Magneto-Fluid Dynamics Seminar

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The Stability of Chaotic Flows: Generation of Multifractals

Speaker: Charles Reyl, Institute of Plasma Research, University of Maryland

Location: Warren Weaver Hall 1302

Date: Monday, December 2, 1996, 11:15 a.m.

Synopsis:

We show that at high Reynolds number, smooth, Lagrangian chaotic flows are typically linearly unstable and that the perturbed vorticity tends to concentrate on a fractal. Numerical integration of the relevant linear partial differential equations with Reynolds number up to 10⁶ shows that the wavenumber power spectrum of the perturbed vorticity has a power-law behavior and that the norm of the perturbed vorticity field is multifractal.

A theoretical understanding is provided by adopting a wave-packet picture (whereby vorticity wave-packets are evolved according to ordinary differential equations) which yields scaling results and appropriately describes the small wavelength features of both the power spectrum and the multifractal dimension spectrum.