Necessary and Sufficient Condition for the Stability of Plane Parallel Inviscid Flow

Abstract

Plane parallel flow between rigid plates of an incompressible inviscid fluid is considered. A necessary and sufficient condition for infinitesimal stability is derived in the special case where w″ has only a single zero and w′ > 0 where w(x) is the velocity profile between the plates. A general sufficient condition for instability is also obtained.