On the cooling of a buoyant boundary current

Through a steady-state reduced-gravity model, we examine the downstream evolution of a buoyant boundary current as it is subjected to surface cooling. It is found that the adverse pressure gradient associated with the diminishing buoyancy is countered by falling pressure head, so the overall strength of the current—as measured by the (transport-weighted) mean square velocity—remains unchanged. This constancy also applies to the cross-stream difference of the square velocity because of the vorticity constraint, which leads to the general deduction that the net current shear is enhanced regardless of its upstream sign. As a consequence, if the upstream flow contains near-shore and offshore branches that are comparable in strength, this parity would persist downstream; but if the near-shore branch is weaker to begin with, it may be stagnated by cooling, with the ensuing generation of anti-cyclonic eddies. On account of the geostrophic balance, the buoyant layer narrows as the square root of the buoyancy—the same rate as the falling pressure head, but more rapid than that of the local deformation radius. Some of the model predictions are compared with observations from the Tsushima Current in the Japan/East Sea.