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## Abstract

The vertical structure of coastal-trapped disturbances in several idealized models of a stably stratified lower atmosphere is examined. The vertical structure and phase speeds of the trapped modes depend on the resting stratification and the height of the orographic step. The presence of a stable layer above the boundary layer inversion increases the gravest-mode phase speed and supports the existence of higher vertical modes. Trapped wave solutions for the step orography are obtained for a lower atmosphere with constant buoyancy frequency. The modes are primarily concentrated below the step but penetrate weakly into the stratified region above the step. The phase speed of the gravest trapped mode is greater than the gravest-mode Kelvin wave speed based on the height of the step. Results from a linear two-layer model suggest that the observed vertical structure of isotherms at the leading edge of a 10–11 June 1994 event may arise during a transition from a directly forced, barotropic, alongshore velocity response to a regime influenced by wave propagation, as the coastal-trapped vertical modes excited by the mesoscale pressure gradients begin to disperse at their respective phase speeds. The results suggest also that the observed vertical structure of alongshore velocity, with largest velocities in the stable layer above the boundary layer, may arise from drag at the sea surface.

## Abstract

The vertical structure of coastal-trapped disturbances in several idealized models of a stably stratified lower atmosphere is examined. The vertical structure and phase speeds of the trapped modes depend on the resting stratification and the height of the orographic step. The presence of a stable layer above the boundary layer inversion increases the gravest-mode phase speed and supports the existence of higher vertical modes. Trapped wave solutions for the step orography are obtained for a lower atmosphere with constant buoyancy frequency. The modes are primarily concentrated below the step but penetrate weakly into the stratified region above the step. The phase speed of the gravest trapped mode is greater than the gravest-mode Kelvin wave speed based on the height of the step. Results from a linear two-layer model suggest that the observed vertical structure of isotherms at the leading edge of a 10–11 June 1994 event may arise during a transition from a directly forced, barotropic, alongshore velocity response to a regime influenced by wave propagation, as the coastal-trapped vertical modes excited by the mesoscale pressure gradients begin to disperse at their respective phase speeds. The results suggest also that the observed vertical structure of alongshore velocity, with largest velocities in the stable layer above the boundary layer, may arise from drag at the sea surface.

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## Abstract

A simple theory is presented for steady geostrophic circulation of a stratified fluid in a rectangular basin with a circumpolar connection. The interior flow obeys the *β*-plane Sverdrup vorticity balance, and the circulation is closed by geostrophic boundary currents. The circulation is forced by surface thermal gradients and wind-driven Ekman transport near the latitudes of the circumpolar connection. A thermal circumpolar current arises in response to imposed surface thermal gradients and northward Ekman transport across the gap latitudes. The transport of this model circumpolar current depends on the imposed surface thermal gradients and the gap geometry, but not on the strength of the wind forcing. In contrast, the circulation induced in a related reduced-gravity model by Sverdrup transport into the gap latitudes has zero zonally integrated zonal transport. The thermal current arises as a consequence of the geostrophic constraint, which requires that the northern region fill with warm fluid until it reaches the sill depth, where return geostrophic flow can be supported. Thus, the structure of the middepth, midlatitude thermocline is directly influenced by the geometry of the gap. A similar constraint evidently operates in the Southern Ocean.

## Abstract

A simple theory is presented for steady geostrophic circulation of a stratified fluid in a rectangular basin with a circumpolar connection. The interior flow obeys the *β*-plane Sverdrup vorticity balance, and the circulation is closed by geostrophic boundary currents. The circulation is forced by surface thermal gradients and wind-driven Ekman transport near the latitudes of the circumpolar connection. A thermal circumpolar current arises in response to imposed surface thermal gradients and northward Ekman transport across the gap latitudes. The transport of this model circumpolar current depends on the imposed surface thermal gradients and the gap geometry, but not on the strength of the wind forcing. In contrast, the circulation induced in a related reduced-gravity model by Sverdrup transport into the gap latitudes has zero zonally integrated zonal transport. The thermal current arises as a consequence of the geostrophic constraint, which requires that the northern region fill with warm fluid until it reaches the sill depth, where return geostrophic flow can be supported. Thus, the structure of the middepth, midlatitude thermocline is directly influenced by the geometry of the gap. A similar constraint evidently operates in the Southern Ocean.

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## Abstract

A recently proposed reduced-gravity model of the warm-water branch of the middepth meridional overturning circulation in a rectangular basin with a circumpolar connection is extended to include time dependence. The model describes the balance between gain of warm water through northward Ekman advection across the circumpolar current, loss of warm water through eddy fluxes southward across the current, net gain or loss of warm water through diabatic processes north of the current, and changes in the thickness of the warm-water layer. The steady solutions are the same as those found previously, when the previous parameterization of diabatic fluxes is used. Time-dependent solutions are considered for the approach of the solution to a new equilibrium when the forcing or parameters are abruptly changed and then held fixed. An initial adjustment occurs through a combination of boundary and equatorial adjustment, followed by planetary wave propagation. The longer-term adjustment to equilibrium consists primarily of the slow change in eastern boundary thickness of the warm layer, which controls the mean depth of the entire layer. An approximate analytical solution of the time-dependent equations yields an explicit expression for the intrinsic time scale of the long-term adjustment, which depends on the eddy and diabatic flux parameters and on the equilibrium solution toward which the time-dependent solution adjusts. Numerical solutions are also considered with a second, advective–diffusive diabatic flux parameterization. These solutions differ quantitatively but not qualitatively from those with the original parameterization. For the range of parameter values considered, the adjustment time scale has dimensional values of several decades to more than a century, but the meridional flux of warm water may respond to changes in external parameters or forcing much more rapidly than this time scale for equilibration of the eastern boundary thickness and thermocline structure.

## Abstract

A recently proposed reduced-gravity model of the warm-water branch of the middepth meridional overturning circulation in a rectangular basin with a circumpolar connection is extended to include time dependence. The model describes the balance between gain of warm water through northward Ekman advection across the circumpolar current, loss of warm water through eddy fluxes southward across the current, net gain or loss of warm water through diabatic processes north of the current, and changes in the thickness of the warm-water layer. The steady solutions are the same as those found previously, when the previous parameterization of diabatic fluxes is used. Time-dependent solutions are considered for the approach of the solution to a new equilibrium when the forcing or parameters are abruptly changed and then held fixed. An initial adjustment occurs through a combination of boundary and equatorial adjustment, followed by planetary wave propagation. The longer-term adjustment to equilibrium consists primarily of the slow change in eastern boundary thickness of the warm layer, which controls the mean depth of the entire layer. An approximate analytical solution of the time-dependent equations yields an explicit expression for the intrinsic time scale of the long-term adjustment, which depends on the eddy and diabatic flux parameters and on the equilibrium solution toward which the time-dependent solution adjusts. Numerical solutions are also considered with a second, advective–diffusive diabatic flux parameterization. These solutions differ quantitatively but not qualitatively from those with the original parameterization. For the range of parameter values considered, the adjustment time scale has dimensional values of several decades to more than a century, but the meridional flux of warm water may respond to changes in external parameters or forcing much more rapidly than this time scale for equilibration of the eastern boundary thickness and thermocline structure.

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## Abstract

A reduced-gravity model is presented of the warm-water branch of the middepth meridional overturning circulation in a rectangular basin with a circumpolar connection. The model describes the balance between production of warm water by Ekman advection across the circumpolar current, dissipation of warm water by eddy fluxes southward across the current, and the net production or dissipation of warm water by diabatic processes north of the current. The results emphasize the role of the eastern boundary condition in setting the thermocline structure north of the current and the nonlinear interactions between wind forcing, eddy fluxes, and diabatic mixing, which together control the structure and amplitude of the model meridional overturning circulation. Solutions are shown to exist in which the northward Ekman transport across the circumpolar current is completely compensated by southward eddy fluxes and the meridional overturning north of the current is entirely driven by diabatic forcing and interior upwelling through the base of the layer. Other solutions are shown to exist in which the interior upwelling into the warm layer at midlatitudes is negligible and the meridional overturning circulation consists of a continuous cell that carried the fluid delivered by the northward Ekman transport across the circumpolar current through midlatitudes to the Northern Hemisphere subpolar gyre, where it cools and returns to depth. The results emphasize that the coupled elements of wind driving, eddy fluxes, and diabatic processes are inextricably intertwined in the middepth meridional overturning circulation.

## Abstract

A reduced-gravity model is presented of the warm-water branch of the middepth meridional overturning circulation in a rectangular basin with a circumpolar connection. The model describes the balance between production of warm water by Ekman advection across the circumpolar current, dissipation of warm water by eddy fluxes southward across the current, and the net production or dissipation of warm water by diabatic processes north of the current. The results emphasize the role of the eastern boundary condition in setting the thermocline structure north of the current and the nonlinear interactions between wind forcing, eddy fluxes, and diabatic mixing, which together control the structure and amplitude of the model meridional overturning circulation. Solutions are shown to exist in which the northward Ekman transport across the circumpolar current is completely compensated by southward eddy fluxes and the meridional overturning north of the current is entirely driven by diabatic forcing and interior upwelling through the base of the layer. Other solutions are shown to exist in which the interior upwelling into the warm layer at midlatitudes is negligible and the meridional overturning circulation consists of a continuous cell that carried the fluid delivered by the northward Ekman transport across the circumpolar current through midlatitudes to the Northern Hemisphere subpolar gyre, where it cools and returns to depth. The results emphasize that the coupled elements of wind driving, eddy fluxes, and diabatic processes are inextricably intertwined in the middepth meridional overturning circulation.

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## Abstract

The influence of localized regions of intensified vertical mixing on the stratification and circulation in a large-scale ocean model is investigated with idealized numerical experiments. Numerical solutions are obtained of a closed-basin, single-hemisphere ocean model based on the planetary geostrophic equations. Mesoscale eddy effects are minimized, and vertical mixing at the turbulent microscale is represented by a vertical diffusivity *κ*
_{
υ
}. Solutions with uniform *κ*
_{
υ
} are contrasted with a “localized mixing” solution, in which *κ*
_{
υ
} increases by two orders of magnitude from its interior value (0.2 × 10^{−4} m^{2} s^{−1}) in a region 500 km wide adjacent to the vertical eastern boundary. When *κ*
_{
υ
} is uniform, the stratification beneath the ventilated thermocline is characterized by a single vertical scale. In contrast, the localized vertical mixing supports a deep diffusive thermocline with two distinct vertical scales: an internal boundary layer centered at the base of the ventilated thermocline (roughly 1000-m depth) and an abyssal thermocline whose vertical scale is set in the region of large *κ*
_{
υ
}. This stratification is qualitatively similar to observed deep ocean stratification. In contrast to the Stommel–Arons meridional abyssal flow that arises in the model when *κ*
_{
υ
} is uniform and small, the localized mixing solution has primarily zonal flow in the abyssal interior, with meridional motion confined to boundary layers. An advective–diffusive balance is established in the region of enhanced mixing. The near-surface circulation is dominated by westward zonal flow in the southern half of the interior, northward flow along the western boundary, and eastward flow in the northern half of the interior, while the pattern of flow in the abyssal interior is essentially the reverse. The circulation is closed by upwelling in the mixing region and downwelling along the northern boundary. Meridional motion in the mixing region is consistent with the Sverdrup vorticity balance, with northward flow at depth and southward flow near the surface. The source water for the deep circulation is confined to a narrow range of the coldest temperature classes in the basin, while the middepth subtropical thermocline is filled with warmer deep water that enters the gyre as cold deep water and then is modified in the eastern mixing region.

## Abstract

The influence of localized regions of intensified vertical mixing on the stratification and circulation in a large-scale ocean model is investigated with idealized numerical experiments. Numerical solutions are obtained of a closed-basin, single-hemisphere ocean model based on the planetary geostrophic equations. Mesoscale eddy effects are minimized, and vertical mixing at the turbulent microscale is represented by a vertical diffusivity *κ*
_{
υ
}. Solutions with uniform *κ*
_{
υ
} are contrasted with a “localized mixing” solution, in which *κ*
_{
υ
} increases by two orders of magnitude from its interior value (0.2 × 10^{−4} m^{2} s^{−1}) in a region 500 km wide adjacent to the vertical eastern boundary. When *κ*
_{
υ
} is uniform, the stratification beneath the ventilated thermocline is characterized by a single vertical scale. In contrast, the localized vertical mixing supports a deep diffusive thermocline with two distinct vertical scales: an internal boundary layer centered at the base of the ventilated thermocline (roughly 1000-m depth) and an abyssal thermocline whose vertical scale is set in the region of large *κ*
_{
υ
}. This stratification is qualitatively similar to observed deep ocean stratification. In contrast to the Stommel–Arons meridional abyssal flow that arises in the model when *κ*
_{
υ
} is uniform and small, the localized mixing solution has primarily zonal flow in the abyssal interior, with meridional motion confined to boundary layers. An advective–diffusive balance is established in the region of enhanced mixing. The near-surface circulation is dominated by westward zonal flow in the southern half of the interior, northward flow along the western boundary, and eastward flow in the northern half of the interior, while the pattern of flow in the abyssal interior is essentially the reverse. The circulation is closed by upwelling in the mixing region and downwelling along the northern boundary. Meridional motion in the mixing region is consistent with the Sverdrup vorticity balance, with northward flow at depth and southward flow near the surface. The source water for the deep circulation is confined to a narrow range of the coldest temperature classes in the basin, while the middepth subtropical thermocline is filled with warmer deep water that enters the gyre as cold deep water and then is modified in the eastern mixing region.

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## Abstract

The diffusivity dependence of internal boundary layers in solutions of the continuously stratified, diffusive thermocline equations is revisited. If a solution exists that approaches a two-layer solution of the ideal thermocline equations in the limit of small vertical diffusivity *κ*
_{
υ
}, it must contain an internal boundary layer that collapses to a discontinuity as *κ*
_{
υ
} → 0. An asymptotic internal boundary layer equation is derived for this case, and the associated boundary layer thickness is proportional to *κ*
^{1/2}
_{
υ
}
*κ*
_{
υ
} → 0.

## Abstract

The diffusivity dependence of internal boundary layers in solutions of the continuously stratified, diffusive thermocline equations is revisited. If a solution exists that approaches a two-layer solution of the ideal thermocline equations in the limit of small vertical diffusivity *κ*
_{
υ
}, it must contain an internal boundary layer that collapses to a discontinuity as *κ*
_{
υ
} → 0. An asymptotic internal boundary layer equation is derived for this case, and the associated boundary layer thickness is proportional to *κ*
^{1/2}
_{
υ
}
*κ*
_{
υ
} → 0.

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## Abstract

A time-dependent, inviscid, linear theory for the generation of poleward undercurrent flow under upwelling conditions along midlatitude ocean eastern boundaries is proposed. The theory relies on a conceptual separation of time scales between the rapid, coastal-trapped wave response to upwelling winds and the subsequent slow, interior, quasigeostrophic evolution. Solutions are obtained under idealized conditions in which the coastal boundary and the continental-slope topography are uniform alongshore, and the time-dependent wind-stress forcing is applied over a limited meridional range, uniform cross-shore, and directed alongshore. A time-dependent coastal boundary condition on the slow-time-scale interior flow, consisting of the low-frequency, geostrophically balanced sea surface height disturbance over the outer shelf, is obtained from consideration of the fast-time-scale, coastal-trapped response. A quasigeostrophic potential vorticity equation is then solved to determine the interior response to this time-dependent boundary condition. Under upwelling conditions, the results show the formation of a localized region of subsurface poleward flow over the upper continental slope that is qualitatively consistent in amplitude, location, and timing with observations of poleward undercurrents on eastern boundaries. Despite its origin as a sea surface height anomaly, the coastal-boundary condition drives a baroclinic planetary wave response, in which the poleward subsurface flow evolves in planetary vorticity balance with induced subsurface upwelling.

## Abstract

A time-dependent, inviscid, linear theory for the generation of poleward undercurrent flow under upwelling conditions along midlatitude ocean eastern boundaries is proposed. The theory relies on a conceptual separation of time scales between the rapid, coastal-trapped wave response to upwelling winds and the subsequent slow, interior, quasigeostrophic evolution. Solutions are obtained under idealized conditions in which the coastal boundary and the continental-slope topography are uniform alongshore, and the time-dependent wind-stress forcing is applied over a limited meridional range, uniform cross-shore, and directed alongshore. A time-dependent coastal boundary condition on the slow-time-scale interior flow, consisting of the low-frequency, geostrophically balanced sea surface height disturbance over the outer shelf, is obtained from consideration of the fast-time-scale, coastal-trapped response. A quasigeostrophic potential vorticity equation is then solved to determine the interior response to this time-dependent boundary condition. Under upwelling conditions, the results show the formation of a localized region of subsurface poleward flow over the upper continental slope that is qualitatively consistent in amplitude, location, and timing with observations of poleward undercurrents on eastern boundaries. Despite its origin as a sea surface height anomaly, the coastal-boundary condition drives a baroclinic planetary wave response, in which the poleward subsurface flow evolves in planetary vorticity balance with induced subsurface upwelling.

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## Abstract

A simple dynamical model is proposed for the near-surface drift current in a homogeneous, equilibrium sea. The momentum balance is formulated for a mass-weighted mean in curvilinear surface-conforming coordinates. Stokes drifts computed analytically for small wave slopes by this approach for inviscid linear sinusoidal and Pollard–Gerstner waves agree with the corresponding Lagrangian means, consistent with a mean momentum balance that determines mean parcel motion. A wave-modified mixing length model is proposed, with a depth-dependent eddy viscosity that depends on an effective ocean surface roughness length *z*
_{0}
*
_{o}
*, distinct from the atmospheric bulk-flux roughness length

*z*

_{0}

*, and an additional wave-correction factor*

_{a}*ϕ*. Kinematic Stokes drift profiles are computed for two sets of quasi-equilibrium sea states and are interpreted as mean wind drift profiles to provide calibration references for the model. A third calibration reference, for surface drift only, is provided by the traditional 3%-of-wind rule. For 10-m neutral wind

_{w}*U*

_{10}

*≤ 20 m s*

_{N}^{−1}, the empirical

*z*

_{0}

*ranges from 10*

_{o}^{−4}to 10 m, while

*ϕ*ranges from 1.0 to 0.1. The model profiles show a shallow log-layer structure at the smaller wind speeds and a nearly uniform near-surface shear at the larger wind speeds. Surface velocities are oriented 10°–20° from downwind for

_{w}*U*

_{10}

*≤ 10 m s*

_{N}^{−1}and 20°–35° from downwind for 10 ≤

*U*

_{10}

*≤ 20 m s*

_{N}^{−1}. A small correction to the drag coefficient is implied. The model predictions show a basic consistency with several sets of previously published near-surface current measurements, but the comparison is not definitive.

## Abstract

A simple dynamical model is proposed for the near-surface drift current in a homogeneous, equilibrium sea. The momentum balance is formulated for a mass-weighted mean in curvilinear surface-conforming coordinates. Stokes drifts computed analytically for small wave slopes by this approach for inviscid linear sinusoidal and Pollard–Gerstner waves agree with the corresponding Lagrangian means, consistent with a mean momentum balance that determines mean parcel motion. A wave-modified mixing length model is proposed, with a depth-dependent eddy viscosity that depends on an effective ocean surface roughness length *z*
_{0}
*
_{o}
*, distinct from the atmospheric bulk-flux roughness length

*z*

_{0}

*, and an additional wave-correction factor*

_{a}*ϕ*. Kinematic Stokes drift profiles are computed for two sets of quasi-equilibrium sea states and are interpreted as mean wind drift profiles to provide calibration references for the model. A third calibration reference, for surface drift only, is provided by the traditional 3%-of-wind rule. For 10-m neutral wind

_{w}*U*

_{10}

*≤ 20 m s*

_{N}^{−1}, the empirical

*z*

_{0}

*ranges from 10*

_{o}^{−4}to 10 m, while

*ϕ*ranges from 1.0 to 0.1. The model profiles show a shallow log-layer structure at the smaller wind speeds and a nearly uniform near-surface shear at the larger wind speeds. Surface velocities are oriented 10°–20° from downwind for

_{w}*U*

_{10}

*≤ 10 m s*

_{N}^{−1}and 20°–35° from downwind for 10 ≤

*U*

_{10}

*≤ 20 m s*

_{N}^{−1}. A small correction to the drag coefficient is implied. The model predictions show a basic consistency with several sets of previously published near-surface current measurements, but the comparison is not definitive.

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## Abstract

The growth of linear disturbances to stable and unstable time-periodic basic states is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave–mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal-flow correction. Floquet vectors, the eigenmodes for linear disturbances to the oscillatory basic states, split into wave-dynamical and decaying zonal-flow modes. Singular vectors reflect the structure of the Floquet vectors: the most rapid amplification and decay are associated with the wave-dynamical Floquet vectors, while the intermediate singular vectors closely follow the decaying zonal-flow Floquet vectors. Singular values depend strongly on initial and optimization times. For initial times near wave amplitude maxima, the Floquet decomposition of the leading singular vector depends relatively weakly on optimization time. For the unstable oscillatory basic state in the chaotic regime, the leading Floquet vector is tangent to the large-scale structure of the attractor, while the leading singular vector is not. However, corresponding inferences about the accessibility of disturbed states rely on the simple attractor geometry, and may not easily generalize. The primary mechanism of disturbance growth on the wave timescale in this model involves a time-dependent phase shift along the basic wave cycle. The Floquet vectors illustrate that modal disturbances to time-dependent basic states can have time-dependent spatial structure, and that the latter need not indicate nonmodal dynamics. The dynamical splitting reduces the “butterfly effect,” the ability of small-scale disturbances to influence the evolution of an unstable large-scale flow.

## Abstract

The growth of linear disturbances to stable and unstable time-periodic basic states is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave–mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal-flow correction. Floquet vectors, the eigenmodes for linear disturbances to the oscillatory basic states, split into wave-dynamical and decaying zonal-flow modes. Singular vectors reflect the structure of the Floquet vectors: the most rapid amplification and decay are associated with the wave-dynamical Floquet vectors, while the intermediate singular vectors closely follow the decaying zonal-flow Floquet vectors. Singular values depend strongly on initial and optimization times. For initial times near wave amplitude maxima, the Floquet decomposition of the leading singular vector depends relatively weakly on optimization time. For the unstable oscillatory basic state in the chaotic regime, the leading Floquet vector is tangent to the large-scale structure of the attractor, while the leading singular vector is not. However, corresponding inferences about the accessibility of disturbed states rely on the simple attractor geometry, and may not easily generalize. The primary mechanism of disturbance growth on the wave timescale in this model involves a time-dependent phase shift along the basic wave cycle. The Floquet vectors illustrate that modal disturbances to time-dependent basic states can have time-dependent spatial structure, and that the latter need not indicate nonmodal dynamics. The dynamical splitting reduces the “butterfly effect,” the ability of small-scale disturbances to influence the evolution of an unstable large-scale flow.

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## Abstract

A model for hydraulically supercritical atmospheric marine-layer flow along a smoothly varying coastline is formulated and solved numerically. The model is motivated by a recent comparison of CODE observations to a simple hydraulic theory, which suggested the presence of an expansion fan and a compression jump downstream of topographic features. The marine layer is modeled as a homogeneous rotating fluid layer decelerated by surface friction and forced by imposed upper-level pressure gradients. The equations are solved by a characteristic-based gridpoint scheme. The results indicate that the expansion fan is a robust feature that persists under most conditions in the present more realistic model, but is dramatically altered in structure by the presence of friction, while the jump may weaken rapidly offshore due mainly to offshore variations of the layer height upstream of the jump. The agreement between observations and model predictions is good enough to suggest that a first-order description of the dynamics has been attained in which friction dramatically alters the character of the supercritical flow features. The supercritical flow features cause variations in wind stress of 10%–50% over tens of kilometers.

## Abstract

A model for hydraulically supercritical atmospheric marine-layer flow along a smoothly varying coastline is formulated and solved numerically. The model is motivated by a recent comparison of CODE observations to a simple hydraulic theory, which suggested the presence of an expansion fan and a compression jump downstream of topographic features. The marine layer is modeled as a homogeneous rotating fluid layer decelerated by surface friction and forced by imposed upper-level pressure gradients. The equations are solved by a characteristic-based gridpoint scheme. The results indicate that the expansion fan is a robust feature that persists under most conditions in the present more realistic model, but is dramatically altered in structure by the presence of friction, while the jump may weaken rapidly offshore due mainly to offshore variations of the layer height upstream of the jump. The agreement between observations and model predictions is good enough to suggest that a first-order description of the dynamics has been attained in which friction dramatically alters the character of the supercritical flow features. The supercritical flow features cause variations in wind stress of 10%–50% over tens of kilometers.