Linear stability of a Berman flow in a channel partially filled with a porous medium

The temporal stability of similarity solutions for an incompressible fluid moving in a channel partially filled with a porous medium is analyzed. A constant wall suction acting on the bottom surface of the porous medium drives the fluid; the upper wall of the channel is impermeable. This work extends the work of King and Cox ["Asymptotic analysis of the steady-state and time-dependent Berman problem," J. Eng. Math. 39, 87 (2001)] to a wider class of similarity solutions where coupled flow, both above and through a porous medium, is considered. In this work, a similarity transform is proposed which satisfies both the Navier-Stokes equation in the clear fluid portion of the domain and the Brinkman extended Darcy law relationship in the porous medium. The boundary conditions between the clear fluid and porous regions are those outlined by Ochoa-Tapia and Whitaker ["Momentum transfer at the boundary between a porous medium and a homogeneous fluid I: theoretical development," Int. J. Heat Mass Transfer 38, 2635 (1995)]. The solutions of the steady flow are approximated analytically, in the limit of small wall suction, and numerically. Multiple steady-state solutions were found. The temporal stability of the solutions indicates turning-point bifurcations and instability only occurred with reverse flows. (C) 2005 American Institute of Physics.