Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow

Chaos
D. L. VainshteinA I Neishtadt

Abstract

The steady incompressible flow in a unit sphere introduced by Bajer and 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 has two stationary saddle points (poles of the sphere) and a two-dimensional 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 invariant. The accumulation of such jumps in the course of repeated crossings of the separatrix results in the complete breaking of adiabatic invariance and streamline chaos. (c) 1996 American Institute of Physics.

References

Nov 1, 1986·Physical Review A: General Physics·J R CaryJ L Tennyson

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Citations

Jan 4, 2007·Chaos·D L VainchteinI Mezic
Dec 1, 1996·Chaos·D. L. VainshteinA. I. Neishtadt
Sep 26, 2003·Nature·T H Solomon, Igor Mezić
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F WuH J H Clercx
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fan WuThomas Ward
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A P Itin, S Watanabe
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R ChabreyrieN Aubry
Oct 13, 2007·Physical Review Letters·Dmitri L VainchteinRoman O Grigoriev
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dmitri L VainchteinRoman O Grigoriev

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