STABILITY OF TWO-DIMENSIONAL NATURAL CONVECTION IN A POROUS LAYER

A stability analysis of the two-dimensional natural convection in a porous layer is given. The Galerkin method is used, truncating the series to four and six terms. For finite Prandtl numbers the system of three ordinary differential equations obtained has the same properties as that of Lorenz for the classical Bénard problem. In the case of infinite Prandtl numbers, four ordinary differential equations are examined. The first branch of nontrivial steady-state solutions loses stability at the Rayleigh number equal to 30π2. At this point the subcritical Hopf bifurcation takes place, but unlike the previous case the trajectories are not limited to the neighbourhood of origin.