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The universal structure of high-curvature regions of material lines in chaotic flows

Published online by Cambridge University Press:  10 March 2009

A. LEONARD
A. LEONARD*
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: tony@galcit.caltech.edu
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Abstract

Regions of high curvature of a material line as they evolve in a chaotic flow are considered. In such a region, the curvature as a function of arclength along the line is found to have a universal form with the peak curvature the only parameter involved. The alignment of the principal axes of the strain tensor with respect to the local tangent vector of the curve and the ratio of the two largest finite-time Lyapunov exponents play a key role. Numerical experiments with ABC flow demonstrate the result.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 167 - 175
Copyright
Copyright © Cambridge University Press 2009

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References

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