Transition to oscillatory convective heat transfer in a fluid-saturated porous medium

The transition from steady to time-periodic motion in the analog of Benard convection in a two-dimensional region of fluid-saturated porous media is studied by means of an eigenfunction expansion and a branch-tracing technique. This method leads to the location of the transition at Rayleigh number 9.9 times that at convection onset. The small-amplitude motion has a period 0.012 times shorter than the thermal diffusion time and comes into existence through a Hopf bifurcation. The structure and time progression of the destabilizing disturbance indicates that the dominant effect is an instability convected by the base flow whose strength is coupled to the steepening thermal boundary layers. The effects of truncation of the expansion on the prediction of the transition and its mechanism are discussed.