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- Author or Editor: Timour Radko x
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Abstract
This study offers a systematic stability analysis of unsteady shear flows representing large-scale, low-frequency internal waves in the ocean. The analysis is based on the unbounded time-dependent Couette model. This setup makes it possible to isolate the instabilities caused by uniform shear from those that can be attributed to resonant triad interactions or to the presence of inflection points in vertical velocity profiles. Linear analysis suggests that time-dependent spatially uniform shears are unstable regardless of the Richardson number (Ri). However, the growth rate of instability monotonically decreases with increasing Ri and increases with increasing frequency of oscillations. Therefore, models assuming a steady basic state—which are commonly used to conceptualize shear-induced instability and mixing—can be viewed as singular limits of the corresponding time-dependent systems. The present investigation is focused on the supercritical range of Richardson numbers (Ri > 1/4) where steady parallel flows are stable. An explicit relation is proposed for the growth rate of shear instability as a function of background parameters. For moderately supercritical Richardson numbers (Ri ~ 1), we find that the growth rates obtained are less than, but comparable to, those expected for Kelvin–Helmholtz instabilities of steady shears at Ri < 1/4. Hence, we conclude that the instability of time-dependent flows could represent a viable mixing mechanism in the ocean, particular in regions characterized by relatively weak wave activity and predominantly supercritical large-scale shears.
Abstract
This study offers a systematic stability analysis of unsteady shear flows representing large-scale, low-frequency internal waves in the ocean. The analysis is based on the unbounded time-dependent Couette model. This setup makes it possible to isolate the instabilities caused by uniform shear from those that can be attributed to resonant triad interactions or to the presence of inflection points in vertical velocity profiles. Linear analysis suggests that time-dependent spatially uniform shears are unstable regardless of the Richardson number (Ri). However, the growth rate of instability monotonically decreases with increasing Ri and increases with increasing frequency of oscillations. Therefore, models assuming a steady basic state—which are commonly used to conceptualize shear-induced instability and mixing—can be viewed as singular limits of the corresponding time-dependent systems. The present investigation is focused on the supercritical range of Richardson numbers (Ri > 1/4) where steady parallel flows are stable. An explicit relation is proposed for the growth rate of shear instability as a function of background parameters. For moderately supercritical Richardson numbers (Ri ~ 1), we find that the growth rates obtained are less than, but comparable to, those expected for Kelvin–Helmholtz instabilities of steady shears at Ri < 1/4. Hence, we conclude that the instability of time-dependent flows could represent a viable mixing mechanism in the ocean, particular in regions characterized by relatively weak wave activity and predominantly supercritical large-scale shears.
Abstract
An analytical model of the Atlantic deep stratification and meridional overturning circulation is presented that illustrates the dynamic coupling between the Southern Ocean and the midlatitude gyres. The model, expressed here in terms of the two-and-a-half-layer framework, predicts the stratification and meridional transport as a function of the mechanical and thermodynamic forcing at the sea surface. The approach is based on the classical elements of large-scale circulation theory——ideal thermocline, inertial western boundary currents, and eddy-controlled Antarctic Circumpolar Current (ACC) models——which are combined to produce a consistent three-dimensional view of the global overturning. The analytical tractability is achieved by assuming and subsequently verifying that the pattern of circulation in the model is largely controlled by adiabatic processes: the time-mean and eddy-induced isopycnal advection of buoyancy. The mean stratification of the lower thermocline is determined by the surface forcing in the ACC and, to a lesser extent, by the North Atlantic Deep Water formation rate. Although the vertical small-scale mixing and the diapycnal eddy-flux components can substantially influence the magnitude of overturning, their effect on the net stratification of the midlatitude ocean is surprisingly limited. The analysis in this paper suggests the interpretation of the ACC as an active lateral boundary layer that does not passively adjust to the prescribed large-scale solution but instead forcefully controls the interior pattern.
Abstract
An analytical model of the Atlantic deep stratification and meridional overturning circulation is presented that illustrates the dynamic coupling between the Southern Ocean and the midlatitude gyres. The model, expressed here in terms of the two-and-a-half-layer framework, predicts the stratification and meridional transport as a function of the mechanical and thermodynamic forcing at the sea surface. The approach is based on the classical elements of large-scale circulation theory——ideal thermocline, inertial western boundary currents, and eddy-controlled Antarctic Circumpolar Current (ACC) models——which are combined to produce a consistent three-dimensional view of the global overturning. The analytical tractability is achieved by assuming and subsequently verifying that the pattern of circulation in the model is largely controlled by adiabatic processes: the time-mean and eddy-induced isopycnal advection of buoyancy. The mean stratification of the lower thermocline is determined by the surface forcing in the ACC and, to a lesser extent, by the North Atlantic Deep Water formation rate. Although the vertical small-scale mixing and the diapycnal eddy-flux components can substantially influence the magnitude of overturning, their effect on the net stratification of the midlatitude ocean is surprisingly limited. The analysis in this paper suggests the interpretation of the ACC as an active lateral boundary layer that does not passively adjust to the prescribed large-scale solution but instead forcefully controls the interior pattern.
Abstract
This study is focused on finescale dissipation mechanisms of intrathermocline mesoscale vortices exemplified by meddies, large anticyclonic salt lenses of Mediterranean origin commonly observed in the lower North Atlantic thermocline. High-resolution numerical experiments are diagnosed to quantify the rates of temperature and salinity (T, S) dispersion in salt lenses and to determine the relative contribution of various mixing processes in the decay of their thermohaline signatures. This study finds, in agreement with observations, that meddies dissipate on the characteristic time scale of several years and that their ultimate disintegration can be attributed to thermohaline interleaving driven by double-diffusive mixing. Mechanically generated turbulence, on the other hand, tends to suppress the interleaving and therefore has an adverse net effect on eddy dispersion. It is found that the dispersion properties of static lenses, characterized by density-compensated T–S patterns, and their rapidly rotating counterparts are dramatically different.
Abstract
This study is focused on finescale dissipation mechanisms of intrathermocline mesoscale vortices exemplified by meddies, large anticyclonic salt lenses of Mediterranean origin commonly observed in the lower North Atlantic thermocline. High-resolution numerical experiments are diagnosed to quantify the rates of temperature and salinity (T, S) dispersion in salt lenses and to determine the relative contribution of various mixing processes in the decay of their thermohaline signatures. This study finds, in agreement with observations, that meddies dissipate on the characteristic time scale of several years and that their ultimate disintegration can be attributed to thermohaline interleaving driven by double-diffusive mixing. Mechanically generated turbulence, on the other hand, tends to suppress the interleaving and therefore has an adverse net effect on eddy dispersion. It is found that the dispersion properties of static lenses, characterized by density-compensated T–S patterns, and their rapidly rotating counterparts are dramatically different.
Abstract
The modulation of large-scale eddying flows by gentle variation in topography is examined using a combination of direct numerical simulations and theoretical arguments. The basic state is represented by a laterally uniform zonal current that is restricted to the upper layer of a baroclinically unstable quasigeostrophic two-layer system. Therefore, the observed topographically induced generation of large-scale patterns is attributed entirely to the action of mesoscale eddies. The parameter regime investigated in this study is not conducive to the spontaneous formation of stationary zonal jets. The interaction between the large-scale current, eddies, and topography is described using an asymptotic multiscale model. The ability of the model to explicitly represent the interaction between distinct flow components makes it possible to unambiguously interpret the essential dynamics of the topographic/eddy-induced modulation. The multiscale solutions obtained reflect the balance between the modification of the meridional fluxes of potential vorticity (PV) due to the variation in topography and the corresponding modification of PV fluxes due to the induced large-scale circulation. The predictions of the asymptotic theory are successfully tested by comparing to the ones obtained by direct numerical simulations.
Abstract
The modulation of large-scale eddying flows by gentle variation in topography is examined using a combination of direct numerical simulations and theoretical arguments. The basic state is represented by a laterally uniform zonal current that is restricted to the upper layer of a baroclinically unstable quasigeostrophic two-layer system. Therefore, the observed topographically induced generation of large-scale patterns is attributed entirely to the action of mesoscale eddies. The parameter regime investigated in this study is not conducive to the spontaneous formation of stationary zonal jets. The interaction between the large-scale current, eddies, and topography is described using an asymptotic multiscale model. The ability of the model to explicitly represent the interaction between distinct flow components makes it possible to unambiguously interpret the essential dynamics of the topographic/eddy-induced modulation. The multiscale solutions obtained reflect the balance between the modification of the meridional fluxes of potential vorticity (PV) due to the variation in topography and the corresponding modification of PV fluxes due to the induced large-scale circulation. The predictions of the asymptotic theory are successfully tested by comparing to the ones obtained by direct numerical simulations.
Abstract
A simple theory is developed for the large-scale three-dimensional structure of the Antarctic Circumpolar Current and the upper cell of its overturning circulation. The model is based on a perturbation expansion about the zonal-average residual-mean model developed previously by Marshall and Radko. The problem is solved using the method of characteristics for idealized patterns of wind and buoyancy forcing constructed from observations. The equilibrium solutions found represent a balance between the Eulerian meridional overturning, eddy-induced circulation, and downstream advection by the mean flow. Depth and stratification of the model thermocline increase in the Atlantic–Indian Oceans sector where the mean wind stress is large. Residual circulation in the model is characterized by intensification of the overturning circulation in the Atlantic–Indian sector and reduction in strength in the Pacific Ocean region. Predicted three-dimensional patterns of stratification and residual circulation in the interior of the ACC are compared with observations.
Abstract
A simple theory is developed for the large-scale three-dimensional structure of the Antarctic Circumpolar Current and the upper cell of its overturning circulation. The model is based on a perturbation expansion about the zonal-average residual-mean model developed previously by Marshall and Radko. The problem is solved using the method of characteristics for idealized patterns of wind and buoyancy forcing constructed from observations. The equilibrium solutions found represent a balance between the Eulerian meridional overturning, eddy-induced circulation, and downstream advection by the mean flow. Depth and stratification of the model thermocline increase in the Atlantic–Indian Oceans sector where the mean wind stress is large. Residual circulation in the model is characterized by intensification of the overturning circulation in the Atlantic–Indian sector and reduction in strength in the Pacific Ocean region. Predicted three-dimensional patterns of stratification and residual circulation in the interior of the ACC are compared with observations.
Abstract
Residual-mean theory is applied to the streamwise-averaged Antarctic Circumpolar Current to arrive at a concise description of the processes that set up its stratification and meridional overturning circulation on an f plane. Simple solutions are found in which transfer by geostrophic eddies colludes with applied winds and buoyancy fluxes to determine the depth and stratification of the thermocline and the pattern of associated (residual) meridional overturning circulation.
Abstract
Residual-mean theory is applied to the streamwise-averaged Antarctic Circumpolar Current to arrive at a concise description of the processes that set up its stratification and meridional overturning circulation on an f plane. Simple solutions are found in which transfer by geostrophic eddies colludes with applied winds and buoyancy fluxes to determine the depth and stratification of the thermocline and the pattern of associated (residual) meridional overturning circulation.
Abstract
High-resolution numerical experiments are diagnosed to study the integral effects of geostrophic eddy fluxes on the large-scale ocean circulation. Three characteristic large-scale flows are considered: 1) an anticyclonic single gyre, 2) a double gyre, and 3) an unblocked zonal flow, a simple analog of the Antarctic Circumpolar Current. It is found that buoyancy and potential vorticity budgets in the presence of eddies are dominated by a balance between vertical advection into the control volume by Ekman pumping and eddy transfer across the density surfaces achieved by diapycnal eddy fluxes, with small-scale mixing making only a minor contribution. Possible oceanographic implications of the results are discussed.
Abstract
High-resolution numerical experiments are diagnosed to study the integral effects of geostrophic eddy fluxes on the large-scale ocean circulation. Three characteristic large-scale flows are considered: 1) an anticyclonic single gyre, 2) a double gyre, and 3) an unblocked zonal flow, a simple analog of the Antarctic Circumpolar Current. It is found that buoyancy and potential vorticity budgets in the presence of eddies are dominated by a balance between vertical advection into the control volume by Ekman pumping and eddy transfer across the density surfaces achieved by diapycnal eddy fluxes, with small-scale mixing making only a minor contribution. Possible oceanographic implications of the results are discussed.
Abstract
The dynamics of a warm lens created by a surface buoyancy flux and Ekman pumping in an initially homogeneous, unbounded fluid on a β plane is studied in a set of high-resolution numerical experiments. A simple analytical model for the equilibrium structure of the lens is developed that assumes that the input of vorticity and buoyancy from the Ekman layer is balanced through transfer by baroclinic eddies that carry the warm fluid laterally away from the lens. The importance of eddy-induced diapycnal flux in the western intensification region is emphasized by developing a boundary layer theory based entirely on the cross-frontal mass exchange due to eddies. The theory is successfully tested against direct numerical eddy-resolving simulations. Possible oceanographic implications of the study for understanding subtropical gyres and the Antarctic Circumpolar Current are discussed.
Abstract
The dynamics of a warm lens created by a surface buoyancy flux and Ekman pumping in an initially homogeneous, unbounded fluid on a β plane is studied in a set of high-resolution numerical experiments. A simple analytical model for the equilibrium structure of the lens is developed that assumes that the input of vorticity and buoyancy from the Ekman layer is balanced through transfer by baroclinic eddies that carry the warm fluid laterally away from the lens. The importance of eddy-induced diapycnal flux in the western intensification region is emphasized by developing a boundary layer theory based entirely on the cross-frontal mass exchange due to eddies. The theory is successfully tested against direct numerical eddy-resolving simulations. Possible oceanographic implications of the study for understanding subtropical gyres and the Antarctic Circumpolar Current are discussed.
Abstract
A model for the vertical structure of ocean gyres is presented that extends the ideal thermocline theories of Rhines and Young and Luyten et al. to include a cross-layer volume flux associated with geostrophic eddy transfer. A two-and-one-half-layer model is considered that assumes that the intensity of the eddy transfer depends on the local strength of the current. The ideal thermocline models emerge in the limit where the parameter characterizing the cross-layer volume flux is asymptotically small. Inclusion of the eddy-induced volume flux resolves the nonuniqueness of the Sverdrup dynamics in the unventilated pool attached to the western boundary layer. In the ventilated region, solutions of the model equations converge to their ideal counterparts. The circulation is closed explicitly by developing a western boundary layer theory based entirely on the effects of the cross-isopycnal volume flux due to eddies. Unlike most models of western intensification, the leaky boundary layer here is active, and its dynamics are essential for determining the structure of the interior field.
Abstract
A model for the vertical structure of ocean gyres is presented that extends the ideal thermocline theories of Rhines and Young and Luyten et al. to include a cross-layer volume flux associated with geostrophic eddy transfer. A two-and-one-half-layer model is considered that assumes that the intensity of the eddy transfer depends on the local strength of the current. The ideal thermocline models emerge in the limit where the parameter characterizing the cross-layer volume flux is asymptotically small. Inclusion of the eddy-induced volume flux resolves the nonuniqueness of the Sverdrup dynamics in the unventilated pool attached to the western boundary layer. In the ventilated region, solutions of the model equations converge to their ideal counterparts. The circulation is closed explicitly by developing a western boundary layer theory based entirely on the effects of the cross-isopycnal volume flux due to eddies. Unlike most models of western intensification, the leaky boundary layer here is active, and its dynamics are essential for determining the structure of the interior field.
Abstract
This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri < ¼) cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline rarely drops below ¼, whereas the observations of turbulent patches are common, the authors hypothesize that some turbulent mixing events can be attributed to the finescale instabilities associated with double-diffusive processes.
Abstract
This study examines dynamics of finescale instabilities in thermohaline–shear flows. It is shown that the presence of the background diapycnal temperature and salinity fluxes due to double diffusion has a destabilizing effect on the basic current. Using linear stability analysis based on the Floquet theory for the sinusoidal basic velocity profile, the authors demonstrate that the well-known Richardson number criterion (Ri < ¼) cannot be directly applied to doubly diffusive fluids. Rigorous instabilities are predicted to occur for Richardson numbers as high as—or even exceeding—unity. The inferences from the linear theory are supported by the fully nonlinear numerical simulations. Since the Richardson number in the main thermocline rarely drops below ¼, whereas the observations of turbulent patches are common, the authors hypothesize that some turbulent mixing events can be attributed to the finescale instabilities associated with double-diffusive processes.
