The effect of rotation on double-diffusive convection in a laterally heated vertical slot

Abstract

The effect of rotation about a vertical axis on the linear stability of a salt-stratified fluid enclosed in a vertical slot when subjected to a temperature difference between the walls is investigated. It is found that for large salinity stratifications there are three distinct regimes of instability for different values of the rotation rate. For small rotation rates the convection cells resemble the thin, almost flat, convection cells predicted by non-rotating theory. The effect of the rotation is to marginally destabilize the fluid whilst inducing a small slope in the convection cells along the parallel walls. As the rotation rate is increased there is an abrupt change in the form of the most unstable convection cells as their aspect ratio and slope parallel to the walls both become of order one in magnitude. As the rotation rate is further increased there is a second less abrupt transition when the internal Rossby radius of deformation based on the vertical scale of the cells becomes of the same order of size as the slot width. After this point the slope of the cells increases in proportion to the rotation rate. The asymptotic nature of these three regimes is found.The effect of rotation on double-diffusive instabilities caused by more general horizontal temperature and salinity gradients in a salt-stratified fluid is also investigated, with particular reference to the case of heating the salinity gradient from a single sidewall. This analysis is restricted to the case where the rotation rate is low.