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The effects of truncation on surface-wave Hamiltonians

Published online by Cambridge University Press:  26 April 2006

D. Michael Milder
D. Michael Milder
Affiliation:
Areté Associates, P.O. Box 6024, Sherman Oaks, CA 91413, USA
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Abstract

The Hamiltonian form of the equations for surface waves can generate very nonlinear, realistic-looking solutions even when the Hamiltonian is truncated to low order – two or three terms – in its slope expansion. A perturbation analysis of these equations shows that most of the basic fluid behaviour is retained in the low-order terms; however, the lowest-order nonlinear equations become dramatically unstable at wavenumbers greater than g/w2, where w is the local vertical surface velocity. One more term in the Hamiltonian mitigates this instability, extending the regime of stable slopes and wavenumbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 249 - 262
Copyright
© 1990 Cambridge University Press

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