TIME-DEPENDENT DOUBLE DIFFUSION IN A STABLY STRATIFIED FLUID UNDER LATERAL HEATING

Abstract

A numerical study is made of double diffusive convection in a rectangle. The fluid is initially at rest with a pre-existing stably stratified solutal gradient. The motion is initiated by abruptly raising the temperature at one vertical sidewall. Comprehensive and systematically-organized numerical solutions to the full, Navier-Stokes equations under the Boussinesq fluid assumption have been acquired. Far-reaching analyses are made of the numerical results over a wide range of the solutal Rayleigh numbers R(s) using the thermal Rayleigh number, R(t) = 10(7). Elaborate plots displaying the details of the evolutions of the flow, temperature and solutal fields in the cavity are presented. The vertical profiles of the velocity, temperature, solute, and the local Nusselt number are constructed, delineating the influence of solutal buoyancy effect relative to the thermal effect. The behaviour of the details of the computed flow characteristics is in good qualitative agreement with the available experimental visualizations. The categorization of the basic character of the flow into the supercritical (Ra > Ra(c)) and subcritical regimes (Ra < Ra(c)), which is based on experimental observations, is satisfactorily verified by the numerical results. The present numerical simulations are also supportive of the prior observations, which illustrated the qualitative difference in the time-dependent patterns of the formation of the layered structure in the supercritical and subcritical regimes. By assessing the present numerical results, the previous estimate of the value of Ra(c) congruent-to 1.5 x 10(4) is found to be reasonably accurate.