CONVECTIVE INSTABILITY OF A FLUID MIXTURE IN A POROUS-MEDIUM WITH TIME-DEPENDENT TEMPERATURE-GRADIENT

The convective instability of a fluid mixture in a porous medium is co nsidered when the medium is heated from below or from above (Soret eff ect). The prescribed temperature gradient is assumed to periodically v ary with the time. The two-dimensional instability thresholds are esti mated, first for an oscillatory instability and then for a stationary one, using a linear asymptotic analysis. It is shown that a subharmoni c instability develops. This subharmonic instability is always the pre ponderant instability in the phenomenon. In the plane of the parameter s, the neighbourhood of a polycritical point is then studied, in the c ase of a small forcing frequency, by a local (inner) expansion: the mo tion appears as the solution of a Mathieu equation which is asymptotic ally matched with the outer expansion. The displacement of the polycri tical point is then estimated, and the case of vanishing forcing frequ ency is considered..