Instabilities of Gravity Currents along a Slope

Abstract

This work examines the linear stability of rotationally influenced density currents with zero potential vorticity flowing over a sloping seafloor at the base of an ocean of finite depth. This configuration serves as a crude model of a type of current that is common in the ocean. The normal modes of the jet are classified according to the physical process primarily responsible for the mode in the limit of long alongjet wavelengths. Several classes of unstable normal mode are found. The theory of resonant instabilities provides a simple explanation of the origin of these instabilities and allows one to identify the physical mechanisms primarily responsible for the instabilities. In addition to previously recognized instabilities, two new types of instability that rely on the presence of topography are found. The first, which is relatively weak, arises as a result of a resonance between gravity waves on the jet and topographic Rossby waves. The second is more powerful, occurs at relatively long wavelengths, and is brought about by resonance between a vortical wave on the jet and topographic Rossby waves.