On the existence of three-dimensional convection in a rectangular box containing fluid-saturated porous material

Abstract

On the basis of a stability analysis of finite amplitude, two-dimensional convection, we have determined the dimensions of boxes containing fluid-saturated porous material in which convection is necessarily unsteady or steady and three-dimensional. For certain box sizes, convective rolls are unstable at Rayleigh numbers Ra lower than 380, the value below which rolls are stable forms of convection between infinite parallel planes. For Ra = 100 and 200, it appears unlikely that there are any box dimensions for which there is not a stable (possibly multicellular) two-dimensional steady motion. At Ra = 340 and 400, boxes in which rolls are unstable have heights which range from one to five times their horizontal dimensions.