Vortex instability from a near–vertical heated surface in a porous medium. I Linear instability

In this paper we consider the stability of thermal boundary–layer flow in a porous medium. In particular, we are concerned about the susceptibility of streamwise vortex disturbances to growth when the heated surface is very close to the vertical. This regime allows both the basic flow and the disturbance equations to satisfy the boundary–layer approximation, and hence the present analysis forms a mathematically consistent framework. It is shown that the usual method of analysing linear instability is too restrictive and that disturbances grow from positions much closer to the leading edge than are predicted using the parallel flow approximation.