ALBERT

Description: The role of baroclinic eddies in transferring thermal gradients laterally, and thus determining the stratification of the ocean, is examined. The hypothesis is that the density differences imposed at the surface by differential heating are a source of available potential energy that can be partially released by mesocale eddies with horizontal scales on the order of 100 km. Eddy fluxes balance the diapycnal mixing of heat and thus determine the vertical scale of penetration of horizontal thermal gradients (i.e., the depth of the thermocline). This conjecture is in contrast with the current thinking that the deep stratification is determined by a balance between diapycnal mixing and the large-scale thermohaline circulation. Eddy processes are analyzed in the context of a rapidly rotating primitive equation flow driven by specified surface temperature, with isotropic diffusion and viscosity. The barotropic component of the eddies is found to be responsible for most of the heat flux, and so the eddy transport is horizontal rather than isopycnal. This eddy transport takes place in the shallow surface layer where eddies, as well as the mean temperature, undergo diabatic, irreversible mixing. Scaling laws for the depth of the thermocline as a function of the external parameters are proposed. In the classical thermocline theory, the depth of the thermocline depends on the diffusivity, the rotation rate, and the imposed temperature gradient. In this study the authors find an additional dependence on the viscosity and on the domain width.

Description: A parameterization for eddy buoyancy fluxes for use in coarse-grid models is developed and tested against eddy-resolving simulations. The development is based on the assumption that the eddies are adiabatic (except near the surface) and the observation that the flux of buoyancy is affected by barotropic, depth-independent eddies. Like the previous parameterizations of Gent and McWilliams (GM) and Visbeck et al. (VMHS), the horizontal flux of a tracer is proportional to the local large-scale horizontal gradient of the tracer through a transfer coefficient assumed to be given by the product of a typical eddy velocity scale and a typical mixing length. The proposed parameterization differs from GM and VMHS in the selection of the eddy velocity scale, which is based on the kinetic energy balance of baroclinic eddies. The three parameterizations are compared to eddy-resolving computations in a variety of forcing configurations and for several sets of parameters. The VMHS and the energy balance parameterizations perform best in the tests considered here.

Description: The adiabatic pole-to-pole cell of the residual overturning circulation (ROC) is studied in a two-hemisphere, semienclosed basin, with a zonally reentrant channel occupying the southernmost eighth of the domain. Three different models of increasing complexity are used: a simple, analytically tractable zonally averaged model; a coarse-resolution numerical model with parameterized eddies; and an eddy-resolving general circulation model. Two elements are found to be necessary for the existence of an adiabatic pole-to-pole cell: 1) a thermally indirect, wind-driven overturning circulation in the zonally reentrant channel, analogous to the Deacon cell in the Antarctic Circumpolar Current (ACC) region, and 2) a set of outcropping isopycnals shared between the channel and the semienclosed region of the Northern Hemisphere. These points are supported by several computations varying the domain geometry, the surface buoyancy distribution, and the wind forcing. All three models give results that are qualitatively very similar, indicating that the two requirements above are general and robust. The zonally averaged model parameterizes the streamfunction associated with adiabatic buoyancy fluxes as downgradient diffusion of buoyancy thickness, with a diffusivity in the semienclosed region of the Northern Hemisphere much larger than that in the ACC region. In the simple model, the disparity in diffusivities is necessary to obtain a substantial pole-to-pole ROC. The simple model also illustrates how the geometry of the isopycnals is shaped by the interhemispheric ROC, leading to three major thermostads, which the authors identify with the major water masses of the Atlantic: that is, North Atlantic Deep Water, Antarctic Intermediate Water, and Antarctic Bottom Water.

Description: It is demonstrated that eddy fluxes of buoyancy at the eastern and western boundaries maintain alongshore buoyancy gradients along the coast. Eddy fluxes arise near the eastern and western boundaries because on both coasts buoyancy gradients normal to the boundary are strong. The eddy fluxes are accompanied by mean vertical flows that take place in narrow boundary layers next to the coast where the geostrophic constraint is broken. These ageostrophic cells have a velocity component normal to the coast that balances the geostrophic mean velocity. It is shown that the dynamics in these thin ageostrophic boundary layers can be replaced by effective boundary conditions for the interior flow, relating the eddy flux of buoyancy at the seaward edge of the boundary layers to the buoyancy gradient along the coast. These effective boundary conditions are applied to a model of the thermocline linearized around a mean stratification and a state of rest. The linear model parameterizes the eddy fluxes of buoyancy as isopycnal diffusion. The linear model produces horizontal gradients of buoyancy along the eastern coast on a vertical scale that depends on both the vertical diffusivity and the eddy diffusivity. The buoyancy field of the linear model agrees very well with the mean state of an eddy-resolving computation. Because the east–west difference in buoyancy is related to the zonally integrated meridional velocity, the linear model successfully predicts the meridional overturning circulation.

Description: A model of the thermocline linearized around a specified stratification and the barotropic linear wind-driven Stommel solution is constructed. The forcings are both mechanical (the surface wind stress) and thermodynamical (the surface buoyancy boundary condition). The effects of diapycnal diffusivity and of eddy fluxes of buoyancy, parameterized in terms of the large-scale buoyancy gradient, are included. The eddy fluxes of buoyancy are especially important near the boundaries where they mediate the transport in and out of the narrow ageostrophic down-/upwelling layers. The dynamics of these narrow layers can be replaced by effective boundary conditions on the geostrophically balanced flow. The effective boundary conditions state that the residual flow normal to the effective coast vanishes. The separate Eulerian and eddy-induced components may be nonzero. This formulation conserves the total mass and the total buoyancy while permitting an exchange between the Eulerian and eddy transport of buoyancy within the down-/upwelling layers. In turn, this exchange allows buoyancy gradients along all solid boundaries, including the eastern one. A special focus is on the buoyancy along the eastern and western walls since east–west buoyancy difference determines the meridional overturning circulation. The inclusion of advection of buoyancy by the barotropic flow allows a meaningful distinction between the meridional and the residual overturning circulations while retaining the simplicity of a linear model. The residual flow in both meridional and zonal directions reveals how the subsurface buoyancy distribution is established and, in particular, how the meridional buoyancy gradient is reversed at depth. In turn, the horizontal buoyancy gradient maintains stacked counterrotating cells in the meridional and residual overturning circulations. Quantitative scaling arguments are given for each of these cells, which show how the buoyancy forcing, the wind stress, and the diapycnal and eddy diffusivities, as well as the other imposed parameters, affect the strength of the overturn.

Description: The processes maintaining stratification in the oceanic middepth (between approximately 1000 and 3000 m) are explored using an eddy-resolving general circulation model composed of a two-hemisphere, semienclosed basin with a zonal reentrant channel in the southernmost eighth of the domain. The middepth region lies below the wind-driven main thermocline but above the diffusively driven abyssal ocean. Here, it is argued that middepth stratification is determined primarily in the model’s Antarctic Circumpolar Current. Competition between mean and eddy overturning in the channel leads to steeper isotherms and thus deeper stratification throughout the basin than would exist without the channel. Isotherms that outcrop only in the channel are nearly horizontal in the semienclosed portion of the domain, whereas isotherms that also outcrop in the Northern Hemisphere deviate from horizontal and are accompanied by geostrophically balanced meridional transport. A northern source of deep water (water with temperatures in the range of those in the channel) leads to the formation of a thick middepth thermostad. Changes in wind forcing over the channel influence the stratification throughout the domain. Since the middepth stratification is controlled by adiabatic dynamics in the channel, it becomes independent of the interior diffusivity κ as κ → 0. The meridional overturning circulation (MOC), as diagnosed by the mean meridional volume transport, also shows a tendency to become independent of κ as κ → 0, whereas the MOC diagnosed by water mass transport shows a continuing dependence on κ as κ → 0. A nonlocal scaling for MOC is developed that relates the strength of the northern MOC to the depth of isotherms in the southern channel. The results of this paper compare favorably to observations of large-scale neutral density in the World Ocean.