Modes of finite-amplitude three-dimensional convection in rectangular boxes of fluid-saturated porous material

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Abstract
Steady, three-dimensional convection in rectangular boxes of fluid-saturated porous material with square horizontal cross-section heated from below is found to be non-unique. The properties of a special class of solutions exhibiting a high degree of symmetry are determined as a function of box size and Rayleigh number. The stability of these solutions to general three-dimensional perturbations is also determined. In some cases, when these solutions are found to be unstable, the alternative forms of three-dimensional convection are presented. Multiple three-dimensional steady states are given for a few particular values of box size and Rayleigh number.