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Nonlinear progressive edge waves: their instability and evolution

Published online by Cambridge University Press:  20 April 2006

Harry H. Yeh
Harry H. Yeh
Affiliation:
Department of Civil Engineering, University of Washington, Seattle, Washington 98195, U.S.A.
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Abstract

The fundamental properties of nonlinear progressive edge waves are investigated experimentally in a physical model with a uniformly and mildly sloping beach with a straight shoreline. An evolution equation for the envelope of progressive edge waves is the nonlinear Schrödinger (NLS) equation. It is found that the timescale of viscous-dissipation effects in the experiments is comparable with the timescale of the theoretical evolution process for inviscid progressive edge waves. This lack of timescale separation indicates a major shortcoming of the NLS equation as a model of the laboratory experiments. Even with this limitation, a uniform train of edge waves is found to be unstable to a modulational perturbation as predicted by the NLS equation. However, behaviour of the evolution is both qualitatively and quantitatively different from the theoretical predictions. The evolution of the periodogram for the unstable wavetrain shows an asymmetric development of the sidebands about the fundamental frequency; instability growth is limited to the lower sideband. This behaviour leads to a sequential shift of wave energy to lower frequencies as the waves propagate. It is found that a locally soliton-shaped wave packet is unstable in the laboratory environment. It is estimated that a much-larger-scale experimental facility is required to achieve inviscid experiments for the NLS equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 479 - 499
Copyright
© 1985 Cambridge University Press

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