We present a geometric estimate from below on the growth rate of a small perturbation of a three-dimensional steady flow of an ideal fluid and thus we obtain effective criteria for local instability for Euler’s equations. We use these criteria to demonstrate the instability of several simple flows and to show that any flow with a hyperbolic stagnation point is unstable.

• Received 23 January 1991

DOI:https://doi.org/10.1103/PhysRevLett.66.2204