An implicit formula for boundary current separation

Boundary layer separation occurs in classical fluids when the boundary laye r is decelerated by an adverse pressure gradient. Here a "separation formul a'' is derived for downstream variations in the velocity, or pressure, of a n ocean boundary current. The formula is implicit in the sense that it requ ires an a priori knowledge of the path of the streamlines. Three contributi ng processes are identified: the beta effect, vortex stretching, and change s in streamline curvature. The beta effect acts always to accelerate wester n boundary currents but to decelerate eastern boundary currents, the former consistent with continued attachment but the latter consistent with separa tion. Vortex stretching acts to decelerate anticyclonic slope currents but to accelerate cyclonic slope currents, destabilizing the former but stabili zing the latter. Finally, for coastline curvature to induce separation of a boundary current, it must overcome the stabilizing influences of the beta effect and/or vortex stretching. Scaling analysis indicates that the condit ion for separation for a western boundary current from a vertical sidewall is [GRAPHICS] where r is the radius of curvature of the coastline, U is the speed of the boundary current, and beta* is the gradient of the Coriolis parameter in th e downstream direction.