Linear stability analysis on the onset of buoyancy-driven convection in liquid-saturated porous medium

The onset of convective motion in an initially quiescent, horizontal isotropic porous layer is analyzed by using linear theory. The fluid-saturated porous layer is assumed to be kept isothermal while a single solute diffuses due to an impulsive change in concentration at an upper boundary. In the semi-infinite domain, using the spectral method, the new linear stability equations are derived and solved analytically by introducing the eigenanalysis and the initial value problem approach. Also, the quasi-steady state approximation (QSSA) is considered. By comparing the stability characteristics obtained with and without QSSA, the validity of the QSSA is discussed. For the deep-pool system, the critical time to onset of convection is found to be tau(c) = 167.547 with the critical wavenumber a(c) = 0.0695. The present study complements previous theoretical predictions and also will provide the starting points for further studies. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3703330]