Integrable Vortex Motions in Unbounded and Periodic Domains
In each of the vortex systems investigated, the motion of a passive particle in the field of the vortices is, in general, chaotic. One means of characterizing the advected field is through Thurston-Nielsen theory from topology. Using only information about the motions of the vortices themselves and the fact that the advected fluid is a continuous field, Thurston-Nielsen theory establishes a lower bound on the stretching in the advected field. Some of the vortex motions investigated produce exponential stretching in the flow field. This stretching is as violent as any in turbulent flow, which suggests that the problem of point vortices in two-dimensional flow may lend itself to an understanding of some of the physics present in fully turbulent two-dimensional flows.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign