12 research outputs found
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 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
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On weakly turbulent scaling of wind sea in simulations of fetch-limited 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