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David P. Marshall

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.

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David P. Marshall and Laure Zanna

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.

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Xiaoming Zhai and David P. Marshall

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.

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David R. Munday and David P. Marshall

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.

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Maarten H. P. Ambaum and David P. Marshall

Abstract

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.

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Claire E. Tansley and David P. Marshall

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.

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Helen L. Johnson and David P. Marshall

Abstract

There is a wide range of evidence from both models and palaeoclimatic data that indicates the possibility of abrupt changes in the oceanic meridional overturning circulation (MOC). However, much of our dynamical understanding of the MOC comes from steady-state models that rely upon the assumption of thermodynamic equilibrium and are therefore only valid on millennial time scales. Here a dynamical model for the global teleconnections of MOC anomalies on annual to multidecadal time scales is developed. It is based on a linear theory for the propagation of zonally integrated meridional transport anomalies in a reduced-gravity ocean and allows for multiple ocean basins connected by a circumpolar channel to the south. The theory demonstrates that the equator acts as a low-pass filter to MOC anomalies. As a consequence, MOC anomalies on decadal and shorter time scales are confined to the hemispheric basin in which they are generated and have little impact on the remainder of the global ocean. The linear theory is compared with the results of a global nonlinear numerical integration, which it reproduces to a good approximation.

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David P. Marshall and Helen R. Pillar

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.

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David P. Marshall and Claire E. Tansley

Abstract

Boundary layer separation occurs in classical fluids when the boundary layer is decelerated by an adverse pressure gradient. Here a “separation formula” is derived for downstream variations in the velocity, or pressure, of an ocean boundary current. The formula is implicit in the sense that it requires an a priori knowledge of the path of the streamlines. Three contributing processes are identified: the β effect, vortex stretching, and changes in streamline curvature. The β effect acts always to accelerate western boundary currents but to decelerate eastern boundary currents, the former consistent with continued attachment but the latter consistent with separation. Vortex stretching acts to decelerate anticyclonic slope currents but to accelerate cyclonic slope currents, destabilizing the former but stabilizing the latter. Finally, for coastline curvature to induce separation of a boundary current, it must overcome the stabilizing influences of the β effect and/or vortex stretching. Scaling analysis indicates that the condition for separation for a western boundary current from a vertical sidewall is
i1520-0485-31-6-1633-eq1
where r is the radius of curvature of the coastline, U is the speed of the boundary current, and β* is the gradient of the Coriolis parameter in the downstream direction.
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David P. Marshall and Helen L. Johnson

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.

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