Eddy-driven buoyancy gradients on eastern boundaries

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 {\sl 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 parametrizes 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.