CHANGES IN THE ADIABATIC INVARIANT AND STREAMLINE CHAOS IN CONFINED INCOMPRESSIBLE STOKES-FLOW

The steady incompressible flow in a unit sphere introduced by Bajer an d Moffatt [J. Fluid Mech. 212, 337 (1990)] is discussed. The velocity field of this flow differs by a small perturbation from an integrable field whose streamlines are almost all closed. The unperturbed flow ha s two stationary saddle points (poles of the sphere) and a two-dimensi onal separatrix passing through them. The entire interior of the unit sphere becomes the domain of streamline chaos for an arbitrarily small perturbation. This phenomenon is explained by the nonconservation of a certain adiabatic invariant that undergoes a jump when a streamline crosses a small neighborhood of the separatrix of the unperturbed flow . An asymptotic formula is obtained for the jump in the adiabatic inva riant. The accumulation of such jumps in the course of repeated crossi ngs of the separatrix results in the complete breaking of adiabatic in variance and streamline chaos. (C) 1996 American Institute of Physics.