The stability of non-axisymmetric time-periodic vortical flows

Steady inviscid fluid flows with constant vorticity and elliptical streamli nes are known to be unstable. So too are axisymmetric flows with periodical ly strained vorticity. But elliptical instability may be suppressed by cons tant vortex stretching. Here we examine the stability of periodically strai ned, unbounded, non-axisymmetric flows with spatially uniform vorticity. Be cause of asymmetry, the analysis requires recently developed techniques. We find that the flows are normally highly unstable, with sensitive dependenc e on disturbance wavenumber orientation. Our results reveal a wealth of fin e structure that is absent in axisymmetric cases, but which was recently fo und for other non-axisymmetric periodic flows. However, when the frequency of the imposed periodic motion is sufficiently large, instability is suppre ssed, as the requisite internal resonances are impossible. We also briefly examine the limiting case of continuous stretching. Though elliptical insta bility is inhibited, other exponentially growing disturbances are present. In fluctuating environments, elliptical instability is just one of many pos sible types of parametric instability; and its inhibition by stretching is likely to be overshadowed by other periodically driven instabilities. Such unbounded-flow models may shed light on the local interaction between small and large scales within turbulent flows. (C) 1999 The Japan Society of Flu id Mechanics and Elsevier Science B.V. All rights reserved.