Notes on Convection in a Porous Medium: (i) an Effctive Rayleigh Number for an Anisotropic Layer, (ii) the Malkus Hypothesis and Wavenumber Selection

Studies of convection in a layer of a saturated anisotropic porous medium uniformly heated from below are reviewed. Emphasis is placed on the usefulness of an effective Rayleigh number, defined (for certain boundary conditions) as the square harmonic-mean square root of horizontally-based and vertically-based Rayleigh numbers. The status of the Malkus hypothesis, together with its relationship with observed cell size, is also discussed. A possible explanation is provided for the observed phenomenon that in a porous medium the cell size decreases as the amplitude of convection increases, whereas in a clear fluid the cell size increases.