Hydrodynamic instability for certain ABC flows

Abstract

Abstract A sufficient condition for instability of the Euler equations [see (1.5)] is used to demonstrate the instability of certain ABC flows. In the parameter range A = 1, B 2 + C 2 > 1, instability follows from the presence of hyperbolic stagnation points. In the parameter range A = 1, B = C = «ε1, instability follows from the existence of hyperbolic closed trajectories and the associated exponential stretching of the fluid particles. This result is proved analytically in Section 2 and illustrated numerically via Poincaré sections in Section 3.