Da. Nield, NOTES ON CONVECTION IN A POROUS-MEDIUM .1. AN EFFECTIVE RAYLEIGH NUMBER FOR AN ANISOTROPIC LAYER .2. THE MALKUS HYPOTHESIS AND WAVE-NUMBER SELECTION, Transport in porous media, 27(2), 1997, pp. 135-142
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.