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 sem i-infinite horizontal heated surface embedded in a fluid-saturated por ous medium is developed. Due to the inadequacies of existing parallel- flow theories the problem has been re-examined using asymptotic techni ques that use the distance downstream of the leading edge of the surfa ce as the large parameter. The parallel-flow theories predict that at each downstream location there are two possible vortex wavenumbers whi ch 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 q uasi-parallel approach and its properties may only be deduced by numer ical computations of the full governing equations. We illustrate how o ur theory, which has similarities with that employed in the analysis o f high wavenumber Gortler vortices in boundary layers above concave wa lls, may be used to isolate the most unstable vortex mode.