Abstract
The stability of an infinite horizontal layer of fluid with a density stratification due to both temperature and solute gradients, subject to an initial vertical flow field, is studied for different sets of homogeneous boundary conditions. Sufficient conditions for the maintenance of the original stratification, i.e., for stability, are obtained as a relation between R aT , the thermal Rayleigh number, and R as , the solute Rayleigh number. The relation R as R aT <-( P s P T ) is obtained as a sufficient condition for stability for all sets of boundary conditions, where P T and P S are the thermal and solute Prandtl number, respectively. This condition may thus be applied to cases in which the physical boundary conditions are not well defined; e.g., to practical engineering use of solar ponds. In addition, in conjunction with a similar result for initial horizontal flow fields, the result gives a sufficient condition for stability of arbitrary initial flows under all combinations of boundary conditions.
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