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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 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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Richard Wardle and John Marshall

Abstract

The parametric representation of buoyancy and momentum transport by baroclinic eddies in a primitive equation “β plane” channel is studied through a transformation of the governing equations. Adoption of the“transformed Eulerian mean” and the assumption that the eddies (but not the mean flow) are quasigeostrophic in nature leads to 1) the eddies being represented symbolically by one term, an eddy potential vorticity flux, rendering a representation that incorporates both eddy momentum and eddy buoyancy fluxes, and 2) the advecting velocities being those of the residual mean circulation. A closure is employed for the eddy potential vorticity flux that directs it down the mean potential vorticity gradient. Care is taken to ensure that the resulting force does not generate any net momentum in the channel but only acts to redistribute it.

The approach is investigated by comparing a zonally averaged parameterized model with a three-dimensional eddy-resolving calculation of flow in a stress-driven channel. The stress at the upper surface is communicated down the water column to the bottom by eddy form drag. Moreover, lateral eddy momentum fluxes act to strengthen and sharpen the mean flow, transporting eastward momentum from the flanks to the center of the jet, up its large-scale gradient. Both vertical momentum transfer and lateral, upgradient momentum transfer by eddies, is captured in the parameterized model.

Finally, advantages of the parametric approach are demonstrated in two further contexts: 1) the spindown of a baroclinic zone and 2) the maintenance of surface winds by eddy momentum flux in the atmosphere.

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Christophe Herbaut and John Marshall

Abstract

Idealized nonhydrostatic numerical calculations that resolve both plumes and geostrophic eddies are used to mimic isobaric float observations taken in the Labrador Sea Deep Convection Experiment and study mechanisms of buoyancy transport through mixed layers. The plumes and eddies are generated in a periodic channel, initialized with a vertical profile of temperature, and cooled by surface heat loss varying across the channel. Probability density functions and time series of vertical velocity and temperature computed from the floats are interpreted in terms of the kinematics of plumes and geostrophic eddies, and their role in buoyancy transport. Estimates from Eulerian time series from the numerical model suggest that geostrophic eddies and plumes have a comparable contribution to vertical heat flux.

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Timour Radko and John Marshall

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.

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Sonya Legg and John Marshall

Abstract

A point-vortex heton model of the lateral dispersion of cold water formed in open-ocean deep convection is developed and studied as an idealized representation of the sinking and spreading phase of open-ocean deep convection. The overturning and geostrophic adjustment of dense fluid on and below the radius of deformation scale, formed by cooling on the large-scale, are parameterized in the model by introducing paired. discrete point vortices (hetons) of cyclonic sense in the surface layer, anticyclonic below, driving a cold baroclinic vortex. The convection site is imagined to be made up of many such baroclinic vortices, each with a vertically homogeneous core carrying cold, convectively tainted waters. The point vortices are introduced at a rate that depends on the large-scale cooling and the intensity assumed for each vortex. The interaction of many cold baroclinic vortices, making up a cloud, is studied using point-vortex Green's function techniques. The current solenoids of the individual elements sum together to drive a large-scale rim current around the convection site, cyclonic above, anticyclonic below, which is associated with a baroclinic zone on a scale of the order of the ambient radius of deformation. For parameters typical of open-ocean deep convection, the cloud of point vortices breaks down baroclinically on a time scale of a few days, into Rossby radius-scale “clumps.” These extended hetons efficiently flux the cold water away laterally from the convection site and affect an inward transfer of heat sufficient to offset loss to the atmosphere.

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John Marshall and George Nurser

Abstract

No abstract available.

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John C. Marshall

Abstract

The combined problem of determining the ocean circulation and improving the geoid from satellite altimetry is formulated and studied. Minimum variance estimation is used to form optimum estimates of the ocean topography and the geoid. These estimates are a function of the altimeter observations, prior knowledge of the ocean circulation and prior knowledge of the geoid. Particular emphasis is placed on the use of a dynamical ocean model as a source of a priori oceanographic information capable of discriminating between geoid errors and ocean topography. The technique is illustrated in a simulation study of Gulf Stream variability, in which an ocean topography, degraded by noise representing the uncertainty in a gravimetric geoid, is reconstructed by assimilation into an ocean model. At the same time an improved estimate of the geoid is made.

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Jason Goodman and John Marshall

Abstract

An analytical model of the mutual interaction of the middle-latitude atmosphere and ocean is formulated and studied. The model is found to support coupled modes in which oceanic baroclinic Rossby waves of decadal period grow through positive coupled feedback between the thermal forcing of the atmosphere induced by SST anomalies and the resulting wind stress forcing of the ocean. Growth only occurs if the atmospheric response to thermal forcing is equivalent barotropic, with a particular phase relationship with the underlying SST anomalies. The dependence of the growth rate and structure of the modes on the nature of the assumed physics of air–sea interaction is explored, and their possible relation to observed phenomena discussed.

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John C. Marshall

Abstract

An attempt is made to incorporate into a two-layer, zonally averaged, channel ocean model the important transfers achieved by a geostrophic eddy field, using gross parameterizations rather than resolving individual eddy events. It is shown that a representation of the eddy field as an explicit diffuser of potential vorticity can give a reasonable description of the interaction between the eddies and mean flow, provided care is taken to satisfy the attendant constraints that the zonally invariant channel geometry imposes on the eddy fields.

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