We describe the main regimes of the wind wave dynamics, which correspond to the continuity of the fluxes of the wave momentum, energy, and action, on the basis of the wave turbulence theory. Basing on the experimental data about the wave growth, the energy flux into the largescale range (inverse cascade within the wave turbulence theory) is evaluated. The intensity of the direct energy cascade to the short-wave range is estimated basing on experimental parameterization of the wind wave frequency spectra, which corresponds to the Kolmogorov—Zakharov spectrum E(ω) ∝ ω−4. The obtained estimates show that intensity of the direct cascade exceeds that of the inverse one by two orders of magnitude. An approximate solution for the direct energy cascade is found as a perturbation of the classical Zakharov—Zaslavsky solution for the inverse cascade with a zero energy flux. The results are discussed in correlation with the development of spectral wind wave models.
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References
L. Cavaleri, J.-H. G. M. Alves, F. Ardhuin, et al., Progr. Ocean., 75, 603 (2007).
K. Hasselmann, J. Fluid Mech., 12, 481 (1962).
V. E. Zakharov and N. N. Filonenko, Dokl. Akad. Nauk SSSR, 170, 6, 1292 (1966).
V. E. Zakharov and M. M. Zaslavsky, Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana, 18, 9, 970 (1982).
V. V. Geogdzhaev and V. E. Zakharov, JETP Lett., 106, No. 184, 3, 184 (2017).
S. Kitaigoroskii, Izv. Akad. Nauk SSSR, Ser. Geofiz., 1, 105 (1962).
Y. Toba, J. Oceanogr. Soc. Japan, 29, 209 (1973).
J. A. Battjes, T. J. Zitman, and L. H. Holthuijsen, J. Phys. Oceanogr., 17, No. 8, 1288 (1987).
K. Hasselmann, T. P. Barnett, E. Bouws, et al., Dtsch. Hydrogh. Zeitschr. Suppl., 12, No. A8 (1973).
M. A. Donelan, J. Hamilton, and W. H. Hui, Phil. Trans. Roy. Soc. Lond. A, 315, 509 (1985).
G. S. Golitsyn, Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana, 46, 1, 10 (1982).
S. I. Badulin, A. N. Pushkarev, D. Resio, and V. E. Zakharov, Nonlin. Proc. Geophys., 2, 891 (2005).
S. I. Badulin, A. V. Babanin, D. Resio, and V. E. Zakharov, J. Fluid Mech., 591, 339 (2007).
S. I. Badulin, A. V. Babanin, D. Resio, and V. E. Zakharov, Proc. IUTAM Symposium, Moscow, 25–30 August 2006, Springer, New York, 6, 175 (2008).
E. Gagnaire-Renou, M. Benoit, and S. I. Badulin, J. Fluid Mech., 669, 178 (2011).
V. E. Zakharov, Procedia IUTAM. 2018. V. 26. IUTAM Symposium Wind Waves, September4–8, 2017, London, p. 43.
V. E. Zakharov and S. I. Badulin, Doklady Earth Sci., 440, 1440 (2011).
V. E. Zakharov, Eur. J. Mech. B/Fluids, 18, 327 (1999).
A. Pushkarev and V. Zakharov, Ocean Modelling, 103, 18 (2016).
K. Hasselmann, D. B. Ross, and P. Müller, J. Phys. Oceanogr., 6, 200 (1976).
Y. Toba, J. Oceanogr. Soc. Japan, 28, 109 (1972).
V. E. Zakharov and M. M. Zaslavsky, Izv. Akad. Nauk SSSR, Ser. Fiz. Atm. Okeana, 19, No. 4, 406 (1983).
S. Abdalla and L. Cavaleri, J. Geophys. Res., 107, No. C7, 3080 (2002).
R. L. Snyder, F. W. Dobson, J. A. Elliot, and R. B. Long, J. Fluid Mech., 102, 1 (1981).
W. J. Plant, J. Geophys. Res., 87, No. C3, 1961 (1982).
R. W. Stewart, Boundary-Layer Meteorol., 6, 151 (1974).
M. A. Donelan and W. J. Pierson Jr., J. Geophys. Res., 92, No. C5, 4971 (1987).
S. V. Hsiao and O. H. Shemdin, J. Geophys. Res., 88, No. C14, 9841 (1983).
V. E. Zakharov and M. M. Zaslavsky, Izv. Akad. Nauk USSR, Ser. Fiz. Atm. Okeana, 19, No. 3, 282 (1983).
S. L. Weber, J. Phys. Oceanogr., 24, 1388 (1994).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 8–9, pp. 614–621, August–September 2018.
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Badulin, S.I., Geogdzhaev, V.V. Evaluation of Wind Wave Growth Parameters Basing on Spectral Fluxes. Radiophys Quantum El 61, 545–552 (2019). https://doi.org/10.1007/s11141-019-09915-8
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DOI: https://doi.org/10.1007/s11141-019-09915-8