Aeta Meehanica 43, 37--47 (1982) ACTA MECHANICA @ by Springer-Verlag 1982 Thermal Instability in a Porous Medium with Random Vibrations By B. S. Dandapat and A. S. Gupta, Kharagpur, India With 4 Figures (Received November 28, 1980; revised January 26, 1981) Summary Onset of thermal convection in a layer of saturated porous medium, heated from below, is examined when the layer is subjected to random vibrations. It is shown that when the vibrations are characterized by a white noise process, they hasten the onset of convection. Further, decrease in permeability tends to stabilize the flow field. 1. Introduction Several experiments were conducted by Morrison [1], Morrison, Rogers and Horto n [2], and Rogers and Sehilberg [3] for observing the onset of convection in a horizontal layer of a saturated porous medium heated from below. The observed critical temperature gradient was smaller by an .order of magnitude than the gradient predicted from the theoretical investigations of Horton and Rogers [4], and Lapwood [5]. Extension of these theoretical studies was made by Wooding [6], [7]. The quantitative disagreement between the theory and experiments was sought to be removed by Rogers and Morrison [8], Morrison and Rogers [9], and Rogers [10] by allowing for the temperature dependence of viscosity, an initially steady nonlinear temperature distribution, and a columnar rather than cellular form of convection. However the experiments mentioned above involved a time- dependent situation and so cannot be regarded as a satisfactory test of the Lap- wood theory which assumes an initially steady temperature distribution. Elder [11] and Combarnous and Le Fur [12] determined experimentally the point at which thermal convection began and found good agreement with the theory. An extension of Lapwood's theory was made by Gheorghitza [13] who assumed the porous medium to be nonhomogeneous. The global stability of convective flow in a porous medium using energy method was studied by Westbook [14]. Dependence of Nusselt number on the Rayleigh number in steady convection in a porous medium was investigated by Palm, Weber and Kvernvold [15]. Using a variational method, the bounds on heat transport in a porous medium were determined by Busse and Joseph [16]: Strauss and Schubert [17] and Horne [18] studied two- dimensional and three-dimensional natural convection in a confined porous medium heated from below. 0001-5970/82/0043/0037/$02.20