We analyze well-known model for wind energy input and wave-breaking absorption in energy transfer equation via its numerical comparison with recently developed alternative model. The comparison is done for time and space-independent velocity of the wind for the waves growing along the fetch coordinate. Significant differences have been found for integral as well as spectral characteristics of these models. It is shown that slight modification of the analyzed model significantly improves its properties and provides better description of the physical situation.
Ocean wind waves, statistical descriptions of waves, energy transfer equation, wave energy spectra, nonlinear wave-wave interaction, wind input term, dissipation due to wave-breaking
1. Badulin, S., et al. (2007) , Weakly turbulent laws of wind-wave growth, J. Fluid Mech., 591, p. 339-378.
2. Badulin, S. I., et al. (2005) , Self-similarity of wind-driven sea, Nonlinear Proc. in Geophysics, 12, p. 891-945.
3. Banner, M. L., R. Young (1975) , Modeling Spectral Dissipation in the Evolution of Wind Waves. Part I: Assessment of Existng Model, JPO, 24, p. 5-6.
4. Charnock, H. (1955) , Wind stress on a water surface, Q.J.R. Meteorol. Soc., 81, p. 639-640.
5. Donelan, M. A., et al. (2012) , Modeling waves and wind stress, Journal of Geophysical Research: Oceans, 117, p. C00J23, https://doi.org/10.1029/2011JC007787 (http://dx.doi.org/10.1029/ 2011JC007787).
6. Dyachenko, A. I., et al. (2015) , Evolution of one-dimensional wind-driven sea spectra, JETP Letters, 102, p. 577-581.
7. Fedorenko, R. P. (1994) , Introduction into computational physics, Nauka, Moscow (in Russian).
8. Gagnaire-Renou, E., et al. (2011) , On weakly turbulent scaling of wind sea in simulations of fetch-limited growth, Journal of Fluid Mechanics, 669, p. 178-213, https://doi.org/10.1017/S0022112010004921.
9. Hasselmann, K. (1962) , On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory, Journal of Fluid Mechanics, 12, p. 481-500.
10. Kats, A. V., V. M. Kontorovich (1974) , Anisotropic turbulent distributions for waves with a non-decay dispersion law, Soviet Physics JETP, 38, p. 102-107.
11. Kats, A. V., V. M. Kontorovich, et al. (1975) , Power like solutions of the kinetic Boltzmann equation for distributions 20 of particles with spectral fluxes, JETP Letters, 21, p. 5-6.
12. Phillips, O. M. (1966{}) , The dynamics of the upper ocean, Cambridge monographs on mechanics and applied mathematics, 261 pp., U. P., Oxford.
13. Pushkarev, A., V. Zakharov (2016) , Limited fetch revisited: comparison of wind input terms, in surface wave modeling, Ocean Modeling, 103, p. 18-37, https://doi.org/10.1016/j.ocemod.2016.03.005.
14. SWAN: http://swanmodel.sourceforge.net/, 2015.
15. Tolman H. L. (2013), User manual and system documentation of WAVEWATCH III, Environmental Modeling Center, Marine Modeling and Analysis Branch
16. Tolman, H. L., D. Chalikov (1996) , Source Terms in a Third-Generation Wind Wave Model, Journal of Physical Oceanography, 26, p. 2497-2518, https://doi.org/10.1175/1520-0485(1996)026%3C2497:STIATG%3E2.0.CO;2.
17. Tracy, B. and D. Resio (1982), Theory and calculation of the nonlinear energy transfer between sea waves in deep water, WES report 11, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS/
18. Zakharov, V., et al. (2017) , Balanced source terms for wave generation within the Hasselmann equation, Nonlin. Processes Geophys., 24, p. 581-597, https://doi.org/10.5194/npg-24-581-2017.
19. Zakharov, V. E. (2010) , Energy balances in a wind-driven sea, Physica Scripta, T142, p. 014-052.
20. Zakharov, V. E, S. I. Badulin (2011) , On energy balance in wind-driven sea, Doklady Akademii Nauk, 440, p. 691-695.
21. Zakharov, V. E., N. N. Filonenko (1967) , The energy spectrum for stochastic oscillations of a fluid surface, Sov. Phys. Docl., 11, p. 881-884.
