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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
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
The factors controlling the transport of the Antarctic Circumpolar Current (ACC) have recently been a topic of heated debate. At the latitudes of Drake Passage, potential vorticity contours are uninterrupted by coastlines, and large amplitude flows are possible even with weak forcing and dissipation. The relationship between the dynamics of circumpolar currents and inertial recirculations in closed basins is discussed. In previous studies, Sverdrup balance and baroclinic adjustment theories have both been proposed as theories of the ACC transport. These theories predict the circumpolar transport as various simple functions of the surface wind stress. A series of experiments is performed with a simple channel model, with different wind strengths and different idealized basin geometries, to investigate the relationship between wind strength and circumpolar transport. The results show that baroclinic adjustment theories do predict transport in the special case of a periodic channel with no topographic variations, or when the wind forcing is very weak. More generally, the transport is determined by a complex interplay between wind forcing, eddy fluxes, and topographic effects. There is no support for the idea that Sverdrup balance determines the transport through Drake Passage.
Abstract
The factors controlling the transport of the Antarctic Circumpolar Current (ACC) have recently been a topic of heated debate. At the latitudes of Drake Passage, potential vorticity contours are uninterrupted by coastlines, and large amplitude flows are possible even with weak forcing and dissipation. The relationship between the dynamics of circumpolar currents and inertial recirculations in closed basins is discussed. In previous studies, Sverdrup balance and baroclinic adjustment theories have both been proposed as theories of the ACC transport. These theories predict the circumpolar transport as various simple functions of the surface wind stress. A series of experiments is performed with a simple channel model, with different wind strengths and different idealized basin geometries, to investigate the relationship between wind strength and circumpolar transport. The results show that baroclinic adjustment theories do predict transport in the special case of a periodic channel with no topographic variations, or when the wind forcing is very weak. More generally, the transport is determined by a complex interplay between wind forcing, eddy fluxes, and topographic effects. There is no support for the idea that Sverdrup balance determines the transport through Drake Passage.
Abstract
The classical problem of flow past a cylinder is revisited in the context of understanding two oceanographic phenomena: separation of the Gulf Stream from the North American coastline at Cape Hatteras and the interaction of the Antarctic Circumpolar Current with topographic obstacles. Numerical solutions are presented for eastward, barotropic flow past a cylinder in a β-plane channel. The solutions are dependent on two nondimensional parameters: the Reynolds number, Re, and a nondimensional β parameter,
Abstract
The classical problem of flow past a cylinder is revisited in the context of understanding two oceanographic phenomena: separation of the Gulf Stream from the North American coastline at Cape Hatteras and the interaction of the Antarctic Circumpolar Current with topographic obstacles. Numerical solutions are presented for eastward, barotropic flow past a cylinder in a β-plane channel. The solutions are dependent on two nondimensional parameters: the Reynolds number, Re, and a nondimensional β parameter,
Abstract
Abstract
Abstract
The response of the upper, warm limb of the thermohaline circulation in the North Atlantic to a rapid change in deep-water formation at high latitudes is investigated using a reduced-gravity ocean model. Changes in deep-water formation rate initiate Kelvin waves that propagate along the western boundary to the equator on a timescale of months. The response in the North Atlantic is therefore rapid. The Southern Hemisphere response is much slower, limited by a mechanism here termed the &ldquo=uatorial buffer.” Since to leading order the flow is in geostrophic balance, the pressure anomaly decreases in magnitude as the Kelvin wave moves equatorward, where the Coriolis parameter is lower. Together with the lack of sustained pressure gradients along the eastern boundary, this limits the size of the pressure field response in the Southern Hemisphere. Interior adjustment is by the westward propagation of Rossby waves, but only a small fraction of the change in thermohaline circulation strength is communicated across the equator to the South Atlantic at any one time, introducing a much longer timescale into the system.
A new quantitative theory is developed to explain this long-timescale adjustment. The theory relates the westward propagation of thermocline depth anomalies to the net meridional transport and leads to a “delay equation” in a single parameter—the thermocline depth on the eastern boundary—from which the time-varying circulation in the entire basin can be calculated. The theory agrees favorably with the numerical results. Implications for predictability, abrupt climate change, and the monitoring of thermohaline variability are discussed.
Abstract
The response of the upper, warm limb of the thermohaline circulation in the North Atlantic to a rapid change in deep-water formation at high latitudes is investigated using a reduced-gravity ocean model. Changes in deep-water formation rate initiate Kelvin waves that propagate along the western boundary to the equator on a timescale of months. The response in the North Atlantic is therefore rapid. The Southern Hemisphere response is much slower, limited by a mechanism here termed the &ldquo=uatorial buffer.” Since to leading order the flow is in geostrophic balance, the pressure anomaly decreases in magnitude as the Kelvin wave moves equatorward, where the Coriolis parameter is lower. Together with the lack of sustained pressure gradients along the eastern boundary, this limits the size of the pressure field response in the Southern Hemisphere. Interior adjustment is by the westward propagation of Rossby waves, but only a small fraction of the change in thermohaline circulation strength is communicated across the equator to the South Atlantic at any one time, introducing a much longer timescale into the system.
A new quantitative theory is developed to explain this long-timescale adjustment. The theory relates the westward propagation of thermocline depth anomalies to the net meridional transport and leads to a “delay equation” in a single parameter—the thermocline depth on the eastern boundary—from which the time-varying circulation in the entire basin can be calculated. The theory agrees favorably with the numerical results. Implications for predictability, abrupt climate change, and the monitoring of thermohaline variability are discussed.
Abstract
Downstream of Drake Passage, the Antarctic Circumpolar Current (ACC) veers abruptly northward along the continental slope of South America. This spins down the ACC, akin to the western boundary currents of ocean gyres. During this northward excursion, the mean potential vorticity (PV) increases dramatically (decreases in magnitude) by up to a factor of 2 along mean geostrophic streamlines on middepth buoyancy surfaces. This increase is driven by drag near the continental slope, or by breaking eddies further offshore, and is balanced by a remarkably steady, eddy-driven decrease of mean PV along these northern circumpolar streamlines in the open ocean. We show how two related eddy processes that are fundamental to ACC dynamics—poleward buoyancy fluxes and downward fluxes of eastward momentum—are also concomitant with materially forcing PV to increase on the northern flank of a jet at middepth, and decrease on the southern flank. For eddies to drive the required mean PV decrease along northern streamlines, the ACC merges with the subtropical gyres to the north, so these streamlines inhabit the southern flanks of the combined ACC–gyre jets. We support these ideas by analyzing the time-mean PV and its budget along time-mean geostrophic streamlines in the Southern Ocean State Estimate. Our averaging formalism is Eulerian, to match the model’s numerics. The thickness-weighted average is preferable, but its PV budget cannot be balanced using Eulerian 5-day averaged diagnostics, primarily because the z-level buoyancy and continuity equations’ delicate balances are destroyed upon transformation into the buoyancy-coordinate thickness equation.
Significance Statement
The Antarctic Circumpolar Current is the world’s largest ocean current and a key controller of Earth’s climate. As the westerly winds that drive this current shift poleward under global warming, it is vital to know whether the current will follow. To begin addressing this, we study the current’s fundamental dynamics, and constraints, under present-day conditions. By analyzing angular momentum and stratification together, we show that the current is weakened near boundaries and strengthened by eddies elsewhere. The strengthening effects of eddies are isolated to the current by merging the current with oceanic gyres to the north. This gives a new perspective on why the current travels so far northward alongside South America, and may provide dynamical constraints on future changes.
Abstract
Downstream of Drake Passage, the Antarctic Circumpolar Current (ACC) veers abruptly northward along the continental slope of South America. This spins down the ACC, akin to the western boundary currents of ocean gyres. During this northward excursion, the mean potential vorticity (PV) increases dramatically (decreases in magnitude) by up to a factor of 2 along mean geostrophic streamlines on middepth buoyancy surfaces. This increase is driven by drag near the continental slope, or by breaking eddies further offshore, and is balanced by a remarkably steady, eddy-driven decrease of mean PV along these northern circumpolar streamlines in the open ocean. We show how two related eddy processes that are fundamental to ACC dynamics—poleward buoyancy fluxes and downward fluxes of eastward momentum—are also concomitant with materially forcing PV to increase on the northern flank of a jet at middepth, and decrease on the southern flank. For eddies to drive the required mean PV decrease along northern streamlines, the ACC merges with the subtropical gyres to the north, so these streamlines inhabit the southern flanks of the combined ACC–gyre jets. We support these ideas by analyzing the time-mean PV and its budget along time-mean geostrophic streamlines in the Southern Ocean State Estimate. Our averaging formalism is Eulerian, to match the model’s numerics. The thickness-weighted average is preferable, but its PV budget cannot be balanced using Eulerian 5-day averaged diagnostics, primarily because the z-level buoyancy and continuity equations’ delicate balances are destroyed upon transformation into the buoyancy-coordinate thickness equation.
Significance Statement
The Antarctic Circumpolar Current is the world’s largest ocean current and a key controller of Earth’s climate. As the westerly winds that drive this current shift poleward under global warming, it is vital to know whether the current will follow. To begin addressing this, we study the current’s fundamental dynamics, and constraints, under present-day conditions. By analyzing angular momentum and stratification together, we show that the current is weakened near boundaries and strengthened by eddies elsewhere. The strengthening effects of eddies are isolated to the current by merging the current with oceanic gyres to the north. This gives a new perspective on why the current travels so far northward alongside South America, and may provide dynamical constraints on future changes.
Abstract
Closing a gyre with a western boundary current imposes a constraint on its vertical structure that requires there to be no net vertical flux of potential vorticity through any closed pressure contour in steady state. This constraint resembles the traditional similarity balance for the internal thermocline, with additional terms representing friction in the western boundary current and convection in the mixed layer. The terms in the integral constraint are diagnosed in a planetary geostrophic ocean model and are used to understand the coexistence of ventilated and internal thermoclines within the subtropical gyre.
Abstract
Closing a gyre with a western boundary current imposes a constraint on its vertical structure that requires there to be no net vertical flux of potential vorticity through any closed pressure contour in steady state. This constraint resembles the traditional similarity balance for the internal thermocline, with additional terms representing friction in the western boundary current and convection in the mixed layer. The terms in the integral constraint are diagnosed in a planetary geostrophic ocean model and are used to understand the coexistence of ventilated and internal thermoclines within the subtropical gyre.
