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The superharmonic instability of Stokes waves in deep water

Published online by Cambridge University Press:  26 April 2006

W. J. Jillians
W. J. Jillians
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA Present address: Department of Aerospace Engineering, University of Southern California, Los Angeles CA 90089, USA.
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Abstract

The method of Tanaka (1983) is used to solve the eigenvalue problem determining the form of the first superharmonic instability of periodic Stokes waves. Comparisons are made with other approaches to this problem and a discussion of the advantages of Tanaka's method is given. The accurately resolved eigenfunction solution is then taken as the initial state for commencing the computational time-stepping method of Dold & Peregrine (1985), by which we investigate the full nonlinear development of the growing and decaying modes of this instability. It is observed that all unstable modes develop to breaking in the periodic regime and this result is compared and contrasted with the solitary wave case.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 563 - 579
Copyright
© 1989 Cambridge University Press

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