VORTEX INSTABILITY OF FREE CONVECTION BOUNDARY LAYERS IN POROUS MEDIA

We consider the vortex instability of an inclined free convection boundary layer which is formed ad-jacent to an impermeable heated surface that is em-bedded in a porous medium. Many authors have adopted boundary layer theory as the framework within which the stability of this flow is considered. Neutral curves have been obtained showing how the critical distance from the leading edge varies with the wavenumber of the vortex disturbance. However it is now well-known that such critical distances are too close to the leading edge for the boundary layer approximation to be either valid or accurate. The only exception is when the heated surface is almost vertical but upward-facing. In that case even nonlinear vortices may be studied, but oth-erwise it is essential that the fully elliptic governing equations are solved, and this latter case forms the topic of the present paper. On assuming the validity of Darcy’s law and the Boussinesq approximation, the momentum equations are written in velocity potential form, and the result-ing system, which includes the heat transport equa-tion, is transformed into parabolic coordinates in or-der to mimic the shape of the spatially-developing boundary layer. These equations are solved using a combination of finite difference approximations and a spanwise Fourier expansion. It is found that the vortex instability is not an absolute instability because growing disturbances travel downstream faster than they diffuse upstream. However, a steady vortex system may be generated by adopting a suitable boundary condition which in-duces such a pattern. Our computational results are compared with a parabolic simulation which is valid in the near-vertical limit, and the comparison is ex-cellent