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## Abstract

The behavior of subinertial, coastally trapped free waves in a continuously stratified ocean is examined using a two-slope topography in which the continental shelf and slope are each represented by a single uniform slope. Surface-intensified stratification is assumed in which the squared buoyancy frequency profile is of the form *N*
^{2}
*e*
^{βz
}, where *N* is the buoyancy frequency at the surface (*z* = 0) and β the vertical decay scale normalized by the deep-sea depth. The continental slope is typically assumed to be steeper than the shelf. Two qualitatively different types of dispersive behavior are distinguished. When (*N*/*f*)*a*
_{2}>*e*
^{βh/2}, where *f* is the Coriolis parameter, *a*
_{2} the bottom slope of the continental slope, and *h* the shelf-break depth normalized by the deep-sea depth, then free waves may occur at any subinertial frequency, and each dispersion curve rises to *f* at some finite alongshore wavenumber (as in the case of baroclinic Kelvin waves). If (*N*/*f*)*a*
_{2}<*e*
^{βh/2}, then all of the free-wave dispersion curves are limited to frequencies below some subinertial maximum, but are unlimited in wavenumber. This result is independent of the shelf width or shelf slope. Furthermore, for realistic shelf-break depths (*h*≲0.2), the result is only weakly dependent on β, and if (*N*/*f*)*a*
_{2}≳3 then the lowest-mode dispersion curve generally reaches *f* at a relatively small alongshore wavenumber (less than or equal to the wavenumber at which the corresponding fiat-bottom, baroclinic-Kelvin-wave dispersion curve crosses *f*). Thus, because realistic values of (*N*/*f*)*a*
_{2} are typically of order 1 or greater, even seemingly weak stratification may be sufficient to cause the dispersion curves to go to *f*, and the stratification effects may be crucial for accurately modeling coastally trapped wave behavior, especially when short waves are important as in scattering or resonant interaction calculations.

## Abstract

The behavior of subinertial, coastally trapped free waves in a continuously stratified ocean is examined using a two-slope topography in which the continental shelf and slope are each represented by a single uniform slope. Surface-intensified stratification is assumed in which the squared buoyancy frequency profile is of the form *N*
^{2}
*e*
^{βz
}, where *N* is the buoyancy frequency at the surface (*z* = 0) and β the vertical decay scale normalized by the deep-sea depth. The continental slope is typically assumed to be steeper than the shelf. Two qualitatively different types of dispersive behavior are distinguished. When (*N*/*f*)*a*
_{2}>*e*
^{βh/2}, where *f* is the Coriolis parameter, *a*
_{2} the bottom slope of the continental slope, and *h* the shelf-break depth normalized by the deep-sea depth, then free waves may occur at any subinertial frequency, and each dispersion curve rises to *f* at some finite alongshore wavenumber (as in the case of baroclinic Kelvin waves). If (*N*/*f*)*a*
_{2}<*e*
^{βh/2}, then all of the free-wave dispersion curves are limited to frequencies below some subinertial maximum, but are unlimited in wavenumber. This result is independent of the shelf width or shelf slope. Furthermore, for realistic shelf-break depths (*h*≲0.2), the result is only weakly dependent on β, and if (*N*/*f*)*a*
_{2}≳3 then the lowest-mode dispersion curve generally reaches *f* at a relatively small alongshore wavenumber (less than or equal to the wavenumber at which the corresponding fiat-bottom, baroclinic-Kelvin-wave dispersion curve crosses *f*). Thus, because realistic values of (*N*/*f*)*a*
_{2} are typically of order 1 or greater, even seemingly weak stratification may be sufficient to cause the dispersion curves to go to *f*, and the stratification effects may be crucial for accurately modeling coastally trapped wave behavior, especially when short waves are important as in scattering or resonant interaction calculations.

## Abstract

Using a barotropic coastal ocean model with a straight coastline and uniform cross-shelf bottom slope, seven different cross-shelf open boundary conditions (four of which are applied in either implicit or explicit form) are compared in three numerical experiments. 1) A mound of water is allowed to collapse and radiate waves toward the open boundaries. 2) A uniform alongshelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment. 3) A uniform cross-shelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment.

The boundary condition which is most transparent to waves consists of a sponge at the outer edge of the model domain with an Orlanski radiation condition at the outer edge of the sponge. Several open boundary conditions perform adequately in the wind stress experiments, but the Orlanski radiation condition alone (without a sponge) appears to give the best total performance (of these tested) through all of the experiments. It is adequate at transmitting wave energy, and its response is entirely acceptable in the wind stress experiments.

The results suggest that a clamped open boundary is probably the worst choice of cross-shelf open boundary condition for barotropic coastal models. In fact, any open boundary condition which significantly restricts the cross-shelf open boundary should probably be avoided.

## Abstract

Using a barotropic coastal ocean model with a straight coastline and uniform cross-shelf bottom slope, seven different cross-shelf open boundary conditions (four of which are applied in either implicit or explicit form) are compared in three numerical experiments. 1) A mound of water is allowed to collapse and radiate waves toward the open boundaries. 2) A uniform alongshelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment. 3) A uniform cross-shelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment.

The boundary condition which is most transparent to waves consists of a sponge at the outer edge of the model domain with an Orlanski radiation condition at the outer edge of the sponge. Several open boundary conditions perform adequately in the wind stress experiments, but the Orlanski radiation condition alone (without a sponge) appears to give the best total performance (of these tested) through all of the experiments. It is adequate at transmitting wave energy, and its response is entirely acceptable in the wind stress experiments.

The results suggest that a clamped open boundary is probably the worst choice of cross-shelf open boundary condition for barotropic coastal models. In fact, any open boundary condition which significantly restricts the cross-shelf open boundary should probably be avoided.

## Abstract

A simple two-layer, step-shelf model is used to demonstrate that barotropic (surface) edge waves of substantial amplitude can, in principle, be generated by deep-sea internal waves incident upon the coastal topography. Some qualitative features of the results suggest that this mechanism could amount for the edge-wave “noise” observed by Munk and others.

## Abstract

A simple two-layer, step-shelf model is used to demonstrate that barotropic (surface) edge waves of substantial amplitude can, in principle, be generated by deep-sea internal waves incident upon the coastal topography. Some qualitative features of the results suggest that this mechanism could amount for the edge-wave “noise” observed by Munk and others.

## Abstract

The strong salinity and temperature gradients across the shelf/slope front in the Middle Atlantic Bight often compensate such that the cross-front density gradient is nearly eliminated. The suggests that the density field may not be as dynamically important as has been assumed in previous model. Hypothesizing this to be the case, a simple steady model, which allows no density variations, is used to demonstrate that a strong tracer gradient may form near the break. The velocity field is such that an initially smooth tracer distribution develops a sharp front within a relatively short downstream distance. Essential feature of the model are 1) the velocity convergence new the shelf break which acts to sharpen the front on the shelf side, and 2) the increase in bottom slope and depth seaward of the shelf break which leads to rapid diffusion of tracer into the deep ocean. The result is that the front is maintained for a large alongshelf distance despite both diffusion effects and the frictional decay of the alongshelf velocity.

## Abstract

The strong salinity and temperature gradients across the shelf/slope front in the Middle Atlantic Bight often compensate such that the cross-front density gradient is nearly eliminated. The suggests that the density field may not be as dynamically important as has been assumed in previous model. Hypothesizing this to be the case, a simple steady model, which allows no density variations, is used to demonstrate that a strong tracer gradient may form near the break. The velocity field is such that an initially smooth tracer distribution develops a sharp front within a relatively short downstream distance. Essential feature of the model are 1) the velocity convergence new the shelf break which acts to sharpen the front on the shelf side, and 2) the increase in bottom slope and depth seaward of the shelf break which leads to rapid diffusion of tracer into the deep ocean. The result is that the front is maintained for a large alongshelf distance despite both diffusion effects and the frictional decay of the alongshelf velocity.

## Abstract

Recent modeling studies of dense water formation beneath an idealized steady coastal polynya have provided simple analytical expressions for the maximum density anomaly achievable as a function of the polynya geometry and the imposed surface buoyancy flux. These studies have assumed that the buoyancy flux and polynya geometry are both constant and independent parameters. To relax these assumptions, dense water formation is examined beneath a coastal polynya whose size and surface buoyancy flux are computed from atmospheric temperature and wind velocity according to a polynya model developed by Pease. Though highly idealized, the Pease model produces polynyas that open and close on reasonably realistic timescales, and it thermodynamically couples the polynya size and buoyancy flux.

Results reveal several interesting and potentially useful features of the ocean response to time-dependent polynya forcing. First, under reasonable atmospheric conditions, both the maximum density anomaly achievable and the volume flux of dense water formed are nearly independent of polynya width and atmospheric temperature (and, therefore, surface buoyancy flux), but they are strongly dependent on the magnitude of the wind that pushes the ice offshore. Second, variations in polynya size produce horizontal gradients in surface buoyancy flux that are important in setting the scales of the ocean response. Third, timescales of the ocean response (>10 days) are typically longer than timescales associated with polynya openings and closings (a few days). Therefore, the ocean response to time-dependent polynya size and surface buoyancy flux is nearly the same as if the polynya size and surface buoyancy flux were fixed at the time average of the forcing (over 30–60 days). This suggests that reasonable estimates of dense water formed beneath Arctic polynyas may be possible by applying the simple expressions based on steady forcing, but using the seasonal averages of the parameters. Finally, it is difficult to find realistic combinations of atmospheric conditions that produce large quantities of water with density anomaly greater than about 1 kg m^{−3}.

## Abstract

Recent modeling studies of dense water formation beneath an idealized steady coastal polynya have provided simple analytical expressions for the maximum density anomaly achievable as a function of the polynya geometry and the imposed surface buoyancy flux. These studies have assumed that the buoyancy flux and polynya geometry are both constant and independent parameters. To relax these assumptions, dense water formation is examined beneath a coastal polynya whose size and surface buoyancy flux are computed from atmospheric temperature and wind velocity according to a polynya model developed by Pease. Though highly idealized, the Pease model produces polynyas that open and close on reasonably realistic timescales, and it thermodynamically couples the polynya size and buoyancy flux.

Results reveal several interesting and potentially useful features of the ocean response to time-dependent polynya forcing. First, under reasonable atmospheric conditions, both the maximum density anomaly achievable and the volume flux of dense water formed are nearly independent of polynya width and atmospheric temperature (and, therefore, surface buoyancy flux), but they are strongly dependent on the magnitude of the wind that pushes the ice offshore. Second, variations in polynya size produce horizontal gradients in surface buoyancy flux that are important in setting the scales of the ocean response. Third, timescales of the ocean response (>10 days) are typically longer than timescales associated with polynya openings and closings (a few days). Therefore, the ocean response to time-dependent polynya size and surface buoyancy flux is nearly the same as if the polynya size and surface buoyancy flux were fixed at the time average of the forcing (over 30–60 days). This suggests that reasonable estimates of dense water formed beneath Arctic polynyas may be possible by applying the simple expressions based on steady forcing, but using the seasonal averages of the parameters. Finally, it is difficult to find realistic combinations of atmospheric conditions that produce large quantities of water with density anomaly greater than about 1 kg m^{−3}.

## Abstract

The deceleration of an unforced, two-dimensional, finite-width current over a sloping bottom in a stratified fluid is studied to quantify the relative importance of frictional spindown and buoyancy shutdown when both act simultaneously. Frictional spindown decelerates the current through Ekman suction and pumping at the current edges, which transmit stresses into the interior fluid. Buoyancy shutdown is the process by which lateral advection of density in the bottom boundary layer generates thermal wind shears that reduce the bottom stress, thereby halting deceleration.

A theoretical model of a downwelling current suggests that buoyancy shutdown always reduces the deceleration timescale from that for frictional spindown alone and produces a nonzero steady along-isobath current overlying an arrested bottom mixed layer. The model is most sensitive to the Burger number *S* = *Nα*/*f* where *N* is the buoyancy frequency, *α* the bottom slope, and *f* the Coriolis parameter. Larger *S* produces a stronger steady current that is reached more rapidly. Buoyancy shutdown remains important in the deceleration process even when its individual timescale for adjustment is an order of magnitude longer than the frictional spindown timescale. The model suggests that buoyancy shutdown should influence currents over the continental shelf on timescales of about five days and greater.

A primitive-equation numerical model is used to test the theory and its assumptions. Overall, the results are supportive of the theory, except that the theoretical model neglects the cross-isobath component of bottom stress and ignores vertical shears above the bottom mixed layer. As a result, the numerical model current initially decelerates more slowly and then continues to decelerate after the along-isobath stress has vanished, leaving a weaker steady flow, especially with stronger stratification. Interior vertical shears in the numerical model tend to decouple the near-surface flow from the bottom mixed layer, producing more variable steady flows. Details of the flow in the bottom mixed layer are highly dependent on the choice of turbulence closure scheme.

Buoyancy shutdown is also important in the deceleration of upwelling currents, substantially reducing the time to reach steady state from that for frictional spindown alone. Details of both the deceleration and the steady state vary sharply with the turbulent closure scheme, so generalizations are difficult.

## Abstract

The deceleration of an unforced, two-dimensional, finite-width current over a sloping bottom in a stratified fluid is studied to quantify the relative importance of frictional spindown and buoyancy shutdown when both act simultaneously. Frictional spindown decelerates the current through Ekman suction and pumping at the current edges, which transmit stresses into the interior fluid. Buoyancy shutdown is the process by which lateral advection of density in the bottom boundary layer generates thermal wind shears that reduce the bottom stress, thereby halting deceleration.

A theoretical model of a downwelling current suggests that buoyancy shutdown always reduces the deceleration timescale from that for frictional spindown alone and produces a nonzero steady along-isobath current overlying an arrested bottom mixed layer. The model is most sensitive to the Burger number *S* = *Nα*/*f* where *N* is the buoyancy frequency, *α* the bottom slope, and *f* the Coriolis parameter. Larger *S* produces a stronger steady current that is reached more rapidly. Buoyancy shutdown remains important in the deceleration process even when its individual timescale for adjustment is an order of magnitude longer than the frictional spindown timescale. The model suggests that buoyancy shutdown should influence currents over the continental shelf on timescales of about five days and greater.

A primitive-equation numerical model is used to test the theory and its assumptions. Overall, the results are supportive of the theory, except that the theoretical model neglects the cross-isobath component of bottom stress and ignores vertical shears above the bottom mixed layer. As a result, the numerical model current initially decelerates more slowly and then continues to decelerate after the along-isobath stress has vanished, leaving a weaker steady flow, especially with stronger stratification. Interior vertical shears in the numerical model tend to decouple the near-surface flow from the bottom mixed layer, producing more variable steady flows. Details of the flow in the bottom mixed layer are highly dependent on the choice of turbulence closure scheme.

Buoyancy shutdown is also important in the deceleration of upwelling currents, substantially reducing the time to reach steady state from that for frictional spindown alone. Details of both the deceleration and the steady state vary sharply with the turbulent closure scheme, so generalizations are difficult.

## Abstract

Recent observations have suggested that the trapped-front model of Chapman and Lentz is consistent with some aspects of the shelfbreak front in the Middle Atlantic Bight. The sensitivity of the model to the parameterization of vertical mixing is examined to determine which model features are robust and potentially observable and which are variable and less reliable. The basic frontal trapping mechanism, frontal location, surface intensified frontal jet with weak flow at the bottom, and detachment of the bottom boundary layer at the shoreward edge of the foot of the front are all insensitive to the parameterization of vertical mixing. On the other hand, the frontal shape and width and the cross-frontal circulation and momentum balances within the front change dramatically with the parameterization of vertical mixing. Constant mixing coefficients produce strong vertical mixing within the front, which results in steady shoreward flow in the bottom boundary layer there. Mixing coefficients that depend on the local stratification and shear produce weak vertical mixing within the front, which allows oscillating currents that may be frontal-trapped waves.

## Abstract

Recent observations have suggested that the trapped-front model of Chapman and Lentz is consistent with some aspects of the shelfbreak front in the Middle Atlantic Bight. The sensitivity of the model to the parameterization of vertical mixing is examined to determine which model features are robust and potentially observable and which are variable and less reliable. The basic frontal trapping mechanism, frontal location, surface intensified frontal jet with weak flow at the bottom, and detachment of the bottom boundary layer at the shoreward edge of the foot of the front are all insensitive to the parameterization of vertical mixing. On the other hand, the frontal shape and width and the cross-frontal circulation and momentum balances within the front change dramatically with the parameterization of vertical mixing. Constant mixing coefficients produce strong vertical mixing within the front, which results in steady shoreward flow in the bottom boundary layer there. Mixing coefficients that depend on the local stratification and shear produce weak vertical mixing within the front, which allows oscillating currents that may be frontal-trapped waves.

## Abstract

The ocean response to negative buoyancy flux, applied in an isolated region at the surface, is investigated to determine the scales of the equilibrium state, that is, the time to reach equilibrium, the equilibrium density anomaly within the convecting chimney, and, in the case of deep convection, the equilibrium depth of the chimney. Two types of isolated convection, with fundamentally different parameter dependencies, are distinguished based on the importance of the forcing decay region; a region surrounding the isolated forcing region, across which the buoyancy flux decreases to zero. A narrow forcing decay region produces “internally constrained” convection in which the baroclinic Rossby radius is the dominant horizontal length scale, and the resulting equilibrium scales are those found by Visbeck et al. A wide forcing decay region produces “externally constrained” convection in which the forcing decay width is the dominant horizontal length scale, and the equilibrium scales are those found by Chapman and Gawarkiewicz.

*W*is the width of the forcing decay region,

*B*

_{0}is the surface buoyancy flux,

*r*

_{0}is the radius of the forcing region,

*f*is the Coriolis parameter, and

*l*

_{rot}= (

*B*

_{0}/

*f*

^{3})

^{1/2}. If

*W*is less (greater) than 3.2(

*l*

_{rot}/

*r*

_{0})

^{2/3}, then internally (externally) constrained convection results. This estimate is obtained for both shallow convection in which the chimney reaches the bottom almost immediately and deep convection in which the chimney never reaches the bottom. Furthermore, the transition is independent of the ambient stratification and the total water depth.

Calculations made with a primitive equation numerical model support the theoretical ideas and show that the transition between the two types of convection is smooth and well behaved. The results suggest that the forcing decay region may be important in ocean convection situations, especially for large forcing regions.

## Abstract

The ocean response to negative buoyancy flux, applied in an isolated region at the surface, is investigated to determine the scales of the equilibrium state, that is, the time to reach equilibrium, the equilibrium density anomaly within the convecting chimney, and, in the case of deep convection, the equilibrium depth of the chimney. Two types of isolated convection, with fundamentally different parameter dependencies, are distinguished based on the importance of the forcing decay region; a region surrounding the isolated forcing region, across which the buoyancy flux decreases to zero. A narrow forcing decay region produces “internally constrained” convection in which the baroclinic Rossby radius is the dominant horizontal length scale, and the resulting equilibrium scales are those found by Visbeck et al. A wide forcing decay region produces “externally constrained” convection in which the forcing decay width is the dominant horizontal length scale, and the equilibrium scales are those found by Chapman and Gawarkiewicz.

*W*is the width of the forcing decay region,

*B*

_{0}is the surface buoyancy flux,

*r*

_{0}is the radius of the forcing region,

*f*is the Coriolis parameter, and

*l*

_{rot}= (

*B*

_{0}/

*f*

^{3})

^{1/2}. If

*W*is less (greater) than 3.2(

*l*

_{rot}/

*r*

_{0})

^{2/3}, then internally (externally) constrained convection results. This estimate is obtained for both shallow convection in which the chimney reaches the bottom almost immediately and deep convection in which the chimney never reaches the bottom. Furthermore, the transition is independent of the ambient stratification and the total water depth.

Calculations made with a primitive equation numerical model support the theoretical ideas and show that the transition between the two types of convection is smooth and well behaved. The results suggest that the forcing decay region may be important in ocean convection situations, especially for large forcing regions.

## Abstract

The coastal current system along the east coast of North America, from the Labrador shelf to Cape Hatteras, must negotiate complex bathymetry with numerous sharp bends and large cross-shelf channels. The behavior of these shelf currents is studied here using an advectively trapped buoyancy current (ATBC) model, in which a coastal buoyancy current on a sloping bottom forms a surface-to-bottom density front that becomes trapped along an isobath by offshore advection of buoyancy in the bottom boundary layer. Alongfront flow is concentrated in a nearly geostrophic surface-intensified frontal jet. Trapping occurs where the cross-shelf bottom velocity vanishes on the shoreward side of the front, thus terminating offshore buoyancy advection and causing the bottom boundary layer to detach and to flow upward along frontal isopycnals. The dynamics of an ATBC at a sharp bend in bathymetry and at a cross-shelf channel are investigated using a primitive equation numerical model, focusing on the separation of the frontal jet from the topography. The response depends on the relative size of the buoyant inflow that creates the ATBC and a weak alongshelf background current that is typically imposed to ensure the downstream propagation of the buoyant inflow. With no background current, the ATBC separates at either the single bend or the channel, regardless of the strength of the buoyant inflow. With a background current, the ATBC follows the isobaths around the bend until the bottom velocity parallel to the front vanishes, after which the frontal jet separates and flows freely away from the topography while the foot of the front remains attached near the trapping depth. The separation point is highly sensitive to the magnitude of the background current, with changes of a few centimeters per second having a major impact on the response. Unlike most geophysical flows, the separation process is basically linear and does not require large nonlinear inertial contributions to the momentum balances. The model suggests that substantial losses of buoyant Labrador shelf water are likely to occur at the southern tail of the Grand Banks and that ambient/offshore currents probably control the penetration and crossover of the shelfbreak front at the Northeast Channel.

## Abstract

The coastal current system along the east coast of North America, from the Labrador shelf to Cape Hatteras, must negotiate complex bathymetry with numerous sharp bends and large cross-shelf channels. The behavior of these shelf currents is studied here using an advectively trapped buoyancy current (ATBC) model, in which a coastal buoyancy current on a sloping bottom forms a surface-to-bottom density front that becomes trapped along an isobath by offshore advection of buoyancy in the bottom boundary layer. Alongfront flow is concentrated in a nearly geostrophic surface-intensified frontal jet. Trapping occurs where the cross-shelf bottom velocity vanishes on the shoreward side of the front, thus terminating offshore buoyancy advection and causing the bottom boundary layer to detach and to flow upward along frontal isopycnals. The dynamics of an ATBC at a sharp bend in bathymetry and at a cross-shelf channel are investigated using a primitive equation numerical model, focusing on the separation of the frontal jet from the topography. The response depends on the relative size of the buoyant inflow that creates the ATBC and a weak alongshelf background current that is typically imposed to ensure the downstream propagation of the buoyant inflow. With no background current, the ATBC separates at either the single bend or the channel, regardless of the strength of the buoyant inflow. With a background current, the ATBC follows the isobaths around the bend until the bottom velocity parallel to the front vanishes, after which the frontal jet separates and flows freely away from the topography while the foot of the front remains attached near the trapping depth. The separation point is highly sensitive to the magnitude of the background current, with changes of a few centimeters per second having a major impact on the response. Unlike most geophysical flows, the separation process is basically linear and does not require large nonlinear inertial contributions to the momentum balances. The model suggests that substantial losses of buoyant Labrador shelf water are likely to occur at the southern tail of the Grand Banks and that ambient/offshore currents probably control the penetration and crossover of the shelfbreak front at the Northeast Channel.

## Abstract

The adjustment of a narrow, stratified, cyclonic along-isobath current over a uniformly sloping bottom and the coupling between the current and the bottom boundary layer that develops beneath are investigated using a primitive-equation numerical model. The current generates a bottom Ekman layer immediately downstream of its origin, with downslope transport everywhere beneath the current, carrying lighter water under heavier water to produce a vertically well-mixed bottom boundary layer. At the top of the boundary layer, Ekman suction on the shallow side and pumping on the deep side lead to density advection in the vertical, tilted interior isopycnals, and thermal-wind shear of the interior along-isobath velocity. Flow above the bottom boundary layer is nearly perfectly geostrophic and along isopycnals. Buoyancy advection in the bottom boundary layer continues to cause growth of the boundary layer downstream, with subsequent reduction in bottom stress, until the flow reaches a steady downstream equilibrium beyond which only gradual changes occur as a result of viscosity and mixing.

The numerical results are compared with the idealized model of this adjustment process previously proposed by Chapman and Lentz. The same basic dynamics dominate, and some of the scales and parameter dependencies predicted by the idealized model apply to the numerical results. For example, the distance to the downstream equilibrium decreases with increasing buoyancy frequency and/or bottom slope, and the equilibrium structure is nearly independent of the bottom friction coefficient. The equilibrium bottom boundary layer thickness and the interior along-isobath velocity just above the boundary layer closely obey the idealized model scales; that is, the boundary layer thickness decreases with increasing buoyancy frequency and is independent of bottom slope, and the overlying current decreases while its width increases as either the buoyancy frequency or bottom slope decreases. However, the interior vertical shear in the numerical model tends to decouple the overlying current from the bottom boundary layer, so the structure of the bottom boundary layer in the downstream equilibrium is different from the idealized model, and neither the current width nor the surface currents are as sensitive to parameter variations as the idealized model suggests. Finally, the along-isobath current is not geostrophic near the bottom of the bottom boundary layer, as assumed in the idealized model, so the bottom boundary layer is not fully arrested, that is, bottom stress never quite vanishes downstream, suggesting that a completely frictionless downstream equilibrium is unlikely to be achieved.

## Abstract

The adjustment of a narrow, stratified, cyclonic along-isobath current over a uniformly sloping bottom and the coupling between the current and the bottom boundary layer that develops beneath are investigated using a primitive-equation numerical model. The current generates a bottom Ekman layer immediately downstream of its origin, with downslope transport everywhere beneath the current, carrying lighter water under heavier water to produce a vertically well-mixed bottom boundary layer. At the top of the boundary layer, Ekman suction on the shallow side and pumping on the deep side lead to density advection in the vertical, tilted interior isopycnals, and thermal-wind shear of the interior along-isobath velocity. Flow above the bottom boundary layer is nearly perfectly geostrophic and along isopycnals. Buoyancy advection in the bottom boundary layer continues to cause growth of the boundary layer downstream, with subsequent reduction in bottom stress, until the flow reaches a steady downstream equilibrium beyond which only gradual changes occur as a result of viscosity and mixing.

The numerical results are compared with the idealized model of this adjustment process previously proposed by Chapman and Lentz. The same basic dynamics dominate, and some of the scales and parameter dependencies predicted by the idealized model apply to the numerical results. For example, the distance to the downstream equilibrium decreases with increasing buoyancy frequency and/or bottom slope, and the equilibrium structure is nearly independent of the bottom friction coefficient. The equilibrium bottom boundary layer thickness and the interior along-isobath velocity just above the boundary layer closely obey the idealized model scales; that is, the boundary layer thickness decreases with increasing buoyancy frequency and is independent of bottom slope, and the overlying current decreases while its width increases as either the buoyancy frequency or bottom slope decreases. However, the interior vertical shear in the numerical model tends to decouple the overlying current from the bottom boundary layer, so the structure of the bottom boundary layer in the downstream equilibrium is different from the idealized model, and neither the current width nor the surface currents are as sensitive to parameter variations as the idealized model suggests. Finally, the along-isobath current is not geostrophic near the bottom of the bottom boundary layer, as assumed in the idealized model, so the bottom boundary layer is not fully arrested, that is, bottom stress never quite vanishes downstream, suggesting that a completely frictionless downstream equilibrium is unlikely to be achieved.