New solutions of the C. S. Y. equation reveal increases in freak wave occurrence. (English) Zbl 1524.76053
Summary: In this article we study the time evolution of broad banded, random inhomogeneous fields of deep water waves. Our study is based on solutions of the equation derived by D. R. Crawford et al. [“Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves”, ibid. 2, No. 1, 1–16 (1980; doi:10.1016/0165-2125(80)90029-3)]. Our main result is that there is a significant increase in the probability of freak wave occurrence than that predicted from the Rayleigh distribution. This result follows from the investigation of three related aspects. First, we study the instability of JONSWAP spectra to inhomogeneous disturbances whereby establishing a wider instability region than that predicted by Alber’s equation. Second, we study the long time evolution of such instabilities. We observe that, during the evolution, the variance of the free surface elevation and thus, the energy in the wave field, localizes in regions of space and time. Last, we compute the probabilities of encountering freak waves and compare it with predictions obtained from Alber’s equation and the Rayleigh distribution.
MSC:
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 86A05 | Hydrology, hydrography, oceanography |
References:
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