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Large-scale modulations of edge waves

Published online by Cambridge University Press:  20 April 2006

T. R. Akylas
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

The temporal and spatial evolution of large-scale modulations of weakly nonlinear edge waves on a uniformly sloping beach is studied using the full water-wave formulation for beach angles α = π/2N. Equations governing the evolution of envelopes of edge waves, excited by resonant interactions with incident wavetrains, are derived. It is deduced that a uniform train of free periodic edge waves is always unstable to large-scale variations, so that envelope solitons will develop; the resulting three-dimensional solitons are described in detail. In addition, it is shown that steady-state standing subharmonic edge waves, excited by incident wavetrains on a long, mildly sloping beach, can be unstable to large-scale modulations. The possible physical significance of these findings is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 197 - 208
Copyright
© 1983 Cambridge University Press

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