Stability of plane poiseuille flow and plane couette flow over a layer of elastic medium

Abstract

The stability of plane Poiseuille flow of an incompressible viscous fluid between a rigid plate and a layer of incompressible isotropic elastic solid is studied. Two distinct modes of instability are found. The interfacial mode may occur at small Reynolds number when the solid is soft. For this mode, the rigidity of the solid is a stabilizing factor, whereas the viscosity of the fluid is destabilizing. There is a critical elastic parameter beyond which the flow becomes unstable regardless of the viscosity of the fluid. The shear wave mode occurs at large Reynolds number. This mode has the same nature as that of the plane Poiseuille flow between rigid plates. The critical number is however modified by an elastic parameter.

The eigenvalue problem is solved by a numerical technique in which the required initial guesses are computed by the perturbation method.

The stability of plane Couette flow of an incompressible viscous fluid between a Inoving plate and a layer of incompressible isotropic elastic solid is also investigated. It is found that the instability of interfacial mode is essentially similar to that of plane Poiseuille Flow. It requires, however, softer solid or higher critical speed to induce the instability than does the plane Poiseuille flow.