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Abstract
A new framework for understanding the vertical structure of ocean gyres is developed based on vertical fluxes of potential vorticity. The key ingredient is an integral constraint that in a steady state prohibits a net flux of potential vorticity through any closed contour of Bernoulli potential or density. Applied to an ocean gyre, the vertical fluxes of potential vorticity associated with advection, friction, and buoyancy forcing must therefore balance in an integral sense.
In an anticyclonic subtropical gyre, the advective and frictional potential vorticity fluxes are both directed downward, and buoyancy forcing is required to provide the compensating upward potential vorticity flux. Three regimes are identified: 1) a surface “ventilated thermocline” in which the upward potential vorticity flux is provided by buoyancy forcing within the surface mixed layer, 2) a region of weak stratification—“mode water”—in which all three components of the potential vorticity flux become vanishingly small, and 3) an “internal boundary layer thermocline” at the base of the gyre where the upward potential vorticity flux is provided by the diapycnal mixing. Within a cyclonic subpolar gyre, the advective and frictional potential vorticity fluxes are directed upward and downward, respectively, and are thus able to balance without buoyancy forcing.
Geostrophic eddies provide an additional vertical potential vorticity flux associated with slumping of isopycnals in baroclinic instability. Incorporating the eddy potential vorticity flux into the integral constraint provides insights into the role of eddies in maintaining the Antarctic Circumpolar Current and convective chimneys. The possible impact of eddies on the vertical structure of a wind-driven gyre is discussed.
Abstract
A new framework for understanding the vertical structure of ocean gyres is developed based on vertical fluxes of potential vorticity. The key ingredient is an integral constraint that in a steady state prohibits a net flux of potential vorticity through any closed contour of Bernoulli potential or density. Applied to an ocean gyre, the vertical fluxes of potential vorticity associated with advection, friction, and buoyancy forcing must therefore balance in an integral sense.
In an anticyclonic subtropical gyre, the advective and frictional potential vorticity fluxes are both directed downward, and buoyancy forcing is required to provide the compensating upward potential vorticity flux. Three regimes are identified: 1) a surface “ventilated thermocline” in which the upward potential vorticity flux is provided by buoyancy forcing within the surface mixed layer, 2) a region of weak stratification—“mode water”—in which all three components of the potential vorticity flux become vanishingly small, and 3) an “internal boundary layer thermocline” at the base of the gyre where the upward potential vorticity flux is provided by the diapycnal mixing. Within a cyclonic subpolar gyre, the advective and frictional potential vorticity fluxes are directed upward and downward, respectively, and are thus able to balance without buoyancy forcing.
Geostrophic eddies provide an additional vertical potential vorticity flux associated with slumping of isopycnals in baroclinic instability. Incorporating the eddy potential vorticity flux into the integral constraint provides insights into the role of eddies in maintaining the Antarctic Circumpolar Current and convective chimneys. The possible impact of eddies on the vertical structure of a wind-driven gyre is discussed.
Abstract
The problem of western boundary current separation is investigated using a barotropic vorticity model. Specifically, a boundary current flowing poleward along a boundary containing a cape is considered. The meridional gradient of the Coriolis parameter (the β effect), the strength of dissipation, and the geometry of the cape are varied. It is found that 1) all instances of flow separation are coincident with the presence of a flow deceleration, 2) an increase in the strength of the β effect is able to suppress flow separation, and 3) increasing coastline curvature can overcome the suppressive β effect and induce separation. These results are supported by integrated vorticity budgets, which attribute the acceleration of the boundary current to the β effect and changes in flow curvature. The transition to unsteady final model states is found to have no effect upon the qualitative nature of these conclusions.
Abstract
The problem of western boundary current separation is investigated using a barotropic vorticity model. Specifically, a boundary current flowing poleward along a boundary containing a cape is considered. The meridional gradient of the Coriolis parameter (the β effect), the strength of dissipation, and the geometry of the cape are varied. It is found that 1) all instances of flow separation are coincident with the presence of a flow deceleration, 2) an increase in the strength of the β effect is able to suppress flow separation, and 3) increasing coastline curvature can overcome the suppressive β effect and induce separation. These results are supported by integrated vorticity budgets, which attribute the acceleration of the boundary current to the β effect and changes in flow curvature. The transition to unsteady final model states is found to have no effect upon the qualitative nature of these conclusions.
Abstract
A conceptual model of ocean heat uptake is developed as a multilayer generalization of Gnanadesikan. The roles of Southern Ocean Ekman and eddy transports, North Atlantic Deep Water (NADW) formation, and diapycnal mixing in controlling ocean stratification and transient heat uptake are investigated under climate change scenarios, including imposed surface warming, increased Southern Ocean wind forcing, with or without eddy compensation, and weakened meridional overturning circulation (MOC) induced by reduced NADW formation. With realistic profiles of diapycnal mixing, ocean heat uptake is dominated by Southern Ocean Ekman transport and its long-term adjustment controlled by the Southern Ocean eddy transport. The time scale of adjustment setting the rate of ocean heat uptake increases with depth. For scenarios with increased Southern Ocean wind forcing or weakened MOC, deepened stratification results in enhanced ocean heat uptake. In each of these experiments, the role of diapycnal mixing in setting ocean stratification and heat uptake is secondary. Conversely, in experiments with enhanced diapycnal mixing as employed in “upwelling diffusion” slab models, the contributions of diapycnal mixing and Southern Ocean Ekman transport to the net heat uptake are comparable, but the stratification extends unrealistically to the sea floor. The simple model is applied to interpret the output of an Earth system model, the Second Generation Canadian Earth System Model (CanESM2), in which the atmospheric CO2 concentration is increased by 1% yr−1 until quadrupling, where it is found that Southern Ocean Ekman transport is essential to reproduce the magnitude and vertical profile of ocean heat uptake.
Abstract
A conceptual model of ocean heat uptake is developed as a multilayer generalization of Gnanadesikan. The roles of Southern Ocean Ekman and eddy transports, North Atlantic Deep Water (NADW) formation, and diapycnal mixing in controlling ocean stratification and transient heat uptake are investigated under climate change scenarios, including imposed surface warming, increased Southern Ocean wind forcing, with or without eddy compensation, and weakened meridional overturning circulation (MOC) induced by reduced NADW formation. With realistic profiles of diapycnal mixing, ocean heat uptake is dominated by Southern Ocean Ekman transport and its long-term adjustment controlled by the Southern Ocean eddy transport. The time scale of adjustment setting the rate of ocean heat uptake increases with depth. For scenarios with increased Southern Ocean wind forcing or weakened MOC, deepened stratification results in enhanced ocean heat uptake. In each of these experiments, the role of diapycnal mixing in setting ocean stratification and heat uptake is secondary. Conversely, in experiments with enhanced diapycnal mixing as employed in “upwelling diffusion” slab models, the contributions of diapycnal mixing and Southern Ocean Ekman transport to the net heat uptake are comparable, but the stratification extends unrealistically to the sea floor. The simple model is applied to interpret the output of an Earth system model, the Second Generation Canadian Earth System Model (CanESM2), in which the atmospheric CO2 concentration is increased by 1% yr−1 until quadrupling, where it is found that Southern Ocean Ekman transport is essential to reproduce the magnitude and vertical profile of ocean heat uptake.
Abstract
The presence of intense recirculations in the abyssal oceans has been revealed by both observations and modeling studies. A suggested mechanism is the interactions between geostrophic eddies and the mean circulation in the presence of variable bottom topography. Here such interactions are studied using an idealized numerical model, consisting of a single active abyssal layer overlying variable bottom topography. An initial ensemble of eddies quickly organize themselves to generate a mean anticyclonic circulation around seamounts. During this rearrangement energy is approximately conserved while potential enstrophy is dissipated, consistent with previous studies of geostrophic turbulence.
A parameterization of geostrophic eddies is formulated in terms of an eddy-induced transport, U*. Based on results from the eddy-resolving experiments it is hypothesized that U* should dissipate potential enstrophy while conserving energy. Using variational methods, a solution for U* is found that dissipates potential enstrophy most efficiently, subject to energy being conserved. For a shallow water layer, it is shown that U* = κ[ ∇ (Q 2/2) + λ ∇ B], where Q is the potential vorticity, B is the Bernoulli potential, κ(x, y) is an arbitrary function that describes the efficiency with which eddies can rearrange fluid within a layer, and λ is a Lagrange multiplier that is determined through the energetic constraint. Results from a coarse resolution version of the model using the parameterization compare favorably with those obtained using the eddy-resolving model.
Abstract
The presence of intense recirculations in the abyssal oceans has been revealed by both observations and modeling studies. A suggested mechanism is the interactions between geostrophic eddies and the mean circulation in the presence of variable bottom topography. Here such interactions are studied using an idealized numerical model, consisting of a single active abyssal layer overlying variable bottom topography. An initial ensemble of eddies quickly organize themselves to generate a mean anticyclonic circulation around seamounts. During this rearrangement energy is approximately conserved while potential enstrophy is dissipated, consistent with previous studies of geostrophic turbulence.
A parameterization of geostrophic eddies is formulated in terms of an eddy-induced transport, U*. Based on results from the eddy-resolving experiments it is hypothesized that U* should dissipate potential enstrophy while conserving energy. Using variational methods, a solution for U* is found that dissipates potential enstrophy most efficiently, subject to energy being conserved. For a shallow water layer, it is shown that U* = κ[ ∇ (Q 2/2) + λ ∇ B], where Q is the potential vorticity, B is the Bernoulli potential, κ(x, y) is an arbitrary function that describes the efficiency with which eddies can rearrange fluid within a layer, and λ is a Lagrange multiplier that is determined through the energetic constraint. Results from a coarse resolution version of the model using the parameterization compare favorably with those obtained using the eddy-resolving model.
Abstract
A reduced-gravity planetary-geostrophic model of the North Atlantic consisting of two active layers overlying a motionless abyss is developed to investigate the effect of the wind field in shaping the dynamics of the Mediterranean salinity tongue. The model is driven by climatological winds and eastern boundary ventilation in a basin of realistic geometry and includes a parameterization of meddies.
The upper-layer depth from the model shows a clear similarity to observations, both in terms of the location and intensity of the subtropical gyre and also the position of the outcropping line in the northern basin. Potential vorticity in layer two reproduces the sweep of potential-vorticity contours southwestward from the eastern boundary and extending westward into the interior, and provides the pathways along which Mediterranean Water spreads into the model interior.
The authors solve for the steady salinity field in the second layer, including sources of Upper Labrador Sea Water and Antarctic Intermediate Water on the isopycnal surface. The shape and spreading latitude of the model salinity tongues bear a striking resemblance to observations. Both the wind forcing and the occurrence of a mean transport of Mediterranean Water away from the eastern boundary are crucial in obtaining a realistic salinity tongue. The salinity tongues are remarkably stable to variations in the Peclet number.
A simple parameterization of meddies in the model is also included. Where meddies are dissipated locally by collisions with topographic seamounts, for example, they may generate large recirculations extending across to the western boundary. The net effect of these recirculations is to shift the salinity tongue equatorward.
Abstract
A reduced-gravity planetary-geostrophic model of the North Atlantic consisting of two active layers overlying a motionless abyss is developed to investigate the effect of the wind field in shaping the dynamics of the Mediterranean salinity tongue. The model is driven by climatological winds and eastern boundary ventilation in a basin of realistic geometry and includes a parameterization of meddies.
The upper-layer depth from the model shows a clear similarity to observations, both in terms of the location and intensity of the subtropical gyre and also the position of the outcropping line in the northern basin. Potential vorticity in layer two reproduces the sweep of potential-vorticity contours southwestward from the eastern boundary and extending westward into the interior, and provides the pathways along which Mediterranean Water spreads into the model interior.
The authors solve for the steady salinity field in the second layer, including sources of Upper Labrador Sea Water and Antarctic Intermediate Water on the isopycnal surface. The shape and spreading latitude of the model salinity tongues bear a striking resemblance to observations. Both the wind forcing and the occurrence of a mean transport of Mediterranean Water away from the eastern boundary are crucial in obtaining a realistic salinity tongue. The salinity tongues are remarkably stable to variations in the Peclet number.
A simple parameterization of meddies in the model is also included. Where meddies are dissipated locally by collisions with topographic seamounts, for example, they may generate large recirculations extending across to the western boundary. The net effect of these recirculations is to shift the salinity tongue equatorward.
Abstract
A reduced-gravity model is developed to represent the flow of Antarctic Bottom Water (AABW) over realistic bathymetry in an Atlantic domain. The dynamics are based on the steady, planetary–geostrophic, shallow-water equations, including a linear bottom friction and a uniform diapycnal upwelling through the top of the model layer.
The model solutions are broadly consistent with observations of the distribution and transport of AABW. The flows occur predominantly along potential vorticity contours, which are in turn broadly oriented along bathymetric contours. The characteristic weak flow across potential vorticity contours of the Stommel–Arons model is present as a small addition to this stronger forced mode along potential vorticity contours. As a consequence, mass balance is maintained not by hypothesized western boundary currents as in the Stommel–Arons model, but by the interplay between topographic slope currents and interior recirculations. In particular, a transposition is found in the flow of AABW from the western side of the Brazil Basin south of the equator to the western flank of the Mid-Atlantic Ridge north of the equator. This is also consistent with an analytical result derived by extending the Parsons mechanism to an abyssal layer overlying arbitrary bathymetry. The authors suggest that the results provide a more convincing zero-order picture than the Stommel–Arons model for the circulation of AABW and perhaps for abyssal water masses in general.
Abstract
A reduced-gravity model is developed to represent the flow of Antarctic Bottom Water (AABW) over realistic bathymetry in an Atlantic domain. The dynamics are based on the steady, planetary–geostrophic, shallow-water equations, including a linear bottom friction and a uniform diapycnal upwelling through the top of the model layer.
The model solutions are broadly consistent with observations of the distribution and transport of AABW. The flows occur predominantly along potential vorticity contours, which are in turn broadly oriented along bathymetric contours. The characteristic weak flow across potential vorticity contours of the Stommel–Arons model is present as a small addition to this stronger forced mode along potential vorticity contours. As a consequence, mass balance is maintained not by hypothesized western boundary currents as in the Stommel–Arons model, but by the interplay between topographic slope currents and interior recirculations. In particular, a transposition is found in the flow of AABW from the western side of the Brazil Basin south of the equator to the western flank of the Mid-Atlantic Ridge north of the equator. This is also consistent with an analytical result derived by extending the Parsons mechanism to an abyssal layer overlying arbitrary bathymetry. The authors suggest that the results provide a more convincing zero-order picture than the Stommel–Arons model for the circulation of AABW and perhaps for abyssal water masses in general.
Abstract
Abstract
Abstract
Eddy energy generation and energy fluxes are examined in a realistic eddy-resolving model of the North Atlantic. Over 80% of the wind energy input is found to be released by the generation of eddies through baroclinic instability. The eddy energy generation is located near the surface in the subtropical gyre but deeper down in the subpolar gyre. To reconcile the mismatch between the depth of eddy energy production and the vertical structure of the horizontal dispersion of eddy energy, the vertical eddy energy flux is downward in the subtropical gyre and upward in the subpolar gyre.
Abstract
Eddy energy generation and energy fluxes are examined in a realistic eddy-resolving model of the North Atlantic. Over 80% of the wind energy input is found to be released by the generation of eddies through baroclinic instability. The eddy energy generation is located near the surface in the subtropical gyre but deeper down in the subpolar gyre. To reconcile the mismatch between the depth of eddy energy production and the vertical structure of the horizontal dispersion of eddy energy, the vertical eddy energy flux is downward in the subtropical gyre and upward in the subpolar gyre.
Abstract
Motivated by the adjustment of the meridional overturning circulation to localized forcing, solutions are presented from a reduced-gravity model for the propagation of waves along western and eastern boundaries. For wave periods exceeding a few months, Kelvin waves play no role. Instead, propagation occurs through short and long Rossby waves at the western and eastern boundaries, respectively: these Rossby waves propagate zonally, as predicted by classical theory, and cyclonically along the basin boundaries to satisfy the no-normal flow boundary condition. The along-boundary propagation speed is cL d /δ, where c is the internal gravity/Kelvin wave speed, L d is the Rossby deformation radius, and δ is the appropriate frictional boundary layer width. This result holds across a wide range of parameter regimes, with either linear friction or lateral viscosity and a no-slip boundary condition. For parameters typical of contemporary ocean climate models, the propagation speed is coincidentally close to the Kelvin wave speed. In the limit of weak dissipation, the western boundary wave dissipates virtually all of its energy as it propagates toward the equator, independent of the dissipation coefficient. In contrast, virtually no energy is dissipated in the eastern boundary wave. The importance of background mean flows is also discussed.
Abstract
Motivated by the adjustment of the meridional overturning circulation to localized forcing, solutions are presented from a reduced-gravity model for the propagation of waves along western and eastern boundaries. For wave periods exceeding a few months, Kelvin waves play no role. Instead, propagation occurs through short and long Rossby waves at the western and eastern boundaries, respectively: these Rossby waves propagate zonally, as predicted by classical theory, and cyclonically along the basin boundaries to satisfy the no-normal flow boundary condition. The along-boundary propagation speed is cL d /δ, where c is the internal gravity/Kelvin wave speed, L d is the Rossby deformation radius, and δ is the appropriate frictional boundary layer width. This result holds across a wide range of parameter regimes, with either linear friction or lateral viscosity and a no-slip boundary condition. For parameters typical of contemporary ocean climate models, the propagation speed is coincidentally close to the Kelvin wave speed. In the limit of weak dissipation, the western boundary wave dissipates virtually all of its energy as it propagates toward the equator, independent of the dissipation coefficient. In contrast, virtually no energy is dissipated in the eastern boundary wave. The importance of background mean flows is also discussed.
Abstract
When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed.
Abstract
When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a “rotational force” in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed.
