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- Author or Editor: Leif N. Thomas x
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Abstract
An analysis and physical interpretation of near-inertial waves (NIWs) propagating perpendicular to a steady, two-dimensional, strongly baroclinic, geostrophic current are presented. The analysis is appropriate for geostrophic currents with order-one Richardson numbers such as those associated with fronts experiencing strong, wintertime atmospheric forcing. This work highlights the underlying physics behind the properties of the NIWs using parcel arguments and the principles of conservation of density and absolute momentum. Baroclinicity introduces lateral gradients in density and vertical gradients in absolute momentum that significantly modify the dispersion and polarization relations and propagation of NIWs relative to classical internal wave theory. In particular, oscillations at the minimum frequency are not horizontal but, instead, are slanted along isopycnals. Furthermore, the polarization of the horizontal velocity is not necessarily circular at the minimum frequency and the spiraling of the wave’s velocity vector with time and depth can be in the opposite direction from that predicted by classical theory. Ray tracing and numerical solutions illustrate the trapping and amplification of NIWs in regions of strong baroclinicity where the wave frequency is lower than the effective Coriolis frequency. The largest amplification is found at slantwise critical layers that align with the tilted isopycnals of the current. Such slantwise critical layers are seen in wintertime observations of the Gulf Stream and, consistent with the theory, coincide with regions of intensified ageostrophic shear characterized by a banded structure that is spatially coherent along isopycnals.
Abstract
An analysis and physical interpretation of near-inertial waves (NIWs) propagating perpendicular to a steady, two-dimensional, strongly baroclinic, geostrophic current are presented. The analysis is appropriate for geostrophic currents with order-one Richardson numbers such as those associated with fronts experiencing strong, wintertime atmospheric forcing. This work highlights the underlying physics behind the properties of the NIWs using parcel arguments and the principles of conservation of density and absolute momentum. Baroclinicity introduces lateral gradients in density and vertical gradients in absolute momentum that significantly modify the dispersion and polarization relations and propagation of NIWs relative to classical internal wave theory. In particular, oscillations at the minimum frequency are not horizontal but, instead, are slanted along isopycnals. Furthermore, the polarization of the horizontal velocity is not necessarily circular at the minimum frequency and the spiraling of the wave’s velocity vector with time and depth can be in the opposite direction from that predicted by classical theory. Ray tracing and numerical solutions illustrate the trapping and amplification of NIWs in regions of strong baroclinicity where the wave frequency is lower than the effective Coriolis frequency. The largest amplification is found at slantwise critical layers that align with the tilted isopycnals of the current. Such slantwise critical layers are seen in wintertime observations of the Gulf Stream and, consistent with the theory, coincide with regions of intensified ageostrophic shear characterized by a banded structure that is spatially coherent along isopycnals.
Abstract
Submesoscale-resolving numerical simulations are used to investigate a mechanism for sustained mode water formation via cabbeling at thermohaline fronts subject to a confluent strain flow. The simulations serve to further elucidate the mechanism and refine the predictions of the analytical model of Thomas and Shakespeare. Unlike other proposed mechanisms involving air–sea fluxes, the cabbeling mechanism, in addition to driving significant mode water formation, uniquely determines the thermohaline properties of the mode water given knowledge of the source water masses on either side of the front. The process of mode water formation in the simulations is as follows: Confluent flow associated with idealized mesoscale eddies forces water horizontally toward the front. The frontogenetic circulation draws this water near adiabatically from the full depth of the thermohaline front up to the surface 25 m, where resolved submesoscale instabilities drive intense mixing across the thermohaline front, creating the mode water. The mode water is denser than the surrounding stratified fluid and sinks to fill its neutral buoyancy layer at depth. This layer gradually expands up to the surface, and eddies composed entirely of this mode water detach from the front and accumulate in the diffluent regions of the domain. The process continues until the source water masses are exhausted. The temperature–salinity (T–S) relation of the resulting mode water is biased to the properties of the source water that has the larger isopycnal T–S anomaly. This mechanism has the potential to drive O(1) Sv (1 Sv ≡ 106 m3 s−1) mode water formation and may be important in determining the properties of mode water in the global oceans.
Abstract
Submesoscale-resolving numerical simulations are used to investigate a mechanism for sustained mode water formation via cabbeling at thermohaline fronts subject to a confluent strain flow. The simulations serve to further elucidate the mechanism and refine the predictions of the analytical model of Thomas and Shakespeare. Unlike other proposed mechanisms involving air–sea fluxes, the cabbeling mechanism, in addition to driving significant mode water formation, uniquely determines the thermohaline properties of the mode water given knowledge of the source water masses on either side of the front. The process of mode water formation in the simulations is as follows: Confluent flow associated with idealized mesoscale eddies forces water horizontally toward the front. The frontogenetic circulation draws this water near adiabatically from the full depth of the thermohaline front up to the surface 25 m, where resolved submesoscale instabilities drive intense mixing across the thermohaline front, creating the mode water. The mode water is denser than the surrounding stratified fluid and sinks to fill its neutral buoyancy layer at depth. This layer gradually expands up to the surface, and eddies composed entirely of this mode water detach from the front and accumulate in the diffluent regions of the domain. The process continues until the source water masses are exhausted. The temperature–salinity (T–S) relation of the resulting mode water is biased to the properties of the source water that has the larger isopycnal T–S anomaly. This mechanism has the potential to drive O(1) Sv (1 Sv ≡ 106 m3 s−1) mode water formation and may be important in determining the properties of mode water in the global oceans.
Abstract
Ekman transport, the horizontal mass transport associated with a wind stress applied on the ocean surface, is modified by the vorticity of ocean currents, leading to what has been termed the nonlinear Ekman transport. This article extends earlier work on this topic by deriving solutions for the nonlinear Ekman transport valid in currents with curvature, such as a meandering jet or circular vortex, and for flows with the Rossby number approaching unity. Tilting of the horizontal vorticity of the Ekman flow by the balanced currents modifies the ocean response to surface forcing, such that, to leading order, winds parallel to the flow drive an Ekman transport that depends only on the shear vorticity component of the vertical relative vorticity, whereas across-flow winds drive transport dependent on the curvature vorticity. Curvature in the balanced flow field thus leads to an Ekman transport that differs from previous formulations derived under the assumption of straight flows. Notably, the theory also predicts a component of the transport aligned with the surface wind stress, contrary to classic Ekman theory. In the case of the circular vortex, the solutions given here can be used to calculate the vertical velocity to a higher order of accuracy than previous solutions, extending possible applications of the theory to strong balanced flows. The existence of oscillations, and the potential for resonance and instability, in the Ekman flow at a curved jet are also demonstrated.
Abstract
Ekman transport, the horizontal mass transport associated with a wind stress applied on the ocean surface, is modified by the vorticity of ocean currents, leading to what has been termed the nonlinear Ekman transport. This article extends earlier work on this topic by deriving solutions for the nonlinear Ekman transport valid in currents with curvature, such as a meandering jet or circular vortex, and for flows with the Rossby number approaching unity. Tilting of the horizontal vorticity of the Ekman flow by the balanced currents modifies the ocean response to surface forcing, such that, to leading order, winds parallel to the flow drive an Ekman transport that depends only on the shear vorticity component of the vertical relative vorticity, whereas across-flow winds drive transport dependent on the curvature vorticity. Curvature in the balanced flow field thus leads to an Ekman transport that differs from previous formulations derived under the assumption of straight flows. Notably, the theory also predicts a component of the transport aligned with the surface wind stress, contrary to classic Ekman theory. In the case of the circular vortex, the solutions given here can be used to calculate the vertical velocity to a higher order of accuracy than previous solutions, extending possible applications of the theory to strong balanced flows. The existence of oscillations, and the potential for resonance and instability, in the Ekman flow at a curved jet are also demonstrated.
Abstract
A simple analytical model is used to elucidate a potential mechanism for steady-state mode water formation at a thermohaline front that involves frontogenesis, submesoscale lateral mixing, and cabbeling. This mechanism is motivated in part by recent observations of an extremely sharp, density-compensated front at the North Wall of the Gulf Stream. Here, the intergyre, along-isopycnal, salinity–temperature difference is compressed into a span of a few kilometers, making the flow susceptible to cabbeling. The sharpness of the front is caused by frontogenetic strain, which is presumably balanced by submesoscale lateral mixing processes. The balance is studied with the simple model, and a scaling is derived for the amount of water mass transformation resulting from the ensuing cabbeling. The transformation scales with the strain rate, equilibrated width of the front, and the square of the isopycnal temperature contrast across the front. At the major ocean fronts where mode waters are found, this isopycnal temperature contrast decreases with increasing density near the isopycnal layers where mode waters reside. This implies that cabbeling should result in a convergent diapycnal mass flux into mode water density classes. The scaling for the transformation suggests that at these fronts the process could generate 0.01–1 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) of mode water. These formation rates, while smaller than mode water formation by air–sea fluxes, should be independent of season and thus could fill select isopycnal layers continuously and play an important role in the dynamics of mode waters on interannual time scales.
Abstract
A simple analytical model is used to elucidate a potential mechanism for steady-state mode water formation at a thermohaline front that involves frontogenesis, submesoscale lateral mixing, and cabbeling. This mechanism is motivated in part by recent observations of an extremely sharp, density-compensated front at the North Wall of the Gulf Stream. Here, the intergyre, along-isopycnal, salinity–temperature difference is compressed into a span of a few kilometers, making the flow susceptible to cabbeling. The sharpness of the front is caused by frontogenetic strain, which is presumably balanced by submesoscale lateral mixing processes. The balance is studied with the simple model, and a scaling is derived for the amount of water mass transformation resulting from the ensuing cabbeling. The transformation scales with the strain rate, equilibrated width of the front, and the square of the isopycnal temperature contrast across the front. At the major ocean fronts where mode waters are found, this isopycnal temperature contrast decreases with increasing density near the isopycnal layers where mode waters reside. This implies that cabbeling should result in a convergent diapycnal mass flux into mode water density classes. The scaling for the transformation suggests that at these fronts the process could generate 0.01–1 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) of mode water. These formation rates, while smaller than mode water formation by air–sea fluxes, should be independent of season and thus could fill select isopycnal layers continuously and play an important role in the dynamics of mode waters on interannual time scales.
Abstract
Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is known that these winds can result in mixing of the plume with the ambient water and that the winds influence the transport, spatial extent, and stability of the plumes. In the present study, the interaction of the Ekman velocity in the surface layer and baroclinic instability supported by the strong horizontal density gradient of the plume is explored with the objective of understanding the potential vorticity and buoyancy budgets. The approach makes use of an idealized numerical model and scaling theory. It is shown that when winds are present the weak stratification resulting from vertical mixing and the strong baroclinicity of the front results in near-zero average potential vorticity q. For weak to moderate winds, the reduction of q by diapycnal mixing is balanced by the generation of q through the geostrophic stress term in the regions of strong horizontal density gradients and stable stratification. However, for very strong winds the wind stress overwhelms the geostrophic stress and leads to a reduction in q, which is balanced by the vertical mixing term. In the absence of winds, the geostrophic stress dominates mixing and the flow rapidly restratifies. Nonlinearity, extremes of relative vorticity and vertical velocity, and mixing are all enhanced by the presence of a coast. Scaling estimates developed for the eddy buoyancy flux, the surface potential vorticity flux, and the diapycnal mixing rate compare well with results diagnosed from a series of numerical model calculations.
Abstract
Downfront, or downwelling favorable, winds are commonly found over buoyant coastal plumes. It is known that these winds can result in mixing of the plume with the ambient water and that the winds influence the transport, spatial extent, and stability of the plumes. In the present study, the interaction of the Ekman velocity in the surface layer and baroclinic instability supported by the strong horizontal density gradient of the plume is explored with the objective of understanding the potential vorticity and buoyancy budgets. The approach makes use of an idealized numerical model and scaling theory. It is shown that when winds are present the weak stratification resulting from vertical mixing and the strong baroclinicity of the front results in near-zero average potential vorticity q. For weak to moderate winds, the reduction of q by diapycnal mixing is balanced by the generation of q through the geostrophic stress term in the regions of strong horizontal density gradients and stable stratification. However, for very strong winds the wind stress overwhelms the geostrophic stress and leads to a reduction in q, which is balanced by the vertical mixing term. In the absence of winds, the geostrophic stress dominates mixing and the flow rapidly restratifies. Nonlinearity, extremes of relative vorticity and vertical velocity, and mixing are all enhanced by the presence of a coast. Scaling estimates developed for the eddy buoyancy flux, the surface potential vorticity flux, and the diapycnal mixing rate compare well with results diagnosed from a series of numerical model calculations.
Abstract
Studies of internal wave-driven mixing in the coastal ocean have been focused on internal tides, while wind-driven near-inertial waves (NIWs) have received less attention in this regard. This study demonstrates a scenario of NIW-driven mixing over the Texas–Louisiana shelf. Supported by a high-resolution simulation over the shelf, the NIWs driven by land–sea breeze radiate downward at a sharp front and enhance the mixing in the bottom boundary layer where the NIWs are focused because of slantwise critical reflection. The criterion for slantwise critical reflection of NIWs is
Abstract
Studies of internal wave-driven mixing in the coastal ocean have been focused on internal tides, while wind-driven near-inertial waves (NIWs) have received less attention in this regard. This study demonstrates a scenario of NIW-driven mixing over the Texas–Louisiana shelf. Supported by a high-resolution simulation over the shelf, the NIWs driven by land–sea breeze radiate downward at a sharp front and enhance the mixing in the bottom boundary layer where the NIWs are focused because of slantwise critical reflection. The criterion for slantwise critical reflection of NIWs is
Abstract
This study describes a specific type of critical layer for near-inertial waves (NIWs) that forms when isopycnals run parallel to sloping bathymetry. Upon entering this slantwise critical layer, the group velocity of the waves decreases to zero and the NIWs become trapped and amplified, which can enhance mixing. A realistic simulation of anticyclonic eddies on the Texas–Louisiana shelf reveals that such critical layers can form where the eddies impinge onto the sloping bottom. Velocity shear bands in the simulation indicate that wind-forced NIWs are radiated downward from the surface in the eddies, bend upward near the bottom, and enter critical layers over the continental shelf, resulting in inertially modulated enhanced mixing. Idealized simulations designed to capture this flow reproduce the wave propagation and enhanced mixing. The link between the enhanced mixing and wave trapping in the slantwise critical layer is made using ray tracing and an analysis of the waves’ energetics in the idealized simulations. An ensemble of simulations is performed spanning the relevant parameter space that demonstrates that the strength of the mixing is correlated with the degree to which NIWs are trapped in the critical layers. While the application here is for a shallow coastal setting, the mechanisms could be active in the open ocean as well where isopycnals align with bathymetry.
Abstract
This study describes a specific type of critical layer for near-inertial waves (NIWs) that forms when isopycnals run parallel to sloping bathymetry. Upon entering this slantwise critical layer, the group velocity of the waves decreases to zero and the NIWs become trapped and amplified, which can enhance mixing. A realistic simulation of anticyclonic eddies on the Texas–Louisiana shelf reveals that such critical layers can form where the eddies impinge onto the sloping bottom. Velocity shear bands in the simulation indicate that wind-forced NIWs are radiated downward from the surface in the eddies, bend upward near the bottom, and enter critical layers over the continental shelf, resulting in inertially modulated enhanced mixing. Idealized simulations designed to capture this flow reproduce the wave propagation and enhanced mixing. The link between the enhanced mixing and wave trapping in the slantwise critical layer is made using ray tracing and an analysis of the waves’ energetics in the idealized simulations. An ensemble of simulations is performed spanning the relevant parameter space that demonstrates that the strength of the mixing is correlated with the degree to which NIWs are trapped in the critical layers. While the application here is for a shallow coastal setting, the mechanisms could be active in the open ocean as well where isopycnals align with bathymetry.
Abstract
Fast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagates downward and toward the anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of |k|. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly dispersive high modes dominate in the surface layer. In the weakly dispersive limit, k = −t∇ζ(x, y, t)/2 provided that (i) the eddy vertical vorticity ζ evolves according to the barotropic quasigeostrophic equation and (ii) k = 0 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave–eddy energy transfers.
Abstract
Fast-moving synoptic-scale atmospheric disturbances produce large-scale near-inertial waves in the ocean mixed layer. In this paper, we analyze the distortion of such waves by smaller-scale barotropic eddies, with a focus on the evolution of the horizontal wavevector k under the effects of straining and refraction. The model is initialized with a horizontally uniform (k = 0) surface-confined near-inertial wave, which then evolves according to the phase-averaged model of Young and Ben Jelloul. A steady barotropic vortex dipole is first considered. Shear bands appear in the jet region as wave energy propagates downward and toward the anticyclone. When measured at a fixed location, both horizontal and vertical wavenumbers grow linearly with the time t elapsed since generation such that their ratio, the slope of wave bands, is time independent. Analogy with passive scalar dynamics suggests that straining should result in the exponential growth of |k|. Here instead, straining is ineffective, not only at the jet center, but also in its confluent and diffluent regions. Low modes rapidly escape below the anticyclonic core such that weakly dispersive high modes dominate in the surface layer. In the weakly dispersive limit, k = −t∇ζ(x, y, t)/2 provided that (i) the eddy vertical vorticity ζ evolves according to the barotropic quasigeostrophic equation and (ii) k = 0 initially. In steady flows, straining is ineffective because k is always perpendicular to the flow. In unsteady flows, straining modifies the vorticity gradient and hence k, and may account for significant wave–eddy energy transfers.
Abstract
Model analyses of an alongshelf flow over a continental shelf and slope reveal upwelling near the shelf break. A stratified, initially uniform, alongshelf flow undergoes a rapid adjustment with notable differences onshore and offshore of the shelf break. Over the shelf, a bottom boundary layer and an offshore bottom Ekman transport develop within an inertial period. Over the slope, the bottom offshore transport is reduced from the shelf’s bottom transport by two processes. First, advection of buoyancy downslope induces vertical mixing, destratifying, and thickening the bottom boundary layer. The downward-tilting isopycnals reduce the geostrophic speed near the bottom. The reduced bottom stress weakens the offshore Ekman transport, a process known as buoyancy shutdown of the Ekman transport. Second, the thickening bottom boundary layer and weakening near-bottom speeds are balanced by an upslope ageostrophic transport. The convergence in the bottom transport induces adiabatic upwelling offshore of the shelf break. For a time period after the initial adjustment, scalings are identified for the upwelling speed and the length scale over which it occurs. Numerical experiments are used to test the scalings for a range of initial speeds and stratifications. Upwelling occurs within an inertial period, reaching values of up to 10 m day−1 within 2 to 7 km offshore of the shelf break. Upwelling drives an interior secondary circulation that accelerates the alongshelf flow over the slope, forming a shelfbreak jet. The model results are compared with upwelling estimates from other models and observations near the Middle Atlantic Bight shelf break.
Abstract
Model analyses of an alongshelf flow over a continental shelf and slope reveal upwelling near the shelf break. A stratified, initially uniform, alongshelf flow undergoes a rapid adjustment with notable differences onshore and offshore of the shelf break. Over the shelf, a bottom boundary layer and an offshore bottom Ekman transport develop within an inertial period. Over the slope, the bottom offshore transport is reduced from the shelf’s bottom transport by two processes. First, advection of buoyancy downslope induces vertical mixing, destratifying, and thickening the bottom boundary layer. The downward-tilting isopycnals reduce the geostrophic speed near the bottom. The reduced bottom stress weakens the offshore Ekman transport, a process known as buoyancy shutdown of the Ekman transport. Second, the thickening bottom boundary layer and weakening near-bottom speeds are balanced by an upslope ageostrophic transport. The convergence in the bottom transport induces adiabatic upwelling offshore of the shelf break. For a time period after the initial adjustment, scalings are identified for the upwelling speed and the length scale over which it occurs. Numerical experiments are used to test the scalings for a range of initial speeds and stratifications. Upwelling occurs within an inertial period, reaching values of up to 10 m day−1 within 2 to 7 km offshore of the shelf break. Upwelling drives an interior secondary circulation that accelerates the alongshelf flow over the slope, forming a shelfbreak jet. The model results are compared with upwelling estimates from other models and observations near the Middle Atlantic Bight shelf break.
Abstract
An inverse method for inferring vertical velocities from high-resolution hydrographic/velocity surveys is formulated and applied to observations collected at the subpolar front of the Japan/East Sea (JES) taken during several cold-air outbreaks. The method is distinct from vertical velocity inferences based on the omega equation in that the driving mechanism for the ageostrophic flow is inferred rather than assumed and hence is particularly appropriate for application to wind- or buoyancy-forced upper-ocean currents where friction, mixing, inertial/superinertial motions, or higher-order effects can contribute along with shear/strain of the geostrophic flow to force vertical motions.
The inferred vertical circulation at the subpolar front of the JES has amplitudes
Abstract
An inverse method for inferring vertical velocities from high-resolution hydrographic/velocity surveys is formulated and applied to observations collected at the subpolar front of the Japan/East Sea (JES) taken during several cold-air outbreaks. The method is distinct from vertical velocity inferences based on the omega equation in that the driving mechanism for the ageostrophic flow is inferred rather than assumed and hence is particularly appropriate for application to wind- or buoyancy-forced upper-ocean currents where friction, mixing, inertial/superinertial motions, or higher-order effects can contribute along with shear/strain of the geostrophic flow to force vertical motions.
The inferred vertical circulation at the subpolar front of the JES has amplitudes
