The stability of flow in a channel or duct occupied by a porous medium

The hydrodynamic stability of flow of an incompressible fluid through a plane-parallel channel or circular duct filled with a saturated porous medium, modeled by the Brinkman equation, is discussed on the basis of an analogy with a magnetohydrodynamic problem (Hartmann flow). Flow in a circular duct is found to be stable to small disturbances for all values of the Reynolds number, but for a plane-parallel channel the flow is unstable if the Reynolds number exceeds a critical value, dependent on a Darcy number.