Instability of unsteady flows or configurations Part 1. Instability of a horizontal liquid layer on an oscillating plane

Abstract

A layer of viscous liquid with a free surface is set in motion by the lower boundary moving simple-harmonically in its own plane. The stability of this motion is investigated. Since the primary flow is time-dependent, the time variable cannot be separated from at least one space variable, and a new approach must be used to investigate the problem. In this paper the stability of long waves is studied by a perturbation method which has not been applied before to problems of stability of unsteady flows, and it is found that the flow under consideration can be unstable for long waves.