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Knotted vortex filaments in an ideal fluid

Published online by Cambridge University Press:  26 April 2006

J. P. Keener
J. P. Keener
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA
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Abstract

Knotted closed-curve solutions of the equation of self-induced vortex motion are studied. It is shown that there are invariant torus knots which translate and rotate as rigid bodies. The general motion of ‘small-amplitude’ torus knots and iterated (cabled) torus knots is described and found to be almost periodic in time, and for some, but not all, initial data, the topology of the knot is shown to be invariant.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 211 , February 1990 , pp. 629 - 651
Copyright
© 1990 Cambridge University Press

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