Shocks in a coastal boundary current

Abstract

We studied shocks in a coastal boundary current with zero potential vorticity. By coastal boundary current, we mean a semigeostrophic light fluid flow over an infinitely deep dense fluid and along a coast on its right hand side, with its lower interface exposed to the ocean surface at some finite distance from the coast. The shocks are assumed to conserve mass and momentum. It is found that the shocks can be classified into two categories, “coastal shocks” and “frontal shocks”, by the signs of the upper layer flux relative to the shocks. Coastal shocks, for which the relative upper layer flux is negative, always propagate downstream. The upper layer at the coast is thicker on the upstream sides of coastal shocks than on the downstream sides. Frontal shocks, for which the relative upper layer flux is positive, propagate upstream as well as downstream. In most cases, the current is wider on the downstream sides of frontal shocks than on the upstream sides. However, under the circumstances that the current is nearly separated from the coast, the current is wider on the upstream sides of frontal shocks. Coastal and frontal shocks both dissipate energy of the current. We also demonstrate that special shocks with no light fluid on the downstream sides cannot exist irrespective of the potential vorticity distribution.