The effect of rotation on double-diffusive interleaving

Abstract

In this paper we investigate the effect of vertical rotation on the linear stability of an unbounded region of vertically stratified fluid, which has compensating horizontal temperature and salinity gradients, so there is no overall horizontal density gradient. We find the most unstable perturbations for given linear vertical and horizontal gradients and show how the addition of rotation affects the results found for the non-rotating case by Holyer (1983), using molecular diffusivities. By using a transformation that, for the non-oscillatory instability, links the rotating case to the non-rotating case we show that the growth rate, the across-front slope and the wavenumber of the intrusion with the maximum growth rate is unchanged. The basic difference between the non-rotating and the rotating case, for the non-oscillatory instability, is that in the rotating case the interleaving layers slope both along and perpendicular to the direction of the horizontal temperature and salinity gradients and not just along them. The oscillatory instability has no simple transformation between the rotating and the non-rotating cases, and the addition of rotation changes the growth rate and the wavenumber of the instabilities.