Water Wave Packets Over Variable Depth
In this paper, we develop higher-order nonlinear Schrödinger equations with variable coefficients to describe how a water wave packet will deform and eventually be destroyed as it propagates shoreward from deep to shallow water. It is well-known that in the framework of the usual nonlinear Schrödinger equations, a wave packet can only exist in deep water, more precisely when kh > 1.363 , where k is the wavenumber and h is the depth. Using a combination of asymptotic analysis and numerical simulations we find that in the framework of the higher-order nonlinear Schrödinger equations, the wave packet can penetrate into shallow water kh < 1.363 or not even reach kh > 1.363 , depending on the sign of the initial value in deep water of a certain parameter of the wave packet that measures its speed.
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Document Type: Research Article
Affiliations: Loughborough University
Publication date: May 1, 2011