A RESONANT GRAVITY-DRIVEN FLOW OF A POWER-LAW FLUID OVER A SLIPPERY TOPOGRAPHY SUBSTRATE

Abstract

The gravity-driven flow of a power-law fluid over a slippery topography substrate is studied. The fluid flow, due to the gravity, is assumed to be steady and confined to the limit of small amplitude of the wall corrugation. As an analytic approach, we apply the Karman– Pohlhausen integral boundary-layer method and derive an asymptotic equation valid for rather thin films. Our results support the view that the resonance is associated with an interaction of the undulated film with capillary-gravity waves travelling against the mean flow direction in the linear case. The influence of the slip condition on the linear resonance phenomena for different power-law indices n is the main factor in this work.