The linear vortex instability of flow induced by a horizontal heated surface in a porous medium

A linearized vortex instability theory for convection induced by a semi-infinite horizontal heated surface embedded in a fluid-saturated porous medium is developed. Due to the inadequacies of existing parallel-flow theories the problem has been re-examined using asymptotic techniques that use the distance downstream of the leading edge of the surface as the large parameter. The parallel-flow theories predict that at each downstream location there are two possible vortex wavenumbers which lead to neutrally stable modes. It is demonstrated how one of these disturbances is only weakly dependent on non-parallel terms, whereas the second mode is crucially dependent upon the non-parallelism within the flow. Consequently, this second mode cannot be described by any quasi-parallel approach and its properties may only be deduced by numerical computations of the full governing equations. We illustrate how our theory, which has similarities with that employed in the analysis of high wavenumber Görtler vortices in boundary layers above concave walls, may be used to isolate the most unstable vortex mode.