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A. J. George Nurser

Abstract

Fronts are ubiquitous in the ocean. Recent work by Dewar has considered the formation of oceanic fronts in a simple layered model.

In this contribution, the position and structure of similar fronts within a coupled mixed layer-thermocline model are studied. A subtropical gyre is considered. The mixed layer is chosen to be warm and light along the southern boundary of this gyre but cooler and denser to the east and north. This contrast in mixed layer properties drives the formation of a front within the southern flank of the subtropical gyre. For the model dynamics require the mixed layer to be deeper where it is dense and shallower where it is less dense. The more rapid northward Ekman drift due to the concentration of the Ekman transport within the thinner mixed layer to the south tries to override the weaker drift associated with the thicker mixed layer to the north. There are sharp jumps in mixed layer thickness and isopycnal depths over this front. It also carries substantial transports. This front is of particular interest because it is a site of anomalously strong subduction driven by the buoyancy yielded up by the northward Ekman drift as it moves across the front into cooler, denser waters.

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A. J. George Nurser

Abstract

The subtropical recirculation regions are considered as examples of nonlinear free flow—“baroclinic Fofonoff gyres.” In the interior, where relative vorticity may be neglected, the quad-geostrophic assumption may be relaxed, and the layered treatment extended to a continuously stratified model. The implied density field is compared with observations.

The deformation of the inertial gyre caused by the presence of an anticyclonic wind stress curl is then considered. In addition to the recirculating “free” component of the flow along latitude circles, there is a meridional component whose depth-integrated transport is set by the magnitude of the imposed wind stress curl. It is found that the “bowl” within which the recirculation is contained deepens towards the north and west, and exhibits the “champagne glass“ structure found in the quasi-geostrophic eddy-resolving numerical models.

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Mei-Man Lee and A. J. George Nurser

Abstract

Subduction—the transport of fluid across the base of mixed layer—exchanges water masses and tracers between the ocean surface and interior. Eddies can affect subduction in a variety of ways. First, eddies shoal the mixed layer by restratifying water columns through baroclinic instabilities. Second, eddies induce an isopycnic transport that leads to the entrainment of warm waters and subduction of cold waters, which effectively counters the wind-driven overturning circulation. In this study, the authors use an idealized model to examine these two mechanisms by which eddies influence subduction and to discuss how eddy subduction may be better approximated using the concept of vertical transport streamfunction than the conventional meridional transport streamfunction.

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A. J. George Nurser and Mei-Man Lee

Abstract

In , the “vertical” transport streamfunction was defined as resulting from isopycnic averaging at constant height in the same way that the meridional streamfunction results from averaging at constant latitude. Part II here discusses the relationship between these two isopycnic streamfunctions and the Eulerian residual streamfunction that arises from the transformed Eulerian mean (TEM). It is known that the meridional isopycnic streamfunction can be approximated by a Taylor expansion to give an Eulerian residual streamfunction involving the horizontal eddy flux. This Taylor expansion approximation works well in the interior, removing the spurious mixing associated with the simple Eulerian-averaged streamfunction. However, it fails near the surface where isopycnals outcrop to the surface. It can be shown in a similar way that the vertical isopycnic streamfunction can formally be approximated by a residual streamfunction involving the vertical eddy flux. However, if horizontal isopycnal displacements are large, this approximation fails even in the ocean interior. Inspired by the two different residual streamfunctions, a more general form of TEM formulation is explored. It is shown that the different TEM residual streamfunctions arise from decomposing the eddy flux into a component along isopycnals, which leads to advective flow, and a remaining diffusive component, which is oriented either vertically or horizontally. In theory the diffusive flux can be oriented in any direction, although in practice the orientation should be such that neither the advective flow nor the diffusive flux cross any boundary (surface, sidewalls, and bottom). However, it is not clear how to merge the continuously changing orientation in a physically meaningful way. A variety of approaches are discussed.

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Harry L. Bryden and A. J. George Nurser

Abstract

The density distribution in the abyssal Atlantic Ocean suggests that mixing associated with overflows across deep sills may account for substantial amounts of deep mixing. Estimates of the strait mixing are made from published estimates of the overflows and the difference between Antarctic Bottom Water densities across the Vema Channel and the Romanche Fracture Zone to demonstrate that the strait mixing is an order of magnitude larger than the abyssal mixing estimated for a standard diffusivity of 1 × 10–4 m2 s–1.

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A. J. George Nurser and John C. Marshall

Abstract

The transport of mass between a mixed layer, exposed to mechanical and thermodynamic forcing, and an adiabatic thermocline is studied for gyre-scale motions. It is shown that if the mixed layer can be represented by a vertically homogeneous layer, whose base velocity and potential density are continuous, then, at any instant, the rate at which fluid is subducted per unit area of the sloping mixed-layer base, S, is given bywhere h is the depth of the mixed layer, Qb = −fρ̄−1∂ρ/∂z|zh is th large-scale potential vorticity is the base, ℋnet is the heat input per unit area less that which warms the Ekman drift, αE, Cw, and ρ̄ are the volume expansion coefficient, heat capacity, and mean density of water, respectively. It is assumed that the mixed layer is convectively controlled and much deeper than the layer directly stirred by the wind. The field of S is studied in a steady thermocline model in which patterns of Ekman pumping and diabatic heating drive flow to and from a mixed layer overlying a stratified thermocline.

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John C. Marshall and A. J. George Nurser

Abstract

A continuously stratified, steady thermocline model is formulated in which a mixed layer of variable depth and density overlies a stratified thermocline. Rather than prescribe the distribution of density and vertical velocity at the top of the permanent themocline, we explicitly represent the dynamics of the vertically homogeneous layer layer that overlies it; the density distribution at the sea surface, the depth of the mixed layer, and the structure of the thermocline are all found for prescribed patterns of Ekman pumping and surface buoyancy fluxes. If the potential vorticity of the thermocline is assumed to have a uniform value on isopycnal surfaces, it is shown that the problem can be reduced to one of finding the distribution of a single scalar field, the mixed-layer density, by the method of characteristics. Given this field and knowledge of the potential vorticity distribution in the thermocline, all other variables of the model can be found. The resulting model seems ideally suited to the study of the interaction of a mixed layer with a stratified thermocline, since it explicitly represents the lateral geostrophic flow through the sloping base of the mixed layer.

Idealized solutions are presented for both subtropical and subtrophical and in which, in response to patterns of wind and diabatic forcing, isopycnals outcrop into a mixed layer of variable thickness and density. The effect of both warming and cooling of the mixed layer on the structure of the gyre is investigated.

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A. J. George Nurser and Mei-Man Lee

Abstract

Simple Eulerian averaging of velocities, density, and tracers at constant position is the most natural way of averaging. However, Eulerian averaging gives incorrect watermass distributions and properties as well as spurious diabatic circulations such as the Deacon cell. Instead of averaging at constant height, averaging along isopycnals removes such fictitious mixing and diabatic circulations. Such isopycnal averaging is normally performed at constant latitude, that is, averaging along isopynals as they heave up and down. As a result, height information is lost and the sea surface becomes much warmer (or lighter) than with simple Eulerian averaging. In fact, averaging can be performed along arbitrarily aligned surfaces. This study considers a particular case in which isopycnal averaging is performed at constant height. Thus, this new isopycnal averaging follows isopycnals as they meander horizontally at constant z. Height information is now retained at the cost of losing latitudinal information. The advantage of this averaging is that it avoids the problem of giving a surface that is too warm. Associated with this new isopycnal averaging, a “vertical” transport streamfunction in (ρ, z) space can be defined, in analogy to the conventional meridional overturning streamfunction in (y, ρ) space. Here in Part I, this constant-height isopycnal averaging is explained and illustrated in an idealized zonal channel model. In Part II the relationship between the two different isopycnal averagings and the Eulerian mean eddy flux divergence is explored.

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A. J. George Nurser and Richard G. Williams

Abstract

The effect of cooling on the separated boundary current predicted by the model of Parsons is studied. The separating current is found to strengthen and to move southwards and eastwards. The model is also robust to limited heating. in which case the separating current weakens and moves northwards.

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A. J. George Nurser and Stephen M. Griffies

Abstract

We detail the physical means whereby boundary transfers of freshwater and salt induce diffusive fluxes of salinity. Our considerations focus on the kinematic balance between the diffusive fluxes of salt and freshwater, with this balance imposed by mass conservation for an element of seawater. The flux balance leads to a specific balanced form for the diffusive salt flux immediately below the ocean surface and, in the Boussinesq approximation, to a specific form for the salinity flux. This balanced form should be used in specifying the surface boundary condition for the salinity equation and the contribution of freshwater to the buoyancy budget.

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