MARGINAL STABILITY IN INHOMOGENEOUS POROUS MEDIA

Marginal stability is examined in a saturated porous layer of thickness h heated from below, in which the permeability k and the thermometric conductivity K* vary markedly in the vertical direction. A straightforward perturbation treatment, with numerical solutions provided by a digital computer, shows that the over-all temperature gradient [T(0) - T(h)]/h necessary for marginal stability is independent of the directions of increase of k and K*, and decreases noticeably with increasing changes of k and K* over the layer. The horizontal wavelength of the first unstable mode is found to decrease somewhat less rapidly with increasing changes in k and K*. © 1969 The American Institute of Physics.