Stability of plane Poiseuille-Couette flow in a fluid layer overlying a porous layer
Journal
Journal of Fluid Mechanics
Journal Volume
826
Pages
376-395
Date Issued
2017
Author(s)
Abstract
This paper performs a linear stability analysis to investigate the stability of plane Poiseuille-Couette flow in a fluid layer overlying a porous medium saturated with the same fluid. The effect of superimposed Couette flow on the associated Poiseuille flow in such a two-layer system is explored carefully. The result shows that the presence of Couette flow may destabilize the Poiseuille flow at small depth ratio d, defined by the ratio of the depth of the fluid layer to the depth of the porous layer, and induce a trimodal structure to the neutral curves. At moderate d, the Couette component generally produces a stabilization effect on the flow. When the velocity of the upper moving wall is large enough, a bi-modal behaviour of the neutral curves appears and a shift of instability mode occurs from the long-wave fluid-layer mode to the porous-layer mode with higher wavenumber. These stability characteristics are remarkably different from those of the plane Poiseuille-Couette flow in a single fluid layer in that the flow becomes absolutely stable when the wall velocity is over 70% of the maximum velocity of the Poiseuille component of flow. The stability of pure Couette flow in such a two-layer system is also studied. It is found that the flow is still absolutely stable with respect to infinitesimal disturbances, which is the same as the stability characteristic of a single-layer plane Couette flow.
Type
journal article