An Implicit Formula for Boundary Current Separation

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Abstract
Boundary layer separation occurs in classical fluids when the boundary layer is decelerated by an adverse pressure gradient. Here a “separation formula” is derived for downstream variations in the velocity, or pressure, of an ocean boundary current. The formula is implicit in the sense that it requires an a priori knowledge of the path of the streamlines. Three contributing processes are identified: the β effect, vortex stretching, and changes in streamline curvature. The β effect acts always to accelerate western boundary currents but to decelerate eastern boundary currents, the former consistent with continued attachment but the latter consistent with separation. Vortex stretching acts to decelerate anticyclonic slope currents but to accelerate cyclonic slope currents, destabilizing the former but stabilizing the latter. Finally, for coastline curvature to induce separation of a boundary current, it must overcome the stabilizing influences of the β effect and/or vortex stretching. Scaling analysis indicates that the condition for separation for a western boundary current from a vertical sidewall is

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