4.2. Isotropic case
The value α 0 can be determined in isotropic case as follows:
S ( ω) ω4
α0 = 4 3 1 3
(24)
g P
According to the weak turbulence theory, the value α 0 is a constant, not depending on ω. As our estimates show:
α 0 = 0.303 0.033 for time moment t>20000 sec.
4.3. Non-isotropic case
Similar numerical simulations of the non -linear spectrum evolution are fulfilled for non-isotropic source function
generating wave energy (12) with different values of the parameters n and A.
The time evolution of wave integral parameters (i.e. total energy, wave action and momentum) is shown in Fig.3. A
full stabilization of these parameters is observed at t ≥ 10000 sec.
1
2
2
3
1000
100
10
1
0.1
0.01
0.001
0.0001
1e-005
1e-006
1e-007
t(sec)
1e-008
100
1000
10000
Tim e (s ec )
Fig.3
Time evolution of : 1- total energy, 2- wave action; 3 - momentum
Estimation results of the limited spectrum at t=20000 sec. for the most narrow angular distribution are presented in
Fig.4 (frequency spectrum) and Fig.5 (frequency-angular spectrum). It should be pointed out that the main features
of the frequency spectrum are nearly the same as in the isotropic case.
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