On the Horton-Rogers-Lapwood convective instability with vertical vibration: Onset of convection

We present a numerical and analytical study of diffusive convection in a rectangular saturated porous cell heated from below and subjected to high frequency vibration. The configuration of the Horton-Rogers-Lapwood problem is adopted. The classical Darcy model is shown to be insufficient to describe the vibrational flow correctly. The relevant system is described by time-averaged Darcy-Boussinesq equations. These equations possess a pure diffusive steady equilibrium solution provided the vibrations are vertical. This solution is linearly stable up to a critical value of the stability parameter depending on the strength of the vibration. The solutions in the neighborhood of the bifurcation point are described analytically as a function of the strength of vibration, and the larger amplitude states are computed numerically using a spectral collocation method. Increasing the vibration amplitude delays the onset of convection and may even create subcritical solutions. The majority of primary bifurcations are of a special type of symmetry-breaking bifurcation even if the system is subjected to vertical vibration. (C) 2000 American Institute of Physics. [S1070-6631(00)00411-6].