NOTES ON CONVECTION IN A POROUS-MEDIUM .1. AN EFFECTIVE RAYLEIGH NUMBER FOR AN ANISOTROPIC LAYER .2. THE MALKUS HYPOTHESIS AND WAVE-NUMBER SELECTION

Studies of convection in a layer of a saturated anisotropic porous med ium uniformly heated from below are reviewed. Emphasis is placed on th e usefulness of an effective Rayleigh number, defined (for certain bou ndary conditions) as the square harmonic-mean square root of horizonta lly-based and vertically-based Rayleigh numbers. The status of the Mal kus hypothesis, together with its relationship with observed cell size , is also discussed. A possible explanation is provided for the observ ed phenomenon that in a porous medium the cell size decreases as the a mplitude of convection increases, whereas in a clear fluid the cell si ze increases.