Oscillatory convection in a two-dimensional porous box with asymmetric lateral boundary conditions

Abstract

The onset of convection in a two-dimensional porous cavity is investigated where the cavity is subject to asymmetric boundary conditions at the lateral walls: one vertical wall is thermally conducting and impermeable, while the other is thermally insulating and open. At the open boundary the saturating fluid flows freely in and out from a hydrostatic reservoir in contact with the porous medium. The top and bottom of the box are impermeable and perfectly conducting. It is shown that the mode for onset of convection is oscillatory in time. This corresponds to a disturbance traveling as a wave through the box from the impermeable wall to the open wall. The preferred eigensolution, its oscillation frequency, and critical Rayleigh number are calculated numerically for different aspect ratios of the porous box, and these values are confirmed by means of suitable asymptotic analyses.