Abstract
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 Schrodinger 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.
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