We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr¨odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.

Interaction of two quasi-monochromatic waves in shallow water

ONORATO, Miguel;OSBORNE, Alfred Richard;SERIO, Marina
2003-01-01

Abstract

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr¨odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.
2003
15
12
3871
3874
Mechanics of Materials; Computational Mechanics; Physics and Astronomy (all); Fluid Flow and Transfer Processes; Condensed Matter Physics
Onorato, M; Ambrosi, D.; Osborne, A.R.; Serio, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1619746
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