4.4 Influence of Mesoscale Effects on Wind Wave Evolution
151
low-frequency spectrum range produces a larger displacement of the spectral
maximum frequency to the low-frequency range.
A simplified approximation of the relative increase of non-linear energy
transfer due to quasi-oscillations can be derived from the ratios ( 4. 76) and
( 4. 77):
(4.78)
where F(p) = 1 f(;%), p = 211ln('y).
Thus, it is possible to assume that the relative increase of the non-linear
energy transfer does not depend on the quasi-oscillation period, but is governed by the oscillation amplitude of the spectral maximum 11 and the average
spectrum peakness 'Y· The function F = F(11) for various values of the parameter 'Y is shown in Fig. 4.26. It is monotonically increased with the growing
value 11 and the parameter 'Y· The value F is equal to 1.0 at "( = 1.0.
Since the peakness spectrum parameter 'Y ~ 1 decreases with developing
waves (Babanin&Soloviev, 1998), the JONSWAP spectrum for the great
fetch X transforms to the Pierson~ Moskowitz spectrum with 'Y = 1. The effect
of quasi-oscillation becomes smaller for a developed wind sea. For the wind
5.00
F
4
3
4.00
2
3.00
2.00
1.00
0.00 - + - - - - - - - , - - - , - - - - - - - , - - - - - - . - - - - r - - - - - ,
0.00
1.00
2.00
ll
3.00
Fig. 4.26. Relation between function F and parameter 11 for different average
spectrum peakness values ofT 1 ( <>) ~ 1 = 1.0; 2 (.6.) ~ 1 = 3.3; 3 ( o) - 1 = 7.0;
4 ( +) - 1 = 10.0