NONLINEAR STABILITY PROBLEM OF A ROTATING DOUBLY DIFFUSIVE POROUS LAYER

Lyapunov direct method is applied to study the non-linear conditional stability problem of a rotating doubly diffusive convection in a sparsely packed porous layer. For a Darcy number greater than or equal to 1000, and for any Prandtl number, Taylor number, and solute Rayleigh number it is found that the non-linear stability bound coincides with linear instability bound. For a Darcy number less than 1000, for a Prandtl number greater than or equal to one, and for a certain range of Taylor number, a coincidence between the linear and nonlinear (energy) stability thermal Rayleigh number values is still maintained. However, it is noted that for a Darcy number less than 1000, as the value of the solute Rayleigh number or the Taylor number increases, the coincidence domain between the two theories decreases quickly. (C) 1995 Academic Press, Inc.