Hydrodynamic instability for certain ABC flows

摘要

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 rangeA= 1,B2+C2 1, instability follows from the presence of hyperbolic stagnation points. In the parameter rangeA= 1,B=C= #xAB;#x3F5;1, 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 Poincar#xE9; sections in Section 3.