A numerical study of the adjustment of a narrow stratified current over a sloping bottom

The adjustment of a narrow, stratified, cyclonic along-isobath current over a uniformly sloping bottom and the coupling between the current and the bo ttom boundary layer that develops beneath are investigated using a primitiv e-equation numerical model. The current generates a bottom Ekman layer imme diately downstream of its origin, with downslope transport everywhere benea th the current, carrying lighter water under heavier water to produce a ver tically well-mixed bottom boundary layer. At the top of the boundary layer, Ekman suction on the shallow side and pumping on the deep side lead to den sity advection in the vertical, tilted interior isopycnals, and thermal-win d shear of the interior along-isobath velocity. Flow above the bottom bound ary layer is nearly perfectly geostrophic and along isopycnals. Buoyancy ad vection in the bottom boundary layer continues to cause growth of the bound ary layer downstream, with subsequent reduction in bottom stress, until the flow reaches a steady downstream equilibrium beyond which only gradual cha nges occur as a result of viscosity and mixing. The numerical results are compared with the idealized model of this adjustm ent process previously proposed by Chapman and Lentz. The same basic dynami cs dominate, and some of the scales and parameter dependencies predicted by the idealized model apply to the numerical results. For example, the dista nce to the downstream equilibrium decreases with increasing buoyancy freque ncy and/or bottom slope, and the equilibrium structure is nearly independen t of the bottom friction coefficient. The equilibrium bottom boundary layer thickness and the interior along-isobath velocity just above the boundary layer closely obey the idealized model scales; that is, the boundary layer thickness decreases with increasing buoyancy frequency and is independent o f bottom slope, and the overlying current decreases while its width increas es as either the buoyancy frequency or bottom slope decreases. However, the interior vertical shear in the numerical model tends to decouple the overl ying current from the bottom boundary layer, so the structure of the bottom boundary layer in the downstream equilibrium is different from the idealiz ed model, and neither the current width nor the surface currents are as sen sitive to parameter variations as the idealized model suggests. Finally, th e along-isobath current is not geostrophic near the bottom of the bottom bo undary layer. as assumed in the idealized model, so the bottom boundary lay er is not fully arrested, that is, bottom stress never quite vanishes downs tream, suggesting that a completely frictionless downstream equilibrium is unlikely to be achieved.