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Capillary–gravity waves of solitary type on deep water

Published online by Cambridge University Press:  26 April 2006

Michael S. Longuet-Higgins
Michael S. Longuet-Higgins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, England and Institute of Oceanographic Sciences, Wormley, Surrey
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Abstract

On physical grounds it was recently suggested that limiting capillary–gravity waves of solitary type may exist on the surface of deep water (Longuet-Higgins 1988). This paper describes accurate numerical calculations which support the conjecture. The limiting wave has a phase speed c = 0.9267 (gτ)¼. It is one of a family of solitary waves having speeds c [les ] 1.30 (gτ)¼. The maximum angle of inclination αmax of the free surface is a monotonically decreasing function of the speed c. Physical arguments suggest that αmax has a positive lower bound.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 451 - 470
Copyright
© 1989 Cambridge University Press

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