Other
Scientific paper
Apr 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aps..apr.s3003d&link_type=abstract
American Physical Society, April Meeting, April 28 - May 1, 2001 Washington, DC Bulletin of the American Physical Society, Vol.
Other
Scientific paper
The free relaxation of turbulence in inviscid, incompressible 2D fluids (Euler fluids) plays an important role in geophysical and astrophysical flows, as well as in magnetized plasmas. Such flows can be described as a collection of intense self-trapped vortices interacting, merging, and shearing apart as they move through a diffuse background vorticity. The background can either be present initially (as in the potential vorticity gradient created by planetary rotation), or can be created by filamentation of the intense vortices. This talk will review recent theories and experiments analyzing the interaction between intense vortices and a diffuse background vorticity. The experiments employ magnetized pure electron plasma columns as a simulacrum of a 2D Euler fluid. The plasma evolves according to 2D ``E × B'' dynamics, which is isomorphic to Euler flow dynamics, with the plasma density proportional to the vorticity of the flow. The experiments observe that the intense vortices can strongly affect the background dynamics, launching surface waves on vorticity edges; these waves can eventually break and filament.(J. Fajans and D. Durkin, Phys. Rev. Lett. 85), 4052 (2000); D.Z. Jin and D. Dubin, Phys. Fluids (in press). Theory for the filamentation time matches the experiments. Experiments also show that even a diffuse background can substantially alter the motion of the intense vortices. For example, a background vorticity gradient causes an intense vortex to move up or down the gradient. New experimental and theoretical results(Y. Kimamoto et al.), Phys. Rev. Lett. 85, 3173 (2000); D. Schecter and D. Dubin, Phys. Rev. Lett. 83, 2191 (1999). will be presented for this venerable problem, which show that the rate at which the intense vortex moves can change by an order of magnitude or more, depending on whether the vortex rotates with or against the background shear flow. Another example is the surprising spontaneous formation of vortex crystal states during the free-relaxation of turbulence.(K.S. Fine et al.), Phys. Rev. Lett. 75, 3277 (1995); D.Z. Jin and D. Dubin, Phys. Rev. Lett. 80, 4434 (1998). Theory and numerical simulations have shown that these geometrically regular patterns of intense vortices form because the background is mixed by the intense vortices. This is consistent with the second law of thermodynamics, since the order of the pattern of intense vortices is increased at the expense of a decrease in order of the background. Theory can quantitatively predict the characteristics of these vortex crystal states by maximization of the background fluid entropy, subject to constraints of the fixed number of intense vortices and of the robust flow invariants.
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