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Abstract
Near-inertial waves (NIWs) radiate energy out of the mixed layer when they develop small lateral scales. Refraction of these waves by gradients in planetary and vertical vorticity has traditionally been invoked to explain this phenomenon. Here, a new mechanism for the enhancement of NIW radiation is described involving the interaction of NIWs with vertical circulations at fronts undergoing frontogenesis. Frontal vertical circulations drive a Doppler shift that is proportional to the wave’s vertical wavenumber m and that changes sign across a front, inducing large lateral differences in wave phase within a few inertial periods. Theory predicts that the process should generate a vertical energy flux that varies inversely with m in contrast to the m −3 dependence expected from refraction. As a consequence, high-mode NIWs are much more effective at radiating energy when fronts and their vertical circulation are present. Numerical simulations initialized with fronts, an array of eddies that drive frontogenesis, and NIWs of various modes are used to test the theory. In the simulations, the interaction of the NIWs with the frontal vertical circulations generates wave beams that radiate down from the fronts. The resultant downward energy flux varies with m following the theoretical scaling laws. In the beams, the Eulerian frequency is inertial within a few percent, yet the waves’ potential and kinetic energies are comparable, thus indicating a superinertial intrinsic frequency. The downshift in Eulerian frequency from the intrinsic frequency is due to horizontal advection of the waves by the eddies.
Abstract
Near-inertial waves (NIWs) radiate energy out of the mixed layer when they develop small lateral scales. Refraction of these waves by gradients in planetary and vertical vorticity has traditionally been invoked to explain this phenomenon. Here, a new mechanism for the enhancement of NIW radiation is described involving the interaction of NIWs with vertical circulations at fronts undergoing frontogenesis. Frontal vertical circulations drive a Doppler shift that is proportional to the wave’s vertical wavenumber m and that changes sign across a front, inducing large lateral differences in wave phase within a few inertial periods. Theory predicts that the process should generate a vertical energy flux that varies inversely with m in contrast to the m −3 dependence expected from refraction. As a consequence, high-mode NIWs are much more effective at radiating energy when fronts and their vertical circulation are present. Numerical simulations initialized with fronts, an array of eddies that drive frontogenesis, and NIWs of various modes are used to test the theory. In the simulations, the interaction of the NIWs with the frontal vertical circulations generates wave beams that radiate down from the fronts. The resultant downward energy flux varies with m following the theoretical scaling laws. In the beams, the Eulerian frequency is inertial within a few percent, yet the waves’ potential and kinetic energies are comparable, thus indicating a superinertial intrinsic frequency. The downshift in Eulerian frequency from the intrinsic frequency is due to horizontal advection of the waves by the eddies.
Abstract
The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FB atm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe )(FB wind/FB atm), where H and δe are the mixed layer and Ekman layer depths, FB wind = S 2 τo /(ρof ), S 2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.
Abstract
The destruction of potential vorticity (PV) at ocean fronts by wind stress–driven frictional forces is examined using PV flux formalism and numerical simulations. When a front is forced by “downfront” winds, that is, winds blowing in the direction of the frontal jet, a nonadvective frictional PV flux that is upward at the sea surface is induced. The flux extracts PV out of the ocean, leading to the formation of a boundary layer thicker than the Ekman layer, with nearly zero PV and nonzero stratification. The PV reduction is not only active in the Ekman layer but is transmitted through the boundary layer via secondary circulations that exchange low PV from the Ekman layer with high PV from the pycnocline. Extraction of PV from the pycnocline by the secondary circulations results in an upward advective PV flux at the base of the boundary layer that scales with the surface, nonadvective, frictional PV flux and that leads to the deepening of the layer. At fronts forced by both downfront winds and a destabilizing atmospheric buoyancy flux FB atm, the critical parameter that determines whether the wind or the buoyancy flux is the dominant cause for PV destruction is (H/δe )(FB wind/FB atm), where H and δe are the mixed layer and Ekman layer depths, FB wind = S 2 τo /(ρof ), S 2 is the magnitude of the lateral buoyancy gradient of the front, τo is the downfront component of the wind stress, ρo is a reference density, and f is the Coriolis parameter. When this parameter is greater than 1, PV destruction by winds dominates and may play an important role in the formation of mode water.
Abstract
Recent work has shown that, when nontraditional (NT) effects associated with the horizontal component of the Coriolis parameter are taken into account, equatorial waves (EWs) experience critical reflection when they reflect off the seafloor at the latitude where their frequency is equal to the inertial frequency. As a result, the vertical shear associated with the wave is strongly enhanced locally and results in bottom-intensified mixing. Using an off-the-shelf parameterization for mixing, these studies have shown that this process could play an important role in driving diapycnal upwelling in the abyssal ocean, but the specific mechanisms generating the mixing have not been studied yet. In this work, we address this limitation by running two-dimensional, high-resolution, nonhydrostatic simulations of the critical reflection of internal waves modified by NT effects. These simulations can resolve the instabilities triggered when the wave reflects off the bottom, allowing us to characterize the energy cascade to smaller scales and to estimate the mixing it generates. We find that shear instabilities drive elevated turbulent diffusivities between 10−1 and −10−3 m2 s−1 over a critical layer of 100–300 m thick. The shear instabilities result directly from the enhancement of kinetic energy in the reflected wave that is confined against the seafloor during the critical reflection process. Simultaneously, higher harmonics are generated and flux energy upward in the water column. These higher harmonics are unstable to parametric subharmonic instability, which absorbs their energy and drive enhanced dissipation above the critical layer, to a height of O(1000) m off the bottom. We show how these results depend on key elements of the EWs and of the medium and discuss the implementation of a parameterization of these effects in global ocean models.
Abstract
Recent work has shown that, when nontraditional (NT) effects associated with the horizontal component of the Coriolis parameter are taken into account, equatorial waves (EWs) experience critical reflection when they reflect off the seafloor at the latitude where their frequency is equal to the inertial frequency. As a result, the vertical shear associated with the wave is strongly enhanced locally and results in bottom-intensified mixing. Using an off-the-shelf parameterization for mixing, these studies have shown that this process could play an important role in driving diapycnal upwelling in the abyssal ocean, but the specific mechanisms generating the mixing have not been studied yet. In this work, we address this limitation by running two-dimensional, high-resolution, nonhydrostatic simulations of the critical reflection of internal waves modified by NT effects. These simulations can resolve the instabilities triggered when the wave reflects off the bottom, allowing us to characterize the energy cascade to smaller scales and to estimate the mixing it generates. We find that shear instabilities drive elevated turbulent diffusivities between 10−1 and −10−3 m2 s−1 over a critical layer of 100–300 m thick. The shear instabilities result directly from the enhancement of kinetic energy in the reflected wave that is confined against the seafloor during the critical reflection process. Simultaneously, higher harmonics are generated and flux energy upward in the water column. These higher harmonics are unstable to parametric subharmonic instability, which absorbs their energy and drive enhanced dissipation above the critical layer, to a height of O(1000) m off the bottom. We show how these results depend on key elements of the EWs and of the medium and discuss the implementation of a parameterization of these effects in global ocean models.
Abstract
The inferred diapycnal upwelling in the abyssal meridional overturning circulation (AMOC) is intensified near the equator, but little is known as to why this is so. In this study, it is shown that the reflection of equatorially trapped waves (ETWs) off the bottom leads to seafloor-intensified mixing and substantial diapycnal upwelling near the equator when the full Coriolis force and the so-called nontraditional effects are taken into account. Using idealized simulations run with the MITgcm of downward-propagating ETWs of various types (i.e., inertia–gravity, Yanai, Kelvin, and Rossby waves) accounting for nontraditional effects, it is demonstrated that the reflection of ETWs off a flat seafloor generates beams of short inertia–gravity waves with strong vertical shear and low Richardson numbers that result in bottom-intensified, persistent, zonally invariant mixing at the inertial latitude of the ETW through the mechanism of critical reflection. The beams are more intense with weaker stratification and, for a given wave type, are stronger for waves with shorter periods and longer vertical wavelengths. The intensity of the beams also differs between wave types because their distinct meridional structures modulate the amount of energy fluxed to the bottom at the inertial latitude. As a result, equatorial inertia–gravity, Rossby, and eastward-propagating Yanai waves yield stronger mixing than Kelvin and westward-propagating Yanai waves in the simulations. It is estimated that this process can result in order 10 Sv (1 Sv ≡ 106 m3 s−1) of diapycnal upwelling per wavelength of ETW in the abyss and thus could play an important role in closing the AMOC.
Abstract
The inferred diapycnal upwelling in the abyssal meridional overturning circulation (AMOC) is intensified near the equator, but little is known as to why this is so. In this study, it is shown that the reflection of equatorially trapped waves (ETWs) off the bottom leads to seafloor-intensified mixing and substantial diapycnal upwelling near the equator when the full Coriolis force and the so-called nontraditional effects are taken into account. Using idealized simulations run with the MITgcm of downward-propagating ETWs of various types (i.e., inertia–gravity, Yanai, Kelvin, and Rossby waves) accounting for nontraditional effects, it is demonstrated that the reflection of ETWs off a flat seafloor generates beams of short inertia–gravity waves with strong vertical shear and low Richardson numbers that result in bottom-intensified, persistent, zonally invariant mixing at the inertial latitude of the ETW through the mechanism of critical reflection. The beams are more intense with weaker stratification and, for a given wave type, are stronger for waves with shorter periods and longer vertical wavelengths. The intensity of the beams also differs between wave types because their distinct meridional structures modulate the amount of energy fluxed to the bottom at the inertial latitude. As a result, equatorial inertia–gravity, Rossby, and eastward-propagating Yanai waves yield stronger mixing than Kelvin and westward-propagating Yanai waves in the simulations. It is estimated that this process can result in order 10 Sv (1 Sv ≡ 106 m3 s−1) of diapycnal upwelling per wavelength of ETW in the abyss and thus could play an important role in closing the AMOC.
Abstract
Flow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.
Abstract
Flow along isobaths of a sloping lower boundary generates an across-isobath Ekman transport in the bottom boundary layer. When this Ekman transport is down the slope it causes convective mixing—much like a downfront wind in the surface boundary layer—destroying stratification and potential vorticity. In this manuscript we show how this can lead to the development of a forced centrifugal or symmetric instability regime, where the potential vorticity flux generated by friction along the boundary is balanced by submesoscale instabilities that return the boundary layer potential vorticity to zero. This balance provides a strong constraint on the boundary layer evolution, which we use to develop a theory that explains the evolution of the boundary layer thickness, the rate at which the instabilities extract energy from the geostrophic flow field, and the magnitude and vertical structure of the dissipation. Finally, we show using theory and a high-resolution numerical model how the presence of centrifugal or symmetric instabilities alters the time-dependent Ekman adjustment of the boundary layer, delaying Ekman buoyancy arrest and enhancing the total energy removed from the balanced flow field. Submesoscale instabilities of the bottom boundary layer may therefore play an important, largely overlooked, role in the energetics of flow over topography in the ocean.
Abstract
Inertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.
Abstract
Inertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.
Abstract
A slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζ
g
modifies the effective Coriolis frequency 
Abstract
A slab mixed layer model and two-dimensional numerical simulations are used to study the generation and energetics of near-inertial oscillations in a unidirectional, laterally sheared geostrophic current forced by oscillatory winds. The vertical vorticity of the current ζ
g
modifies the effective Coriolis frequency
Abstract
Sections of temperature, salinity, dissolved oxygen, and velocity were made crossing the Gulf Stream in late January 2006 to investigate the role of frontal processes in the formation of Eighteen Degree Water (EDW), the Subtropical Mode Water of the North Atlantic. The sections were nominally perpendicular to the stream and measured in a Lagrangian frame by following a floating spar buoy drifting in the Gulf Stream’s warm core. During the survey, EDW was isolated from the mixed layer by the stratified seasonal pycnocline, suggesting that EDW was not yet actively being formed at this time in the season and at the longitudes over which the survey was conducted (64°–70°W). However, in two of the sections, the seasonal pycnocline in the core of the Gulf Stream was broken by an intrusion of cold, fresh, weakly stratified water, nearly saturated in oxygen, that appears to have been subducted from the surface mixed layer north of the stream. The intrusion was identified in three of the sections in profiles with a nearly identical temperature–salinity relation. From the western-to-easternmost sections, where the intrusion was observed, the depth of the intrusion’s salinity minimum descended by ∼90 m in the 71 h it took to complete this part of the survey. This apparent subduction occurred primarily on the upstream side of a meander trough, where the cross-stream velocity was confluent and frontogenetic. Using a variant of the omega equation, the vertical velocity driven by the confluent flow was inferred and yielded downwelling in the vicinity of the intrusion spanning 10–40 m day−1, a range of values consistent with the intrusion’s observed descent, suggesting that frontal subduction was responsible for the formation of the intrusion. In the easternmost section located downstream of the meander trough, the flow was diffluent, driving an inferred vertical circulation that was of the opposite sense to that in the section upstream of the trough. In transiting the two sides of the trough, the intrusion was observed to move toward the center of the stream between the downwelling branches of the opposing vertical circulations, resulting in a downward Lagrangian mean vertical velocity and net subduction. Hydrographic evidence of the subduction of weakly stratified surface waters was seen in the southern flank of the Gulf Stream as well. The solution of the omega equation suggests that this subduction was associated with a relatively shallow vertical circulation confined to the upper 200 m of the water column in the proximity of the front marking the southern edge of the warm core.
Abstract
Sections of temperature, salinity, dissolved oxygen, and velocity were made crossing the Gulf Stream in late January 2006 to investigate the role of frontal processes in the formation of Eighteen Degree Water (EDW), the Subtropical Mode Water of the North Atlantic. The sections were nominally perpendicular to the stream and measured in a Lagrangian frame by following a floating spar buoy drifting in the Gulf Stream’s warm core. During the survey, EDW was isolated from the mixed layer by the stratified seasonal pycnocline, suggesting that EDW was not yet actively being formed at this time in the season and at the longitudes over which the survey was conducted (64°–70°W). However, in two of the sections, the seasonal pycnocline in the core of the Gulf Stream was broken by an intrusion of cold, fresh, weakly stratified water, nearly saturated in oxygen, that appears to have been subducted from the surface mixed layer north of the stream. The intrusion was identified in three of the sections in profiles with a nearly identical temperature–salinity relation. From the western-to-easternmost sections, where the intrusion was observed, the depth of the intrusion’s salinity minimum descended by ∼90 m in the 71 h it took to complete this part of the survey. This apparent subduction occurred primarily on the upstream side of a meander trough, where the cross-stream velocity was confluent and frontogenetic. Using a variant of the omega equation, the vertical velocity driven by the confluent flow was inferred and yielded downwelling in the vicinity of the intrusion spanning 10–40 m day−1, a range of values consistent with the intrusion’s observed descent, suggesting that frontal subduction was responsible for the formation of the intrusion. In the easternmost section located downstream of the meander trough, the flow was diffluent, driving an inferred vertical circulation that was of the opposite sense to that in the section upstream of the trough. In transiting the two sides of the trough, the intrusion was observed to move toward the center of the stream between the downwelling branches of the opposing vertical circulations, resulting in a downward Lagrangian mean vertical velocity and net subduction. Hydrographic evidence of the subduction of weakly stratified surface waters was seen in the southern flank of the Gulf Stream as well. The solution of the omega equation suggests that this subduction was associated with a relatively shallow vertical circulation confined to the upper 200 m of the water column in the proximity of the front marking the southern edge of the warm core.
Abstract
Many ocean fronts experience strong local atmospheric forcing by down-front winds, that is, winds blowing in the direction of the frontal jet. An analytic theory and nonhydrostatic numerical simulations are used to demonstrate the mechanism by which down-front winds lead to frontogenesis. When a wind blows down a front, cross-front advection of density by Ekman flow results in a destabilizing wind-driven buoyancy flux (WDBF) equal to the product of the Ekman transport with the surface lateral buoyancy gradient. Destabilization of the water column results in convection that is localized to the front and that has a buoyancy flux that is scaled by the WDBF. Mixing of buoyancy by convection, and Ekman pumping/suction resulting from the cross-front contrast in vertical vorticity of the frontal jet, drive frontogenetic ageostrophic secondary circulations (ASCs). For mixed layers with negative potential vorticity, the most frontogenetic ASCs select a preferred cross-front width and do not translate with the Ekman transport, but instead remain stationary in space. Frontal intensification occurs within several inertial periods and is faster the stronger the wind stress. Vertical circulation is characterized by subduction on the dense side of the front and upwelling along the frontal interface and scales with the Ekman pumping and convective mixing of buoyancy. Cross-front sections of density, potential vorticity, and velocity at the subpolar front of the Japan/East Sea suggest that frontogenesis by down-front winds was active during cold-air outbreaks and could result in strong vertical circulation.
Abstract
Many ocean fronts experience strong local atmospheric forcing by down-front winds, that is, winds blowing in the direction of the frontal jet. An analytic theory and nonhydrostatic numerical simulations are used to demonstrate the mechanism by which down-front winds lead to frontogenesis. When a wind blows down a front, cross-front advection of density by Ekman flow results in a destabilizing wind-driven buoyancy flux (WDBF) equal to the product of the Ekman transport with the surface lateral buoyancy gradient. Destabilization of the water column results in convection that is localized to the front and that has a buoyancy flux that is scaled by the WDBF. Mixing of buoyancy by convection, and Ekman pumping/suction resulting from the cross-front contrast in vertical vorticity of the frontal jet, drive frontogenetic ageostrophic secondary circulations (ASCs). For mixed layers with negative potential vorticity, the most frontogenetic ASCs select a preferred cross-front width and do not translate with the Ekman transport, but instead remain stationary in space. Frontal intensification occurs within several inertial periods and is faster the stronger the wind stress. Vertical circulation is characterized by subduction on the dense side of the front and upwelling along the frontal interface and scales with the Ekman pumping and convective mixing of buoyancy. Cross-front sections of density, potential vorticity, and velocity at the subpolar front of the Japan/East Sea suggest that frontogenesis by down-front winds was active during cold-air outbreaks and could result in strong vertical circulation.
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.
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.
