Boundary intensification of vertical velocity in a β-plane basin

The buoyancy-driven circulation of simple two-layer models on the beta plane is studied in order to examine the role of beta in determining the magnitude and structure of the vertical motions forced in response to surface heating and cooling. Both analytical and numerical approaches are used to describe the change in circulation pattern and strength as a consequence of the planetary vorticity gradient. The physics is quasigeostrophic at lowest order but is sensitive to small nonquasigeostrophic mass fluxes across the boundary of the basin. The height of the interface between the two layers serves as an analog of temperature, and the vertical velocity at the interface consists of a cross-isopycnal velocity, modeled in terms of a relaxation to a prescribed interface height, as well as an adiabatic representation of eddy thickness fluxes parameterized as lateral diffusion of interface displacement. In the numerical model the lateral eddy diffusion of heat is explicitly represented by a resolved eddy field. In the plausibly more realistic case, when the lateral diffusion of buoyancy dominates the diffusion of momentum, the major vertical velocities occur at the boundary of the basin as in earlier f-plane studies. The effect of the planetary vorticity gradient is to intensify the sinking at the western wall and to enhance the magnitude of that sinking with respect to the f-plane models. The vertical mass flux in the Sverdrup interior exactly balances the vertical flux in the region of the strong horizontal transport of the western boundary current, leaving the net flux to occur in a very narrow region near the western boundary tucked well within the western boundary current. On the other hand, if the lateral diffusion of heat is arbitrarily and unrealistically eliminated, the vertical mass flux is forced to occur in the interior. The circulation pattern is extremely sensitive to small net inflows or outflows across the basin perimeter. The cross-basin flux determines the interface height on the basin's eastern boundary and affects the circulation pattern across the entire basin.