Convection in a rotating cavity

Abstract

Many large scale flows in the ocean are driven by an imposed longitudinal density gradient and the resulting buoyancy-driven flow is both influenced by the Earth's rotation and has a low aspect ratio (i.e. the characteristic vertical scale of the motion is small compared to the characteristic horizontal scale of the motion). The essential features of such flows were incorporated into a laboratory model, by differentially heating and cooling the vertical end walls of a low aspect ratio, rectangular cavity rotating about a vertical axis through its centre. When heating and cooling were initiated at the respective vertical end walls of the cavity, a hot current formed along the surface and a cold current along the bottom. These moved out from each end wall into the interior of the tank, but were confined to the sidewalls (model coastlines) by the effects of rotation. Initially the currents propagated under a balance between buoyancy and inertial forces, with an unstable balance between buoyancy and Coriolis forces in the cross-stream direction. Drag forces eventually slowed the the propagation speeds. The currents were internally stratified in temperature, and became unstable as a result of a rotationally dominated instability, driven by both the potential energy associated with the temperature difference between the currents and the isothermal environment and the velocity shear across the current. The flows were analogous to buoyancy driven coastal currents such as the East Greenland Current, the Norwegian Coastal Current and the Leeuwin Current off Western Australia. As an experiment progressed, the instabilities on the currents grew and broke to produce eddies which eventually filled the cavity. The timescales for development of the stratification within the cavity were found to be dependent on the end wall temperatures, but independent of rotation. In its statistically steady state the mean circulation consisted of baroclinic boundary currents superimposed on two basin-scale counter-rotating gyres and a nearly linear vertical temperature gradient. These observations can be explained in terms of potential vorticity dynamics in the presence of a relative slope between isopotential surfaces and horizontal boundaries. Measurements of the potential vorticity were made in the laboratory flow and the quantity proved to be a very effective dynamical tracer. The steady state flow may have interesting implications for the large scale circulation of the oceans.