Long-wave transition to instability of flows in horizontally extended domains of porous media

Abstract

A new mechanism of transition to instability is treated arising for vertical motions with phase transition in horizontally infinite two dimensional domains of a porous medium. Destabilization of a plane interface takes place at zero wave number being accompanied by reversible bifurcations indicating the formation of a secondary flow with a shifted phase transition interface. Sub- and supercritical structures in a neighborhood of the threshold of instability obey the weakly nonlinear diffusion equation. Homoclinic solutions of this equation corresponding to the horizontally nonhomogeneous phase transition interface and bifurcating from the basic state are found to be unstable both in subcritical as well as in supercritical cases. We consider two examples of motion in a porous medium: the first one describes vertical flows with phase transition in a high-temperature geothermal reservoirs, consisting of two high-permeability layers, which are separated by a low-permeability stratum. The second example relates to to the Rayleigh-Taylor instability of a water layer located over an air-vapor layer in a porous medium under isothermal condition in presence of capillary forces at the phase transition interface. © 2008 Springer.