Numerical Simulations of Modulated Waves in a Higher-Order Dysthe Equation

The nonlinear stage of the modulational (Benjamin–Feir) instability of unidirectional deep-water surface gravity waves is simulated numerically by the fifth-order nonlinear envelope equations. The conditions of steep and breaking waves are concerned. The results are compared with the solution of the...

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Bibliographic Details
Published inWater Waves An interdisciplinary journal Vol. 2; no. 1; pp. 59 - 77
Main Authors Slunyaev, Alexey, Pelinovsky, Efim
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2020
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Summary:The nonlinear stage of the modulational (Benjamin–Feir) instability of unidirectional deep-water surface gravity waves is simulated numerically by the fifth-order nonlinear envelope equations. The conditions of steep and breaking waves are concerned. The results are compared with the solution of the full potential Euler equations and with the lower-order envelope models (the 3-order nonlinear Schrödinger equation and the standard 4-order Dysthe equations). The generalized Dysthe model is shown to exhibit the tendency to re-stabilization of steep waves with respect to long perturbations.
ISSN:2523-367X
2523-3688
DOI:10.1007/s42286-019-00011-y