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Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear Schrödinger equation by K.L. Henderson; D.H. Peregrine; J.W. Dold is a Engineering article available to read on EtoBox.

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The time evolution of a uniform wave train with a small modulation which grows is computed with a fully nonlinear irrotational flow solver. Many numerical runs have been performed varying the initial steepness of the wave train and the number of waves in the imposed modulation. It is observed that the energy becomes focussed into a short group of steep waves which either contains a wave which becomes too steep and therefore breaks or otherwise having reached a maximum modulation then recedes until an almost regular wave train is recovered. This latter case typically occurs over a few hundred time periods. We have also carried out some much longer computations, over several thousands of time periods in which several steep wave events occur. Several features of these modulations are consistent with analytic solutions for modulations using weakly nonlinear theory, which leads to the nonlinear Schrödinger equation. The steeper events are shorter in both space and time than the lower events. Solutions of the nonlinear Schrödinger equation can be transformed from one steepness to another by suitable scaling of the length and time variables. We use this scaling on the modulations and find

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Author

K.L. Henderson; D.H. Peregrine; J.W. Dold

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0165-2125)

Published

1999

Language

EN

Field

Engineering (Physical Sciences)