Eastern-Boundary Contribution to the Residual and Meridional Overturning Circulations

Abstract

Abstract 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.