Effect of Interface Momentum Distribution on the Stability in a Porous-Fluid System

We numerically investigate the linear instability problem of Poiseuille flow in a channel partially filled with a porous medium on the bottom side. We are primarily interested in the influence of the interface momentum distribution including stress continuity and jump interface conditions. A spectral collocation method is applied in solving the fully coupled instability problem arising from the adjacent porous and free channel flows. The results show that the “interface stress coefficient” in a negative range has a larger effect on the trajectory of the eigenvalues than that in the positive range, especially the most unstable mode. Moreover, with a low permeability in the porous region, the interface momentum distribution has less effect on the stability of core flow. And when the “interface stress coefficient” is equal to its minimum negative value, the flow passing through the channel is at its most stable state. If the “interface stress coefficient” varies in a positive range, the degree of fluid stability is predicted to slightly diminish due to stress continuity condition at the interface.

Keywords:

Porous layer , Interface momentum distribution , linear stability , Poiseuille flow