Geodesic
Stability of Kolmogorov spectra for surface gravity waves
Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 3-9
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The Kolmogorov spectrum of waves on water is a result of cascading energy via four-wave interactions. For this spectrum in the isotropic case, we introduce basic small perturbations and calculate the decrement of their damping depending on the frequency. We confirm the stability of the Kolmogorov spectrum. The calculation results are applicable for analyzing the stability of numerical methods for solving the kinetic equation. We show that using the discrete-interaction approximation strongly reduces the damping in certain cases.
Keywords: wind wave, Kolmogorov spectrum, kinetic equation, stability. 
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     author = {V. V. Geogdzhaev},
     title = {Stability of {Kolmogorov} spectra for surface gravity waves},
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V. V. Geogdzhaev. Stability of Kolmogorov spectra for surface gravity waves. Teoretičeskaâ i matematičeskaâ fizika, Tome 203 (2020) no. 1, pp. 3-9. http://geodesic.mathdoc.fr/item/TMF_2020_203_1_a0/

[1] K. Hasselmann, “On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory”, J. Fluid Mech., 12 (1962), 481–500 | DOI | MR

[2] V. E. Zakharov, N. N. Filonenko, “Spektr energii dlya stokhasticheskikh kolebanii poverkhnosti zhidkosti”, Dokl. AN SSSR, 170:6 (1966), 1292–1295

[3] V. E. Zakharov, “Energy balance in a wind-driven sea”, Phys. Scr., 2010:T142 (2010), 014052, 14 pp. | DOI

[4] V. E. Zakharov, S. I. Badulin, “O balanse energii vetrovykh voln”, Dokl. RAN, 440:5 (2011), 691–695 | DOI

[5] A. M. Balk, “On the Kolmogorov–Zakharov spectra of weak turbulence”, Phys. D, 139:1–2 (2000), 137–157 | DOI | MR

[6] S. Hasselmann, K. Hasselmann, J. H. Allender, T. P. Barnett, “Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum. Part II: Parameterizations of the nonlinear energy transfer for application in wave models”, J. Phys. Oceanogr., 15:11 (1985), 1378–1391 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI