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Evolution of vortex knots

Published online by Cambridge University Press:  25 July 1999

RENZO L. RICCA ,
DAVID C. SAMUELS  and
CARLO F. BARENGHI
RENZO L. RICCA
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK; e-mail: ricca@math.ucl.ac.uk
DAVID C. SAMUELS
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK
CARLO F. BARENGHI
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, UK
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Abstract

For the first time since Lord Kelvin's original conjectures of 1875 we address and study the time evolution of vortex knots in the context of the Euler equations. The vortex knot is given by a thin vortex filament in the shape of a torus knot [Tscr ]p,q (p>1, q>1; p, q co-prime integers). The time evolution is studied numerically by using the Biot–Savart (BS) induction law and the localized induction approximation (LIA) equation. Results obtained using the two methods are compared to each other and to the analytic stability analysis of Ricca (1993, 1995). The most interesting finding is that thin vortex knots which are unstable under the LIA have a greatly extended lifetime when the BS law is used. These results provide useful information for modelling complex structures by using elementary vortex knots.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 391 , 25 July 1999 , pp. 29 - 44
Copyright
© 1999 Cambridge University Press

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