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Islands in three-dimensional steady flows

Published online by Cambridge University Press:  26 April 2006

C. C. Hegna  and
A. Bhattacharjee
C. C. Hegna
Affiliation:
Department of Applied Physics, Columbia University, New York, NY 10027, USA
A. Bhattacharjee
Affiliation:
Department of Applied Physics, Columbia University, New York, NY 10027, USA
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Abstract

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 527 - 542
Copyright
© 1991 Cambridge University Press

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