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Asymptotic forms for jets from standing waves

Published online by Cambridge University Press:  30 October 2001

MICHAEL S. LONGUET-HIGGINS
MICHAEL S. LONGUET-HIGGINS
Affiliation:
Institute for Nonlinear Science, University of California, San Diego, La Jolla, CA 92093-0402, USA
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Abstract

Standing gravity waves forced beyond the maximum height for perfect periodicity can produce vertical jets with sharp-pointed tips. In this paper, canonical forms for the wave crests are derived which display sharp cusps in the limit as the time t tends to infinity. The theoretical profile is in general quartic in the space coordinates, and can describe the smooth transition of a fairly low wave crest to a cusped form. There is no singularity as the surface slope passes through 45°.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 447 , 25 November 2001 , pp. 287 - 297
Copyright
© 2001 Cambridge University Press

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