Secondary Instabilities of Flows with Elliptic Streamlines

Abstract

We examine the stability of flows which are the sum of a linear flow with elliptic streamlines and a transverse standing wave. Such flows are exact solutions of the 3D Euler equations for an inviscid incompressible fluid. We examine the stability of such flows under local 3D high frequency perturbations, which can be viewed as secondary perturbations of the elliptic flow itself. We find that these flows are unstable to such perturbations and compute growth rate in several cases. {copyright} {ital 1997} {ital The American Physical Society}