Rayleigh-Jeffreys stability of thermohaline stratified fluids subject to arbitrary temperature and salinity gradients

Abstract

The stability of a horizontal layer of fluid of infinite extent and having a vertical density stratification due to arbitrary temperature and salinity gradients is studied for various sets of homogeneous boundary conditions. A sufficient condition for stability, i.e., for the maintenance of the original stratification is obtained in the form of a relation between the thermal Rayleigh number, Ra T and the solute Rayleigh number, Ra s . For no initial flow, the relation ▪ is obtained as a sufficient condition for all sets of boundary conditions, where P T and P s are the thermal and solute Prandtl numbers, respectively, and df T and df s are mean values of the gradients of the initial temperature and solute distributions. This condition is a natural modification of that previously obtained for the case of constant thermal and salinity gradients [1, 10, 16], namely ▪ The condition is applicable to situations in which the physical boundary conditions are not well-defined, e.g., in practical engineering development and operation of solar ponds.