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..
CONCLUSIONS
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
l
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
obtained.
A good agreement between the Toba experimental data and our results obtained with the help of direct numerical
simulation is observed.
ACKNOWLEDGMENT .
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-
2156.
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