James Stephens

J. C. Stephens, 1997, Technical Report WHOI-97-10, Summer Program in Geophysical Fluid Dynamics, Woods Hole, MA 02543, USA.

Abstract

Gravity currents are important for transporting heat, salt and momentum in oceanic, atmospheric and other environments. The Denmark Straits overflow, for example, in the North Atlantic transports significant quantities of cold water equatorward, whilst the Mediterranean Undercurrent is an important source of heat and salt in the eastern North Atlantic. On a smaller scale, gravity currents may be observed in lakes if the deformation radius is small enough that they feel the Earth’s rotation.

A study of a two-fronted current on a slope in a one layer reduced gravity system was considered by Griffiths et al. (1982). They discovered that a zero potential vorticity current was unstable to linearised perturbations over a finite range of wavenumbers. The instabilities take the form of normal modes that couple the free streamlines of the current and extract both kinetic and potential energy from the flow. In the long wavelength limit, these become sinuous modes.

Here we extend the study conducted by Griffiths et al. to a two layer system. It is found that the presence of the upper layer in combination with the slope serves to modify the shear instability and stabilises the flow to long wavelength perturbations.

The contents of this manuscript have been incorporated into the above paper “Instabilities Of Gravity Currents Along a Slope”, which contains a more complete discussion of such instabilities.