It should be noted that the results presented in Table 1 are in general agreement with (Pushkarev et al., 2002), in
which the following estimations are obtained: for isotropic case: 0.35 < α0 < 0.45 and for non-isotropic one:
0.33 < α 0 < 0.37 and 0.18 < α1 < 0.27 .
The discrepancies between the above mentioned results and ours can be explained as follows. In (Pushkarev et al.,
2002) there are some differences between the values α 0 for isotropic and non-isotropic cases, whereas the values
α 0 should be constant according to its definition. It should be noted that these estimations are obtained within a
more wider confidence interv al and only for two angular distributions. In our computation numerical simulations for
four angular distributions are produced: from isotropic to a very narrow one typical for wind wave generation.
Another reason of the discrepancies can be explained by the fact that there is no evidence that fully stabilized
numerical solution is obtained. (Pushkarev et al., 2001). Moreover, our estimations can be considered to be more
accurate due to the fact that a more precise numerical algorithm and more fine angular resolution are used.
5. COMPARISON WITH TOBA SPECTRUM
Toba (1973) made careful measurements of the spectrum tale and found out that the following approximation
describes a spectrum:
S (ω) = δ g U* ω-4
(26)
where
It is interesting to make a comparison between the Toba spectrum and the Kolmogorov one (17) or (19). In order to
do it the wave energy flux (22) should be defined. It includes the value of wave energy dissipation in a high
frequency range, which is unknown. It can be estimated, supposing that the wind input energy flux is expended to
support the high frequency energy flux directed to a high frequency range of wave spectrum:
ωf
π
∫ ∫ f (ω, β) S (ω, β) dω d β
P=
(27)
- π ωmin
The wind wave input energy increment f can be estimated using a traditional approximation [Kome n et al., 1994] .
It is defined as follows:
ρa 28U*
f ( ω, β) = max0; 0.25
ω
cos(β - βU ) - 1,
(28)
ρW c
where ρa and ρw is a density of air and water, correspondingly.
The angular-frequency spect rum approximation should be substituted into (22) in order to define the energy flux
(22). Unfortunately an angular distribution of the Toba spectrum is unknown. Nevertheless it can be suggested that it
is rather wide in high frequency range. The following estimation can be obtained for the isotropic frequency
dependent spectrum:
ωf
28U *ω
∫
∫
P≅
f (ω ) S (ω) dω = 0.25 ⋅ 10-3δgU*
ω -3
g - 1 dω
(29)
ω
ω >g 28U
min
*
Thus, the energy flux can be estimated as:
2
28 U *
-3
P ≅ 0.125 ⋅10
δgU *
g
(30)
Using (19) and (25), the first Kolmogorov constant can be estimated as follows:
S (ω) ω4
δgU *
= 2.17 δ2 3 = 0.33
α0 =
=
(31)
g 4 3P1 3
4 33
3
98 δU * / g
0.1g
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