title: Instability of plane-parallel flow of incompressible liquid over a saturated porous medium.
abstract: The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
authors: Institute of Continuous Media Mechanics, Ural Branch of RAS, Perm, Russia.|Perm State University, Theoretical Physics Department, Perm, Russia.
authors: T P
authors: TP
authors: Lyubimova
authors: Perm State University, Theoretical Physics Department, Perm, Russia.
authors: D V
authors: DV
authors: Lyubimov
authors: Perm State University, Theoretical Physics Department, Perm, Russia.
authors: D T
authors: DT
authors: Baydina
authors: Institute of Continuous Media Mechanics, Ural Branch of RAS, Perm, Russia.|Perm State University, Theoretical Physics Department, Perm, Russia.
authors: E A
authors: EA
authors: Kolchanova
authors: Institute of Continuous Media Mechanics, Ural Branch of RAS, Perm, Russia.|Perm State University, Theoretical Physics Department, Perm, Russia.
authors: K B
authors: KB
authors: Tsiberkin