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
Subjects
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Original Article
Partial Differential Equations
Modulated waves
Modulational instability
High-order theory
Dysthe equation
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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