On thermohaline convection with linear gradients

Abstract

The thermohaline stability problem previously treated by Stern, Walin and Veronis is examined in greater detail. An error in an earlier paper is corrected and some new calculations made. It is shown, for instance, that direct convection can occur for thermal Rayleigh number R much less than 100 Rs when Rs [gsim ] 0·1, where Rs is the salinity Rayleigh number. A graphical presentation is devised to show the relative importance of the different terms in the equations of motion as a function of R and Rs. The most unstable mode over all wave-numbers for each R, Rs is found and it is shown that where both unstable direct and oscillating modes are present, the most unstable mode is direct in most cases.