Ocean swell within the kinetic equation for water waves

Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.Comment: Submitted to Journal of Geophysical Research 18 July 201

Universality of Sea Wave Growth and Its Physical Roots

Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on the effect of resonant nonlinear wave interactions. The authors assume that these effects are dominating and propose a simple relationship between instant wave steepness and time or fetch of wave development expressed in wave periods or lengths. This law does not contain wind speed explicitly and relies upon this asymptotic theory. The validity of this law is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.Comment: submitted to Journal of Fluid Mechanics 24-Sep-2014, 34 pages, 10 figure

On weakly turbulent scaling of wind sea in simulations of fetch-limited growth

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Weakly turbulent laws of wind-wave growth

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Numerical verification of weakly turbulent law of wind wave growth

Numerical solutions of the kinetic equation for deep water wind waves (the Hasselmann equation) for various functions of external forcing are analyzed. For wave growth in spatially homogeneous sea (the so-called duration-limited case) the numerical solutions are related with approximate self-similar solutions of the Hasselmann equation. These self-similar solutions are shown to be considered as a generalization of the classic Kolmogorov-Zakharov solutions in the theory of weak turbulence. Asymptotic law of wave growth that relates total wave energy with net total energy input (energy flux at high frequencies) is proposed. Estimates of self-similarity parameter that links energy and spectral flux and can be considered as an analogue of Kolmogorov-Zakharov constants are obtained numerically

Flux balance and self-similar laws of wind wave growth

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