A reduced-gravity model of the abyssal circulation with Newtonian cooling and horizontal diffusion

Steady abyssal circulation is investigated with a simple reduced-gravity model where horizontal diffusion of interfacial displacement is taken into account in addition to ordinary vertical diffusion of Newtonian cooling. The horizontal diffusion and viscosity turn out to change the structure of boundary layers and the field of vertical velocity both on ƒ- and β-planes. The dynamics of western boundary layers is classified into the viscous and diffusive regimes. In either regime, horizontal diffusion dominates the distribution of vertical velocity. Downwelling prevails in the western offshore boundary current flowing equatorward, while upwelling is always found in the poleward current. A more intense, opposite vertical motion occurs in a narrower boundary layer horizontal diffusion again plays a crucial role in determining both horizontal and vertical velocities. The present model explains this downwelling in terms of the diffusion of the thickness term in potential vorticity. It is shown that only when the horizontal diffusion is incorporated is the reduced-gravity model capable of reproducing the complicated distribution of vertical velocity in the abyssal layer which has been repeatedly reported in various three-dimensional experiments. The present model is also applicable to the surface layer, extending the Sverdrup-Stommel-Munk theory of the homogeneous ocean to that more suitable for the stratified ocean.