Wave structure in oscillatory couette flow of a dusty gas

Abstract

Using the Laplace transform technique, general solution is obtained for the velocity distribution in a time dependent Couette flow of a dusty gas for small times. The dusty gas contained between two parallel plates is disturbed by the motion of the lower plate with an arbitrary velocityF(t). WhenF(t) contains a factor of the type exp [−(λ2−iω], two distinct types of waves are generated, one of which is oscillatory and the other is non-oscillatory which disappears for λ=0. Reflections of these waves are studied and graphs for the wave speeds are presented. Long time approximations for this type ofF(t) are evaluated, and steady state solutions are obtained forF(t) of the type exp (iωt).