Numerical simulation of surface waves instability on a discrete grid

Abstract

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of propagating and standing waves. We studied separately pure capillary wave unstable due to three-wave interactions and pure gravity waves unstable due to four-wave interactions. The theoretical description of instabilities in all cases is included into the article. The numerical algorithm used in these and many other previous simulations performed by authors is described in details.

47 pages, 40 figures

References in corpus (4)

• Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
• Branch cuts of Stokes wave on deep water. Part I: Numerical solution and Padé approximation
• Modulation instability and capillary wave turbulence
• Influence of the condensate and inverse cascade on the direct cascade in wave turbulence

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