models for the Closure of a Coastal Latent Heat Polynya

Abstract One-dimensional models for the closure of a coastal latent heat polynya due to the onshore drift of frazil ice and consolidated ice are presented in this paper. The models predict the width of a polynya during an opening and closing cycle and include the cases in which the collection thickness of consolidated new ice at the polynya edge (during opening) or at the coast (during closing) is (a) a prescribed constant or (b) parameterized in terms of the depth of frazil ice arriving at the polynya edge (during opening) or the coast (during closing) and the relative velocity of the frazil ice with respect to the “convergence boundary” (i.e., the consolidated ice during opening or the stationary coastal wall during closing). Four dimensionless parameters specify the opening and closing cycle of a polynya, and throughout most of the four-dimensional parameter space the closing timescale is shorter than the opening timescale. In this case, it is found that the heat released from the polynya to the atmosp...

A numerical investigation of slanted convection and subsurface anticyclone generation in an Arctic baroclinic current system

A nonhydrostatic three‐dimensional numerical model is used to investigate convection along slanted isopycnal surfaces and subsurface anticyclone generation in a baroclinic jet system appropriate for the Beaufort Sea environment. The current is initially bounded to the left by a coastal wall and subsequently subject to surface friction exerted by sea ice and cooling at the sea surface. Despite spatially uniform cooling rates used in the model, convection favors limited areas with high cyclonic vorticity. In a meandering current system, rigorous convection occurs primarily in meander troughs where the current turns cyclonically. The cyclonic vorticity enhances convection, which in turn enhances cyclonic vorticity. The positive feedback mechanism, previously known in atmospheric literature as convective instability of the second kind, often strengthens convection and the consequent subsurface anticyclones by as much as 1 order of magnitude. Subsequent seaward detrainment in subsurface depths of interest moves anticyclones from the cyclonic side of the jet to the anticyclonic side. The subsurface anticyclones may be strengthened for the second time because of favorable changes of ambient vorticity. Thus downward convection along slanted isopycnal surfaces of a left‐bounded baroclinic jet (similar to segments of the Beaufort Sea anticyclonic gyre) is an efficient way to produce subsurface anticylcones and propel them seaward afterward.

Adjustment of the Marine Atmospheric Boundary Layer to a Coastal Cape

Abstract During summer, significant changes in marine atmospheric boundary layer (MABL) speed and depth occur over small spatial scales (<100 km) downstream from topographic features along the California coast. In June and July 1996, the Coastal Waves 96 project collected observations of such changes at capes with an instrumented aircraft. This paper presents observations from the 7 June flight, when the layer-averaged speed increased 9 m s−1 and depth decreased by 500 m over a 75-km downwind from Cape Mendocino, accompanied by enhanced surface fluxes and local cloud clearing. The acceleration and thinning are reproduced when the flow is modeled as a shallow transcritical layer of fluid impinging the bends of a coastal wall, leading to the interpretation that they are produced by an expansion fan. Model runs were produced with different coastlines and imposed pressure gradients, with the best match provided by a coastline in which the cape protruded into the flow and forced a response in the subcritical r...

The impact of model configuration in studies of buoyant coastal discharge

Observations and model studies of large-scale buoyant plumes show three major types for the horizontal distribution of density. Type 1 represents the typical coastal freshwater plume of observations. The buoyant discharge turns right in the northern hemisphere (toward downshelf) under earth rotation at its source. Type 2 is common in many numerical model studies. Most of the buoyant water at the inlet turns left (upshelf) along the coast to form a continuously growing intrusion. Type 3 turns right but exhibits a massive anticyclonic bulge which grows with time; its coastal current is weak and carries a small fraction of the inlet fresh water or buoyancy flux. The great majority of observed coastal plumes and their appended coastal currents have been type 1, while models have most often produced type 2 or 3. To remedy this disparity, modelers have imposed an ambient shelf current in the downshelf (right hand) direction of sufficient strength to produce type 1 plumes. Field observations of the Delaware Coastal Current are presented. They show type 1 plumes occur even when the ambient shelf flow is upshelf. Imposing a downshelf ambient current is not, then, a generally applicable remedy to obtain a type 1 plume in model studies. A common element in the configuration of these models is use of the simple inlet, a rectangular breach in the coastal wall with uniform inflow water properties. An analytic treatment of the resulting flow near the coastal wall upshelf of the simple inlet predicts a steady intrusion of buoyant water that increases with depth of the coastal wall. Subsequent numerical experiments with this model configuration confirmed these predictions qualitatively. The simple inlet and the coastal wall are thus suspect. Three changes in model configuration yielded numerical model results that were type 1. The first was adoption of an idealized estuarine inlet in place of the simple inlet. The second was use of a greatly reduced coastal wall. The third was use of inlet channel angles less than normal, With all three of these alterations, upshelf intrusion was very weak, perhaps at a level that would be undetected in field observations. The flow was nearly steady state and no massive bulge was present, despite the absence of ambient shelf motion. Each of these three changes to configuration generated clear differences in the state of the buoyancy-driven coastal current well downshelf, despite use of the same bulk discharge properties such as total volume and freshwater fluxes. Using the results of observations, laboratory models, and numerical models, one may attempt to codify the natural and model settings or configurations that select which plume type occurs. Type 3 plumes seem the clearest to predict. They require weak or absent downshelf ambient current, nearly normal inlet channel angle, a steep coastal bottom slope, and water depths much greater than the typical depth of buoyant water. Type 2 plumes, in contrast, all appear to be shallow water phenomena. In addition they require weak or absent ambient downshelf current, inlet flow angles near normal, and a steep coastal bottom slope or vertical coastal wall. Type 1 plumes are the most common in field observations. They too are shallow water phenomena. Model configurations that favor them include absence of a significant coastal wall and use of more realistic inlet flow fields than the simple inlet.

Modeling of two‐layer eddies and coastal flows with a particle method

An existing particle‐in‐cell (PIC) numerical method developed for the study of two‐layer mesoscale motions with outcropping pycnocline is applied to lens‐like anticyclonic vortices and buoyant coastal currents. From a first series of experiments investigating the evolution of an initially elongated lens‐like anticyclone, it is found that motions induced in the lower layer act only to increase the rotation of the vortex structure and do not appear to affect the process of eccentricity reduction (partial axisymmetrization). Eccentricity reduction, if any, produces a final vortex of aspect ratio between 1.8 and 1.9, a value that is very close to the stability threshold of large, reduced‐gravity lenses. A second series of experiments devoted to vortex mergers determines how the maximal separation distance for which two circular anticyclonic lenses merge spontaneously varies with vortex size (ratio of lens radius to deformation radius) and stratification (ratio of lens central thickness to ocean depth). A third series of experiments considers the interaction of a lens vortex in the upper layer with a potential‐vorticity anomaly in the lower layer. “Second‐hand” relative vorticity, generated in the lower layer under the action of vertical stretching induced by the movement of the upper‐layer vortex, interacts with “first‐hand” relative vorticity, created by the existing potential‐vorticity, to create effects similar to those predicted by studies of two‐layer point vortices (hetons). Finally, the PIC method is generalized to simulate the finite‐amplitude instability of a buoyant geostrophic/hydrostatic intrusion flowing along a vertical coastal wall. Those results, however, are reported here more as a demonstration on how the PIC method can be extended to include coastal boundaries than as a thorough investigation of coastal‐current instabilities.

Obliquely Incident Poincaré Waves on a Sloping Continental Shelf

Abstract An analytical theory of barotropic tides propagating onto a sloping continental shelf from the deep ocean is developed. The plane Poincare waves incident from the deep ocean are obliquely angled, and a full matching of shelf and ocean solutions is implemented. Allowance for a nonzero water depth at the coast requires an additional term, the Bessel function of second kind, in the solution. The full solution is examined for response characteristics for both frictionless tides and for tides affected by a linear bottom friction, and energy dissipation rates are evaluated. Results for narrow continental shelves indicate that a small but nonzero coastal wall depth, in conjunction with the angle of incidence, can play a significant role in modifying the response, while for wider continental shelves both of these features greatly modify the response at resonance.