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David Marshall and John Marshall

Abstract

It is shown that subtle changes in the velocity profile across the seaward extension of midlatitude jets, such as the Gulf Stream, can lead to dramatic changes in the zonal-penetration scale. In particular, if α = dq/dψ > 0, where q is the absolute vorticity and ψ is a streamfunction for the geostrophic flow, then the jet tends to penetrate across to the eastern boundary; conversely if α < 0, the jet turns back on itself creating a tight recirculation on the scale of order |α|−frac12;. This behavior is demonstrated in a quasigeostrophic ocean model in which a jet profile is prescribed as an inflow condition at the western margin of a half-basin, and radiation conditions along the remainder of the western boundary allow the injected fluid to escape. Jet inflows with both vertical and horizontal structure are considered in one and one-half-, two-, and three-layer models.

Finally, the implications of our study for numerical simulations of ocean gyres, which frequently show sensitivity of jet penetration to horizontal and vertical resolution and to choice of boundary conditions, are discussed. In particular, it is demonstrated that poor resolution of the horizontal jet structure may lead to a dramatic reduction in penetration.

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David Marshall and John Marshall

Abstract

The thermodynamic processes attendant on the transfer of fluid between a surface mixed layer and a stratified thermocline beneath are discussed. For a parcel of fluid in the mixed layer to pass into the stratified thermocline—to subduct—it must be stratified by buoyancy input; this buoyancy can be supplied by local air–sea exchange and/or by lateral advective processes.

A series of experiments is described in which a mixed layer, coupled to an ideal-fluid thermocline, undergoes differing seasonal cycles: in one limit the mixed layer is held fixed in a steady, winter configuration; in the other the mixed layer is, more realistically, shallow over most of the year and deepens briefly in late winter. It is shown that the annual subduction rate S ann depends, to first order, only on late winter mixed layer properties. However the annual-mean air–sea buoyancy exchange is sensitive to the details of the seasonal cycle and becomes vanishingly small as the effective subduction period shortens. In this limit the buoyancy is provided through advective processes in the Ekman layer.

The authors conclude that in ocean models that do not explicitly represent a seasonal cycle it is necessary to parameterize the process through a prescription of the winter mixed layer density and depth. The buoyancy forcing diagnosed from such models must be interpreted as the combined contribution of the annual air–sea exchange and lateral advectivc processes in the summer Ekman layer.

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David Marshall

Abstract

Fofonoff solutions to the inviscid barotropic potential vorticity equation are found for the steady, free flow in a basin rotated at an arbitrary angle to a latitude circle. These solutions am used to study the inertial recirculation of the subtropical gyre, which is forced by anomalously low values of potential vorticity within the separated Gulf Stream. It is found, depending on the sense of rotation of the northern boundary relative to latitude circles, that closed potential vorticity contours can exist that allow a large-amplitude inertial response, a resonance of the Fofonoff gyre. A barotropic ocean model is used to confirm thew ideas, in which flow is forced both by potential vorticity anomalies prescribed at the boundaries, and also a field of Ekman pumping, which spins up an anticyclonic gyre. It is shown that the recirculation is sensitive to both the orientation and extension of the inertial jet along the northern boundary.

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David Marshall

Abstract

The influence of the bottom topography on the large-scale ocean circulation is discussed and illustrated with a simple model based on the ideal-fluid thermocline equations. The requirement that fluid remains in linear vorticity balance while conserving its density leads to a coupled problem, but one that can be reduced to a single characteristic equation under an assumption of uniform potential vorticity on density surfaces. The characteristics are intermediate between the f/H contours found in a homogeneous ocean and the f contours found in an ocean with a motionless abyss.

The extent to which topography influences the circulation in upper layers is quantified and is shown to depend on both the strength of the bottom currents and on the vertical profile of stratification. In a realistic limit, in which the abyssal waters are sluggish and weakly stratified, the circulation in surface layers is relatively indifferent to the topography beneath.

The direction in which a current deflects around a topographic obstacle of finite amplitude differs significantly from previous results for small amplitude obstacles. The path of the bottom streamlines is uniquely determined by the bottom density gradient upstream of the obstacle: if the topography shallows, then the abyssal streamlines deflect up the bottom density gradient; conversely if the topography deepens, then the abyssal streamlines deflect down the bottom density gradient. Streamlines for the depth-integrated flow follow a path determined by linear vorticity balance.

The model is generalized in study the interaction of a wind-driven gyre with a midocean ridge. Internal jets, embedded within the large-scale circulation, are found when the topography protrudes sufficiently into the main thermocline of the gyre.

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David Marshall

Abstract

An analytic model of the Antarctic Circumpolar Current (ACC) is presented in which information contained in a hydrographic section is propagated along characteristics. The characteristics are obtained by assuming that potential vorticity is uniform on density surfaces: they lie between the f/H contours found in a homogeneous ocean and the f contours found in a strongly stratified ocean. Solutions describe an inviscid, adiabatic circulation in which fluid parcels negotiate a variable bottom topography while conserving density and conserving potential vorticity.

A family of solutions are obtained for a realistic spherical geometry including coastlines and major topographic features. In the limit of weak bottom currents, the ACC transports 160 Sv (Sv ≡ 106 m3 s−1) of fluid around Antarctica, with circumpolar flow in the upper three kilometers and abyssal gyres bounded by the bottom topography. In the limit of large bottom currents, the ACC exhibits increased sensitivity to the topograph; streamlines resemble f/H contours and do not pass through the Drake Passage.

Arbitrary parameters in the purely inviscid and adiabatic solution, such as the potential vorticity distribution, the cross-stream surface density profile, and the strength of the abyssal currents, can be constrained through the study of integral balances of momentum and buoyancy. In particular, a balanced momentum budget for the ACC demands the existence of closed gyres within the abyssal layers. Integral constraints along time-mean streamlines also demonstrate the importance of transient eddies in the general maintenance of the current.

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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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Malcolm Roberts and David Marshall

Abstract

Use of horizontal diffusion of temperature and salinity in numerical ocean models causes spurious diapycnal transfers—the “Veronis effect”—leading to erosion of the thermocline and reduced poleward heat transports. The authors derive a relation between these diapycnal transfers and the dissipation of vorticity gradients. An increase in model resolution does not significantly reduce the diapycnal transfers since vorticity gradients cascade to smaller scales and must ultimately be dissipated to maintain numerical stability. This is confirmed in an idealized primitive equation ocean model at a variety of resolutions between 1° and 1/8°.

Thus, the authors conclude that adiabatic dissipation schemes are required, even in eddy-resolving ocean models. The authors propose and implement a new biharmonic form of the Gent and McWilliams scheme, which adiabatically dissipates at the grid scale while preserving larger-scale features.

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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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