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The Quarterly Journal of Mechanics and Applied Mathematics 1980 33(1):47-58; doi:10.1093/qjmam/33.1.47
© 1980 by Oxford University Press
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STABILITY OF A SATURATED POROUS LAYER SUBJECT TO A SUDDEN RISE IN SURFACE TEMPERATURE: COMPARISON BETWEEN THE LINEAR AND ENERGY METHODS

JEAN-PAUL CALTAGIRONE

( Laboratoire d'Aérothermique du Centre National de la Recherche Scientifique 4ter, route des Gardes, F92190-Meudon, France )

The stability of a horizontal saturated porous layer subject to a sudden rise in surface temperature at the lower surface, the upper surface being kept at a constant temperature, is investigated by means of a linear theory, the energy method and a two-dimensional numerical model. The linear theory and global stability results enable us to represent, in a Rayleigh number-time plane, the curves of marginal stability limiting the states: unstable for any perturbation, conditionally stable and globally stable. The numerical model based on the method of finite differences represents the phenomena when steady convection appears and modifies in an appreciable manner the temperature distribution within the porous layer. The results obtained with all three theories are then compared and a physical interpretation is given.


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