Instability of the self-similar flow into a cavity

Abstract

In this paper we have investigated the instability of the self-similar flow behind the boundary of a collapsing cavity. The similarity solutions for the flow into a cavity in a fluid obeying a gas law p = Kρ^ϒ , K = constant and 7 ≥ ϒ > 1 has been solved by Hunter, who finds that for the same value of ϒ there are two self-similar flows, one with accelerating cavity boundary and other with constant velocity cavity boundary. We find here that the first of these two flows is unstable. We arrive at this result only by studying the propagation of disturbances in the neighbourhood of the singular point.