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Source publication
The problem of spectra interpretation of nonlinear shallow water waves is studied in terms of interacting Korteweg-de Vries (KdV) solitons and quasi-linear wavetrains. The method of data processing of random wave field is suggested and illustrated by an example. The soliton component obscured in the random wave field can be determined either on the...
Contexts in source publication
Context 1
... now the approach described above to the random initial perturbation arti- ficially generated and presented in Fig. 1. This perturbation has been obtained by means of the inverse Fourier transform of the series of 128 Fourier harmonics having random phases in the interval [0, 2í µí¼] and amplitudes distributed in accordance with the formula (see Fig. 2) ...
Context 2
... wave spectrum, S(ω) ω lim For the creation of the quasi-random wave field it was taken only the low-frequency and most energetic part of this spectrum, 0 ≤ í µí¼ ≤ í µí¼ í µí±í µí±í µí± , where í µí¼ í µí±í µí±í µí± = 0.767 s −1 (see the vertical dashed line in Fig. 2). The limiting frequency, í µí¼ í µí±í µí±í µí± , was chosen for the following reasons. The dispersion relation for the TKdV Eq. (1) ...
Citations
... In the meantime, the knowledge of number of solitons obscured in the random wave field, their parameters and statistics is a matter of independent interest per se. We describe our approach below in detail and give some examples (preliminary results were reported at the conference OCEANS'13 MTS/IEEE in San Diego, USA [11]). ...
... 11 ...
Interpretation of random wave field on a shallow water in terms of Fourier spectra is not adequate, when wave amplitudes are not infinitesimally small. A nonlinearity of wave fields leads to the harmonic interactions and random variation of Fourier spectra. As has been shown by Osborne and his co-authors, a more adequate analysis can be performed in terms of nonlinear modes representing cnoidal waves; a spectrum of such modes remains unchanged even in the process of nonlinear mode interactions. Here we show that there is an alternative and more simple analysis of random wave fields on shallow water, which can be presented in terms of interacting Korteweg - de Vries solitons. The data processing of random wave field is developed on the basis of inverse scattering method. The soliton component obscured in a random wave field is determined and a corresponding distribution function of number of solitons on their amplitudes is constructed. The approach developed is illustrated by means of artificially generated quasi-random wave field and applied to the real data interpretation of wind waves generated in the laboratory wind tank.
