Stability transition of a solute-stratified fluid in a vertical slot imposed with a horizontal temperature gradient

Abstract

When a stable solute-stratified fluid in a vertical slot is imposed with a horizontal temperature gradient, it becomes double-diffusively unstable when the critical condition is exceeded. We conduct a comprehensive three-dimensional stability analysis to investigate the double-diffusive stability with emphasis on the effects of the Prandtl number Pr and the Lewis number Le. The results show that the stability is characterized by five stability modes and seven transitions at which the mode changes from one to another. The occurrence of stability modes and transitions largely depends upon Pr and Le. An extensive comparison between the present results and those of previous analytical and experimental studies is made. The comparison confirms that the present results are in excellent agreement with the asymptotic solutions proposed by Thorpe et al. [J. Fluid Mech. 38, 375–400 (1969)] and Kerr and Tang [J. Fluid Mech. 392, 213–232 (1999)]. It explains why most of the observed flows were predominated by salt-finger convection.