HYDRODYNAMIC INSTABILITY FOR CERTAIN ABC FLOWS

A sufficient condition for instability of the Euler equations [see (1. 5)] is used to demonstrate the instability of certain ABC flows. In th e parameter range A = 1, B2 + C2 > 1, instability follows from the pre sence of hyperbolic stagnation points. In the parameter range A = 1, B = C = epsilon << 1, instability follows from the existence of hyperbo lic closed trajectories and the associated exponential stretching of t he fluid particles. This result is proved analytically in Section 2 an d illustrated numerically via Poincare sections in Section 3.