Abstract
A linear stability analysis of a laminar open-channel flow bounded in the bottom by a porous medium saturated with the same fluid is performed. The Brinkman equation is employed to account for the viscous shear in the transition between the flow in the fluid layer and the flow in and the underlying porous layer. The critical Reynolds number above which the flow is unstable is found to fall into three distinct modes of instability which are attributed to 1) the free surface, where long waves take place at the free surface; 2) the porous layer, where the instability triggered by shorter waves within the fluid layer extends to the porous layer; 3) the shear layer at the interface fluid-porous layer, where the active momentum transfer from the fluid layer to the porous layer causes the instabilities triggered at the fluid layer to extend further deep within the porous layer. We evaluate the correlation between the modes of instability and parameters such as channel bottom slope, permeability of the porous layer, wavenumber and phase velocity.
