Global instabilities in inhomogeneous mixed convection flows in semi-infinite porous media

We study the nonlinear dynamic of mixed convection in semi-infinite porous media heated non-uniformly from below and through which an axial flow is maintained. Because the imposed inhomogeneous temperature profile varies slowly downstream, the WKBJ expansion is used specifically to determine the local absolute instability. Direct numerical simulations are carried out in the case when the inhomogeneity promotes sufficiently extended absolute instability at the inlet. It is found that the frequencies in the oscillating region are identical to the absolute frequencies at the inlet. Moreover, the distance separating the inlet to the spatial position where the trailing front of the globally unstable waves saturated is found to obey to a well defined scaling law.