The effect of rotation on linear and non-linear double-diffusive convection in a sparsely packed, porous medium

Abstract

The linear and non-linear stability of rotating double-diffusive convection in a sparsely packed porous medium is investigated considering a non-Darcy equation. In the case of linear theory both marginal and overstable motions are discussed. In the former case it is shown that the effect of Taylor number and porous parameter is to make the system more stable. In the latter case, however, it is shown that the bottom-heavy solute gradient and rotation destabilize the system under certain conditions. By drawing the stability boundaries in the Rayleigh number plane it is shown that the effect of rotation and porous parameter is to decrease the region of instabilities. Using the theory of self-adjoint operator the variation of critical eigenvalue with physical and boundary parameters is studied. In the case of non-linear theory, both steady and unsteady cases have been considered. In the unsteady case the transient behaviour concerning the variation of Nusselt number with time has been investigated, by solving numerically a seventh-order Lorenz model using the Runge-Kutta-Gill method. Interesting results are obtained by comparing these results with those of the steady case. Finally, the effect of porous parameter on streamfunction, isotherms, isohalines and zonal velocity is studied.