Comparing this value with that obtained with the help of d irect numerical simulations (see Tabl. 1) a conclusion can
be made that they are in a good agreement..
Direct numerical simulations of the Hasselmann kinetic equation for gravity waves in water surface confirms basic
predictions of the weak-turbulent theory. The kinetic equation for surface gravity waves is investigated numerically
taking into account an external generating force and dissipation. An efficient numerical algorithm for simulating non-
linear energy transfer is used to solve the problem.
Three stages of wave development are revealed: unstable wave energy growth within a range of external force
impact, fast energy spectrum tail formation in high frequency range and establishment of a steady state spectrum. In
both isotropic and non -isotropic cases the spectra are found out to be cose to the Zakharov-Filonenko spectrum
ω -4 in the universal range. Reliable estimations of the Kolmogorov constants are found out. Formation of this
asymptotic spectrum happens explosively. Accurate estimations of the first and second Kolmogorov constants are
A good agreement between the Toba experimental data and our results obtained with the help of direct numerical
simulation is observed.
The authors thank Dr. A.Pushkarev for fruitful discussions. The research presented in this paper was conducted
under the US Army Corps of Engineers, RDT&E program, grant DACA 42-00-C0044, ONR grant N 00014 -98-1-
0070, NSF grant NDMS0072803, RFBR 01-05-64846, INTAS-99- 666, INTAS-01-25 , NTAS-01-234., INTAS-01-
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