Linear stability analysis of open-channel flow overlying a porous medium

ABSTRACT

A particular case of an open-channel flow (where the Reynolds number can be large) above a saturated porous bed where Darcy–Brinkman flow takes place is considered. A temporal linear stability analysis was performed to ascertain the conditions that are required for perturbations to grow over a wide range of parameters (i.e. Reynolds number, ratio of the porous to open-channel flow depths, slope of the bottom of the channel, stress-jump coefficient at the top of the porous layer, permeability, and porosity). Three modes of instability were observed, which were attributed to the effects of the free surface, porous layer, and fluid layer. The shift between the modes of instability was also studied. A competing effect was found between the free-surface mode, which is characterized by moderate perturbation growth rates, and the slightly more oscillatory porous-layer mode, which is characterized by higher perturbation growth rates.

Keywords:

• Flows through porous media
• gravity waves
• open channel flows
• shear waves
• stability of laminar flows