Direction Of Kelvin Wave Propagation Research Articles

Separation of the Icelandic Coastal Current from the Reykjanes Peninsula

The Icelandic Coastal Current (ICC) is a buoyant flow fueled by multiple rivers. Satellite observations during the October–November 2019 study period indicate the ICC often separates from the southwest tip of the Reykjanes Peninsula; it subsequently has large offshore excursion during west-southwestward winds. Results from a high-resolution realistic simulation exhibit this ICC behavior and provide detail on the associated currents and salinities. Sensitivity tests with simplified bathymetry, no winds, or no local buoyancy inputs are compared to the standard run to isolate contributions of those factors to flow separation. Analysis indicates that ICC separation occurs because the coast turns more tightly than the inertial radius; this behavior is consistent with inviscid theory. Partial flow deflection over the shelf expression of the Reykjanes Ridge and the widening shelf both increase ICC offshore excursion. The ICC is strongly influenced by the barotropic wind response to west-southwestward winds that includes a downshelf jet (flowing in the direction of Kelvin wave propagation) along the coast upshelf of the peninsula's tip where winds are downwelling-favorable, the downshelf extension of the jet that bends around the peninsula and progresses farther offshore with isobaths, a band of offshore and upshelf currents along the coast downshelf of the peninsula's tip, and surface flow aligned with Ekman transport located offshore beyond the downshelf jet. Similar wind-influence scenarios are discussed for other plumes. There are likely many such hotspots for offshore freshwater transport around the world.

The Evolution of a Buoyant River Plume in Response to a Pulse of High Discharge from a Small Midlatitude River

AbstractA unique feature of small mountainous rivers is that discharge can be elevated by an order of magnitude during a large rain event. The impact of time-varying discharge on freshwater transport pathways and alongshore propagation rates in the coastal ocean is not well understood. A suite of simulations in an idealized coastal ocean domain using the Regional Ocean Modeling System (ROMS) with varying steady background discharge conditions (25–100 m3 s−1), pulse amplitude (200–800 m3 s−1), pulse duration (1–6 days), and steady downwelling-favorable winds (0–4 m s−1) are compared to investigate the downstream freshwater transport along the coast (in the direction of Kelvin wave propagation) following a discharge pulse from the river. The nose of the pulse propagates rapidly alongshore at 0.04–0.32 m s−1 (faster propagation corresponds with larger pulse volume and faster winds) transporting 13%–66% of the discharge. The remainder of the discharge volume initially accumulates in the bulge near the river mouth, with lower retention for longer pulse duration and stronger winds. Following the pulse, the bulge eddy disconnects from the river mouth and is advected downstream at 0–0.1 m s−1, equal to the depth-averaged wind-driven ambient water velocity. As it transits alongshore, it sheds freshwater volume farther downstream and the alongshore freshwater transport stays elevated between the nose and the transient bulge eddy. The evolution of freshwater transport at a plume cross section can be described by the background discharge, the passage of the pulse nose, and a slow exponential return to background conditions.

Vortex competition in coastal outflows

Experiments and field observations have shown that there are at least two modes of behavior for river plumes. In many cases, the plume turns to the right (in the Northern Hemisphere) on leaving the river mouth and follows the direction of Kelvin-wave propagation. Alternatively, a “bulge” can form in the plume and a fraction of the outflow volume becomes trapped near the mouth. This paper discusses how bulge formation can be affected by the vorticity profile at the river mouth. Due to the image effect, regions of cyclonic vorticity tend to propagate rightwards, whereas regions of anticyclonic vorticity propagate leftward upon exit from the source. If an outflow consists of regions of cyclonic vorticity to the left of regions of anticyclonic vorticity, the two image effects are in competition. We explore this phenomenon using a quasi-geostrophic model with piecewise-constant potential vorticity, which allows the vorticity profile at the source to be set as part of the problem. We present analytic solutions valid in the source region and at the head of the plume and show that all of the outflow travels rightwards if and only if the region of cyclonic vorticity is dominant. The initial-value problem for the model is integrated numerically using the method of contour dynamics, and the full parameter space is explored. We find that if the cyclonic and anticyclonic contributions cancel, as in the experiments of Avicola and Huq (2003), then steady solutions are unstable and a bulge can form downstream of the river mouth.

Coastal outflow currents into a buoyant layer of arbitrary depth

The long-wave, reduced-gravity, shallow-water equations (the semi-geostrophic equations) are used to study the outflow of a river into the ocean. While previous models have studied dynamics driven by gradients in density, the focus here is on the effects of potential vorticity anomaly (PVa). The river water is taken to have the same density as a finite-depth upper layer of oceanic fluid, but the two fluids have different, uniform, potential vorticities. Under these assumptions, the governing equations reduce to two first-order, nonlinear partial differential equations which are integrated numerically for a prescribed efflux of river water and PVa. Results are found to depend strongly on the sign of the PVa, with all fluid turning downstream (in the direction of Kelvin-wave propagation) when the river water has positive PVa and anticyclonic flow upstream of the river mouth when the PVa is negative. In all cases, a nonlinear Kelvin wave propagates at finite speed ahead of the river water. Away from the river mouth, the uniformity of one set of Riemann invariants allows for similarity solutions that describe the shape of the outflow, as well as a theory that predicts properties of the Kelvin wave. A range of behaviours is observed, including flows that develop shocks and flows that continue to expand offshore. The qualitative behaviour of the outflow is strongly correlated with the value of a single dimensionless parameter that expresses the ratio of the speed of the flow driven by the Kelvin wave to that driven by image vorticity.

Topographic generation of submesoscale centrifugal instability and energy dissipation

Most of the ocean kinetic energy is contained in the large scale currents and the vigorous geostrophic eddy field, at horizontal scales of order 100 km. To achieve equilibrium the geostrophic currents must viscously dissipate their kinetic energy at much smaller scale. However, geostrophic turbulence is characterized by an inverse cascade of energy towards larger scale, and the pathways of energy toward dissipation are still in question. Here, we present a mechanism, in the context of the Gulf Stream, where energy is transferred from the geostrophic flow to submesoscale wakes through anticyclonic vertical vorticity generation in the bottom boundary layer. The submesoscale turbulence leads to elevated local dissipation and mixing outside the oceanic boundary layers. This process is generic for boundary slope currents that flow in the direction of Kelvin wave propagation. Topographic generation of submesoscale flows potentially provides a new and significant route to energy dissipation for geostrophic flows.

Wind‐modulated buoyancy circulation over the Texas‐Louisiana shelf

AbstractThis numerical investigation examines buoyancy‐driven circulation on the Texas‐Louisiana shelf modulated by seasonal winds. In wintertime, with downcoast (in the direction of Kelvin wave propagation) wind forcing, the Mississippi‐Atchafalaya River plume exhibits a bottom‐advected pattern. The plume is fairly wide and the horizontal density gradients span almost across the entire shelf inshore of 50 m. Within the plume, vertical shear of alongshore flow is in thermal wind balance with the cross‐shore density gradient, and the shear causes a slight reversal of alongshore flow near the bottom. An alongshore flow estimated by the thermal wind relation, along with an assumption of zero bottom velocity, generally well agrees with the actual flow near the surface in regions deeper than 20 m. In spring and summer, the thermal‐wind‐balance‐derived flow deviates from the actual alongshore flow, and an Ekman flow driven by strong onshore wind makes the major contribution to the deviation. Besides, the summertime upcoast wind component transforms the plume to a surface‐advected state, resulting in reduced cross‐shore density gradients and increasing the relative importance of wind‐driven, barotropic alongshore flow, which contributes to the remaining deviation.

The Dispersal of Dense Water Formed in an Idealized Coastal Polynya on a Shallow Sloping Shelf

Abstract This study examines the dispersal of dense water formed in an idealized coastal polynya on a sloping shelf in the absence of ambient circulation and stratification. Both numerical and laboratory experiments reveal two separate bottom pathways for the dense water: an offshore plume moving downslope into deeper ambient water and a coastal current flowing in the direction of Kelvin wave propagation. Scaling analysis shows that the velocity of the offshore plume is proportional not only to the reduced gravity, bottom slope, and inverse of the Coriolis parameter, but also to the ratio of the dense water depth to total water depth. The dense water coastal current is generated by the along-shelf baroclinic pressure gradient. Its dynamics can be separated into two stages: (i) near the source region, where viscous terms are negligible, its speed is proportional to the reduced gravity wave speed and (ii) in the far field, where bottom drag becomes important and balances the pressure gradient, the velocity is proportional to Hc[g′/(LCd)]1/2 in which Hc is the water depth at the coast, g′ the reduced gravity, Cd the quadratic bottom drag coefficient, and L the along-shelf span of the baroclinic pressure gradient. The velocity scalings are verified using numerical and laboratory sensitivity experiments. The numerical simulations suggest that only 3%–23% of the dense water enters the coastal pathway, and the percentage depends highly on the ratio of the velocities of the offshore and coastal plumes. This makes the velocity ratio potentially useful for observational studies to assess the amount of dense water formed in coastal polynyas.

Interaction of Ekman Layers and Islands

Abstract The circulation induced by the interaction of surface Ekman transport with an island is considered using both numerical models and linear theory. The basic response is similar to that found for the interaction of Ekman layers and an infinite boundary, namely downwelling (upwelling) in narrow boundary layers and deformation-scale baroclinic boundary layers with associated strong geostrophic flows. The presence of the island boundary, however, allows the pressure signal to propagate around the island so that the regions of upwelling and downwelling are dynamically connected. In the absence of stratification the island acts as an effective barrier to the Ekman transport. The presence of stratification supports baroclinic boundary currents that provide an advective pathway from one side of the island to the other. The resulting steady circulation is quite complex. Near the island, both geostrophic and ageostrophic velocity components are typically large. The density anomaly is maximum below the surface and, for positive wind stress, exhibits an anticyclonic phase rotation with depth (direction of Kelvin wave propagation) such that anomalously warm water can lie below regions of Ekman upwelling. The horizontal and vertical velocities exhibit similar phase changes with depth. The addition of a sloping bottom can act to shield the deep return flow from interacting with the island and providing mass transport into/out of the surface Ekman layer. In these cases, the required transport is provided by a pair of recirculation gyres that connect the narrow upwelling/downwelling boundary layers on the eastern and western sides of the island, thus directly connecting the Ekman transport across the island.

Friction and Diapycnal Mixing at a Slope: Boundary Control of Potential Vorticity

Abstract Although atmospheric forcing by wind stress or buoyancy flux is known to change the ocean’s potential vorticity (PV) at the surface, less is understood about PV modification in the bottom boundary layer. The adjustment of a geostrophic current over a sloped bottom in a stratified ocean generates PV sources and sinks through friction and diapycnal mixing. The time-dependent problem is solved analytically for a no-slip boundary condition, and scalings are identified for the change in PV that arises during the adjustment to steady state. Numerical experiments are run to test the scalings with different turbulent closure schemes. The key parameters that control whether PV is injected into or extracted from the fluid are the direction of the geostrophic current and the ratio of its initial speed to its steady-state speed. When the current is in the direction of Kelvin wave propagation, downslope Ekman flow advects lighter water under denser water, driving diabatic mixing and extracting PV. For a current in the opposite direction, Ekman advection tends to restratify the bottom boundary layer and increase the PV. Mixing near the bottom counteracts this restratification, however, and an increase in PV will only occur for current speeds exceeding a critical value. Consequently, the change in PV is asymmetric for currents of the opposite sign but the same speed, with a bias toward PV removal. In the limit of a large speed ratio, the change in PV is independent of diapycnal mixing.

Modeling river plume dynamics with the HYbrid Coordinate Ocean Model

The dynamics of large-scale river plumes are investigated in idealized numerical experiments using the HYbrid Coordinate Ocean Model (HYCOM). The focus of this study is to address how the development and structure of a buoyant plume are affected by the outflow properties, as impacted by processes within the estuary and at the point of discharge to the coastal basin. Changes in the outflow properties involved vertical and horizontal redistribution of the river inflow and enhanced vertical mixing inside an idealized estuary. The development of the buoyant plume was evaluated in a rectangular, f-plane basin with flat and sloping bottom conditions and in the absence of other external forcing. The general behavior of a mid-latitude river plume was reproduced, with the development of a surface anticyclonic bulge off the estuary mouth and a surface along-shore coastal current which flows in the direction of Kelvin wave propagation (“downstream”); the momentum balance was predominantly geostrophic. Conditions within the estuary and the outflow properties at the river mouth (where observed profiles may be available) greatly impacted the fate of riverine waters. In flat bottom conditions, larger mixing at the freshwater source enhanced the estuarine gravitational circulation, promoting larger upward entrainment and stronger outflow velocities. Although the overall geostrophic balance was maintained, estuarine mixing led to an asymmetry of the currents reaching the river mouth and to a sharp anticyclonic veering within the estuary, resulting in reduced upstream flow and enhanced downstream coastal current. These patterns were altered when the plumes evolved in the presence of a bottom slope. The anticyclonic veering of the buoyant outflow was suppressed, the offshore intrusion decreased and the recirculating bulge was displaced upstream. The sloping bottom impacts were accompanied by enhanced transport and increased downstream extent of the coastal current in most cases. No major changes in the general properties and especially the vertical structure of the plumes were observed when the vertical coordinates were changed from cartesian–isopycnal, to sigma or to sigma–isopycnal. The findings offer a benchmark for coastal studies with HYCOM, where plume dynamics should be examined in tandem with additional circulation forcing mechanisms, resulting in transitions of the vertical coordinate system that are dictated by the prevailing dynamics.

Buoyancy-Forced Downwelling in Boundary Currents

Abstract The issue of downwelling resulting from surface buoyancy loss in boundary currents is addressed using a high-resolution, nonhydrostatic numerical model. It is shown that the net downwelling is determined by the change in the mixed layer density along the boundary. For configurations in which the density on the boundary increases in the direction of Kelvin wave propagation, there is a net downwelling within the domain. For cases in which the density decreases in the direction of Kelvin wave propagation, cooling results in a net upwelling within the domain. Symmetric instability within the mixed layer drives an overturning cell in the interior, but it does not contribute to the net vertical motion. The net downwelling is determined by the geostrophic flow toward the boundary and is carried downward in a very narrow boundary layer of width E1/3, where E is the Ekman number. For the calculations here, this boundary layer is O(100 m) wide. A simple model of the mixed layer temperature that balances horizontal advection with surface cooling is used to predict the net downwelling and its dependence on external parameters. This model shows that the net sinking rate within the domain depends not only on the amount of heat loss at the surface but also on the Coriolis parameter, the mixed layer depth (or underlying stratification), and the horizontal velocity. These results indicate that if one is to correctly represent the buoyancy-forced downwelling in general circulation models, then it is crucial to accurately represent the velocity and mixed layer depth very close to the boundary. These results also imply that processes that lead to weak mixing within a few kilometers of the boundary, such as ice formation or freshwater runoff, can severely limit the downwelling forced by surface cooling, even if there is strong heat loss and convection farther offshore.

Seasonal variations of the Yellow River plume in the Bohai Sea: A model study

We investigated the behavior of the Yellow River plume in the Bohai Sea through a year and its controlling mechanisms using a numerical model driven by monthly averaged wind stress, heat flux, and river discharge. The model produced a clear seasonal behavior of the Yellow River plume. In summer, the Yellow River plume extends northeastward into the central Bohai Sea; in autumn, it turns southward and flows into Laizhou Bay along the coast; in winter, most of the diluted water is found around southeastern corner of Laizhou Bay; and in spring, a low‐salinity area appears in southwest Laizhou Bay. With the same model, several well‐designed numerical experiments were performed to investigate the effect on the behavior of the Yellow River plume of tidal current, river discharge, wind stress, and thermal stratification. The tidal currents promote the offshore spread of diluted water, while the tide‐induced residual currents prevent the plume from extending further downstream (in the direction of Kelvin wave propagation). Wind stresses lead to pronounced changes in the path and shape of the plume. In autumn and winter, northwesterly or northerly winds drive the buoyant water into Laizhou Bay along the coast. In summer, the combination of southeasterly winds and thermal stratification drives the plume extend northeastward into the central Bohai Sea. By changing only the magnitude of wind stress or river discharge in the experiments, we examined the sensitivity of summertime plume to the magnitude of wind stress and river discharge.

Wind influence on a coastal buoyant outflow

This paper investigates the interplay between river discharge and winds in forcing coastal buoyant outflows. During light winds a plume influenced by the Earth's rotation will flow down shelf (in the direction of Kelvin wave propagation) as a slender buoyancy‐driven coastal current. Downwelling favorable winds augment this down‐shelf flow, narrow the plume, and mix the water column. Upwelling favorable winds drive currents that counter the buoyancy‐driven flow, spread plume waters offshore, and rapidly mix buoyant waters. Two criteria are developed to assess the wind influence on a buoyant outflow. The wind strength index (Ws) determines whether a plume's along‐shelf flow is in a wind‐driven or buoyancy‐driven state. Ws is the ratio of the wind‐driven and buoyancy‐driven along‐shelf velocities. Wind influence on across‐shelf plume structure is rated with a timescale (ttilt) for the isopycnal tilting caused by wind‐driven Ekman circulation. These criteria are used to characterize wind influence on the Delaware Coastal Current and can be applied to other coastal buoyant outflows. The Delaware buoyant outflow is simulated for springtime high–river discharge conditions. Simulation results and Ws values reveal that the coastal current is buoyancy‐driven most of the time (∣Ws∣ < 1 on average). Wind events, however, overwhelm the buoyancy‐driven flow (∣Ws∣ > 1) several times during the high‐discharge period. Strong upwelling events reverse the buoyant outflow; they constitute an important mechanism for transporting fresh water up shelf. Across‐shelf plume structure is more sensitive to wind influence than the along‐shelf flow. Values of ttilt indicate that moderate or strong winds persisting throughout a day can modify plume width significantly. Plume widening during upwelling events is accompanied by mixing that can erase the buoyant outflow.

Three-Dimensional Flow in a Shallow Coastal Upwelling Zone: Alongshore Convergence and Divergence on the New Jersey Shelf

Alongshore flow field divergence is investigated on the inner shelf off the coast of New Jersey during the summer upwelling season of 1996. Velocities obtained from an array of moorings are used to examine the flow field. Empirical orthogonal function (EOF) analyses are employed to extract those features of the flow field that are resolved by the moorings and to construct a measure of alongshore divergence. Multi-input single-output linear systems analysis is used to examine the role of buoyancy intrusions and wind stress in determining alongshore divergence or convergence of the flow field and to construct a proxy for divergence derived from a time series of stratification gradients and wind stress. Alongshore divergence on this shallow shelf (,25-m depth) is shown to be a function of both wind stress and buoyancy intrusions. The latter originate in the Hudson River outflow and produce downshelf flow (i.e., in the direction of Kelvin wave propagation). Examination of the first EOF mode (containing 67% of the variance) reveals that the largest resolved fluctuations are oriented alongshore and are characterized by strong counterclockwise veering with depth. Momentum balances demonstrate that the depth-averaged flow fields are governed by wind stress, bottom stress, and the across-shore pressure gradient. The second EOF mode describes significantly less variance (8%); however, it represents the across- and alongshore variations of the flow field, composing the bulk of the alongshore divergence. The production of alongshore divergence by a combination of wind stress and buoyancy intrusions is a likely outcome in upwelling regimes downshelf of a major buoyancy source.

Enhancement of Wind-Driven Upwelling and Downwelling by Alongshore Bathymetric Variability*

Steady wind-driven flow along a shelf of changing width is described with a frictional barotropic model valid in the limit of small Rossby and Burger number. In these limits, an alongshore wind drives enhanced onshelf transport in a coastal ocean if the shelf widens downwind, and the change in shelf width only affects the flow in the direction of Kelvin wave propagation (‘‘downwave’’) from the change in shelf width. There is enhanced onshore transport of cold, nutrient-laden bottom water if the winds favor upwelling and the shelf narrows in the direction of Kelvin wave propagation. This enhanced transport extends a considerable distance away from the change in shelf width but becomes concentrated near the shelf break far from the change in width. Isobath curvature on the scale of the shelf width significantly modifies local cross-shelf transport. The cross-shelf transport of nutrient-rich water during upwelling is expected to be enhanced from Point Eugenia to La Jolla, San Luis Obispo to Monterey, and Point Reyes to Cape Mendocino on the west coast of North America.

Large scale buoyancy driven circulation on the continental shelf

Abstract Freshwater discharge from rivers and estuaries produces plumes and coastal currents locally. What is the fate of these coastal currents far downstream and over long time scales? The mechanism and processes related to the slow alongshelf evolution of a surface-trapped plume in the presence of an ambient flowfield are studied with the help of a three-dimensional primitive equation numerical model. As the buoyant water enters the coastal ocean, it turns anticyclonically and moves downstream in the direction of Kelvin wave propagation. Close to the source, the plume is surface-trapped. The offshore buoyancy flux in the bottom boundary layer pushes the front seaward detaching it from the coast and moving it offshore. Eventually, the cross-shelf buoyancy flux vanishes shoreward of the front and the front reaches an equilibrium depth at a particular alongshelf location. At this point, the quasi-stationary buoyancy balance is between horizontal and vertical diffusion and cross-shelf buoyancy flux. The density front has switched from a surface-trapped plume to an intermediate or surface-to-bottom type at this location. Horizontal diffusion contributes to effective horizontal mixing and helps spread freshwater offshore. The offshore penetration of buoyant water depends on three dimensionless parameters: scaled inlet volume transport, scaled breadth and scaled “diffusivity”. We develop an empirical relation for predicting maximum penetration, given these three parameters.

Formation of a shelfbreak front by freshwater discharge

Abstract The circulation and transport of freshwater generated by an idealized buoyant source is studied using a three-dimensional primitive equation model. Freshwater enters the continental shelf, turns anticyclonically and moves downstream in the direction of Kelvin wave propagation. In the region close to the source, the flow reaches an equilibrium in the bottom boundary layer so that freshwater does not spread offshore any further. This offshore equilibrium distance increases as we move downstream until the freshwater is able to feel the presence of the shelfbreak. A shelfbreak front forms and the shelfbreak prevents any further offshore spreading of freshwater in the bottom boundary layer. Two complimentary mechanisms are responsible for the slow cross-shelf migration of freshwater and subsequent trapping of shelfbreak fronts: bottom stress and topographic changes. The shelfbreak creates an active, dynamic process preventing leakage from the continental shelf region to the slope region. However, the dynamical process that traps the front to the shelfbreak is still unclear. The location of the shelfbreak front depends on four dimensionless parameters: scaled inlet volume transport, scaled breadth, scaled “diffusivity” and scaled shelf width. We develop empirical relations for predicting the location of the frontal bottom intersection, given these parameters.

Dynamics of a Buoyancy-Driven Coastal Jet: The Gaspé Current

A primitive equation ocean model is applied to the process study of the Gaspé Current and cyclonic circulation over the northwestern Gulf of St. Lawrence (NWG). The model is driven by river discharge and barotropic boundary flows. Two types of model domains are used: an idealized basin with a flat bottom and piecewise coastline, and a realistic basin with model-resolved NWG bathymetry. The model domains are initially filled with horizontally uniform but vertically stratified waters. The river discharge is expressed in terms of lower salinity and a weak barotropic inflow in the upper waters at the estuary head. The early developments of the estuarine plume and coastal current system driven by the river discharge are qualitatively similar in both basins. After a short-period adjustment, a buoyant plume is developed near the estuary mouth, with a surface-intensified coastal current advecting the estuarine water seaward in the direction of Kelvin wave propagation. The coastal current initially follows the coastline closely but later becomes unstable with backward-breaking waves developed along the outer edge of the current. The kinetic energy analysis reveals that the plume–current system is baroclinically unstable with the transient motions resulting primarily from the mean available potential energy. With the river discharge at the head as the only driving force, the offshore front of the estuarine plume expands continuously seaward, leading to a large-scale anticyclonic circulation over the NWG. The addition of a barotropic westward jet along the Quebec shore, however, is able to restrain the seaward expansion of the offshore front of the plume, and therefore form a large-scale cyclonic motion over this region.

The cyclonic turning and propagation of buoyant coastal discharge along the shelf

Buoyant coastal discharge typically forms a current flowing along the coast in the direction of Kelvin wave propagation (hereinafter referred to as the downstream direction). In this paper the opposite, upstream penetration of buoyancy-driven current is studied using numerical modeling. Previous models of coastal buoyancy-driven currents repeatedly predicted the upstream spreading while in the field this feature was not commonly observed. The mechanism responsible for the propagation of buoyant flow along the coast upstream from its source is identified as follows. In many cases, the boundary conditions applied for buoyant discharge oversimplify the actual dynamics at the mouth blocking landward flow in the lower layer. This generates a strong cyclonic vorticity disturbance with corresponding upstream turning of buoyant flow at the source. This process initiates the upstream spreading of buoyant flow. Alternative boundary condition maintaining constant net transport but allowing baroclinic adjustment of buoyant inflow is formulated and shown to reduce the generation of cyclonic vorticity at the mouth. The upstream propagation is further enhanced by the vertical mixing. The buoyant water forms an anticyclonic bulge at the river or estuary mouth. While spreading around the center of this anticyclone, the fresher water gradually becomes saltier due to vertical mixing/diffusion. As a result, the pool of lightest water does not coincide with the center of the anticyclone (in the sense of integral streamfunction) but tends to occupy the upstream and inshore segment of the bulge where the buoyant water comes first. This sets a new center for the anticyclonic turning at the surface and promotes the upstream shift of the anticyclonic bulge. This process sustains continuous growth of the buoyant plume upstream. It is shown that the upstream ambient current does not produce a similar effect. Instead, buoyant flow periodically sheds anticyclones advected upstream with the mean current. Under certain conditions, upstream spreading is also possible in nature. For example, Beardsley et al. (1985) reported substantial upstream penetration of the Changjiang River discharge in the East China Sea during the period of high runoff.

Sensitivity of plume dynamics to the parameterization of vertical mixing

A three-dimensional primitive equation, baroclinic numerical model incorporating a range of turbulence closure schemes is used to investigate the effects of vertical diffusion of momentum and density upon the spread of a freshwater plume, with particular reference to the Ebro plume. Initial calculations show that there are some differences in the horizontal spread and vertical mixing of the plume when diffusion coefficients are computed from a two-equation turbulence energy model compared with a one-equation model. To understand results from the turbulence energy models, the sensitivity of the plume dynamics to variations in the coefficient of vertical eddy viscosity and diffusivity is also considered, with increases in these parameters having a significant effect upon the cross-shore and along-shore spread of the plume. Also, increasing these parameters changes the plume characteristics from supercritical to subcritical and reduces the occurrence of meandering and baroclinic instability along the plume's off-shore edge. However, differences in the southerly spread (the direction of Kelvin wave propagation in the model) of the plume (although not its northerly spread) produced by changes in diffusion coefficients are small compared with the influence of changes in the bottom slope, upon the along-shore southerly spread of the plume, which moves in the direction of Kelvin wave propagation in the near coastal region. Results from the series of calculations are used as a guide in experimental design, with reference to a planned experiment in the Ebro region involving a coastal HF Radar deployment, as well as off-shore measurements. Calculations suggest that surface current measurements from a coastal HF Radar, together with a detailed survey of the density field associated with the plume, may be an appropriate, although indirect, means of determining suitable mixing coefficients to use in plume discharge problems. Detailed measurements of water depth variation will also be required. Copyright © 1999 John Wiley & Sons, Ltd.