Finite amplitude convection in a two-component fluid saturated porous layer

Abstract

The linear and non-linear stability of convection of a two-component fluid known as thermohaline convection is considered in a horizontal porous layer heated from below. The analysis is based on the Boussinesq-Darcy equations for 2-dim. convection under the assumption that the amplitudes of convection are small. The linear theory is based on the Fourier analysis and the critical Rayleigh numbers for both marginal and overstable motions are determined. It is found that a vertical solute gradient sets up overstable motions and a physical reason for this is given. The finite amplitude study is based on a truncated representation of Fourier series and the critical Rayleigh number is determined. The effects of Prandtl number, ratio of diffusivities and the permeability parameter on convection are studied. Nusselt number, Nu, and its analog Nu^s for solute are calculated and it is found that the effect of Prandtl number is very weak in contrast to the existing viscous flow results.