Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 46496 10.2205/2019ES000683 ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ On different approaches to statistical description of ocean waves On different approaches to statistical description of ocean waves Pushkarev Andrei Pushkarev Andrei dr.push@gmail.com Skoltech, Lebedev Physical Institute RAS ru Skoltech, Lebedev Physical Institute RAS ru 19 6 29 10 2021 https://rjes.ru/en/nauka/article/46496/view

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.

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 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 The authors declare that they have no conflicts of interest. This research was funded by Rissian Science Foundation, grant No 19-72-30028 and MIGO group. The authors gratefully acknowledge the support of these foundations.

Badulin, S., et al. (2007) , Weakly turbulent laws of wind-wave growth, J. Fluid Mech., 591, p. 339-378. Badulin, S., et al. (2007) , Weakly turbulent laws of wind-wave growth, J. Fluid Mech., 591, p. 339-378. Badulin, S. I., et al. (2005) , Self-similarity of wind-driven sea, Nonlinear Proc. in Geophysics, 12, p. 891-945. Badulin, S. I., et al. (2005) , Self-similarity of wind-driven sea, Nonlinear Proc. in Geophysics, 12, p. 891-945. 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. 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. Charnock, H. (1955) , Wind stress on a water surface, Q.J.R. Meteorol. Soc., 81, p. 639-640. Charnock, H. (1955) , Wind stress on a water surface, Q.J.R. Meteorol. Soc., 81, p. 639-640. 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). 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). Dyachenko, A. I., et al. (2015) , Evolution of one-dimensional wind-driven sea spectra, JETP Letters, 102, p. 577-581. Dyachenko, A. I., et al. (2015) , Evolution of one-dimensional wind-driven sea spectra, JETP Letters, 102, p. 577-581. Fedorenko, R. P. (1994) , Introduction into computational physics, Nauka, Moscow (in Russian). Fedorenko, R. P. (1994) , Introduction into computational physics, Nauka, Moscow (in Russian). 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. 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. 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. 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. 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. 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. 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. 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. Phillips, O. M. (1966{}) , The dynamics of the upper ocean, Cambridge monographs on mechanics and applied mathematics, 261 pp., U. P., Oxford. Phillips, O. M. (1966{}) , The dynamics of the upper ocean, Cambridge monographs on mechanics and applied mathematics, 261 pp., U. P., Oxford. 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. 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. SWAN: http://swanmodel.sourceforge.net/, 2015. SWAN: http://swanmodel.sourceforge.net/, 2015. Tolman H. L. (2013), User manual and system documentation of WAVEWATCH III, Environmental Modeling Center, Marine Modeling and Analysis Branch Tolman H. L. (2013), User manual and system documentation of WAVEWATCH III, Environmental Modeling Center, Marine Modeling and Analysis Branch 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. 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. 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/ 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/ 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. 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. Zakharov, V. E. (2010) , Energy balances in a wind-driven sea, Physica Scripta, T142, p. 014-052. Zakharov, V. E. (2010) , Energy balances in a wind-driven sea, Physica Scripta, T142, p. 014-052. Zakharov, V. E, S. I. Badulin (2011) , On energy balance in wind-driven sea, Doklady Akademii Nauk, 440, p. 691-695. Zakharov, V. E, S. I. Badulin (2011) , On energy balance in wind-driven sea, Doklady Akademii Nauk, 440, p. 691-695. Zakharov, V. E., N. N. Filonenko (1967) , The energy spectrum for stochastic oscillations of a fluid surface, Sov. Phys. Docl., 11, p. 881-884. Zakharov, V. E., N. N. Filonenko (1967) , The energy spectrum for stochastic oscillations of a fluid surface, Sov. Phys. Docl., 11, p. 881-884.