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Growth rates for fast kinematic dynamo instabilities of chaotic fluid flows

Published online by Cambridge University Press:  26 April 2006

Yunson Du  and
Edward Ott
Yunson Du
Affiliation:
Laboratory for Plasma Research and Department of Physics, University of Maryland, College Park, MD 20742-3511, USA
Edward Ott
Affiliation:
Laboratory for Plasma Research and Department of Physics, University of Maryland, College Park, MD 20742-3511, USA And Department of Electrical Engineering.
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Abstract

It is shown that the exponential growth rate of the fast kinematic dynamo instability can be related to the Lagrangian stretching properties of the underlying chaotic flow. In particular, a formula is obtained relating the growth rate to the finite time Lyapunov numbers of the flow and the cancellation exponent κ. (The latter quantity characterizes the extremely singular nature of the magnetic field with respect to fine-scale spatial oscillation in orientation.) The growth rate formula is illustrated and tested on two examples: an analytically soluble model, and a numerically solved spatially smooth temporally periodic flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 265 - 288
Copyright
© 1993 Cambridge University Press

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Footnotes

With an Appendix by B. J. Bayly and A. Rado.

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