180
5 Wave Evolution in Non-uniform Currents in Deep Water
J
X
2
, . , I I
\xJ
\"
+-+ f
---------. 2
·--4 3
· - - · 4
\,./
<>-----<> 5
0
(i
7
Fig. 5.11. Spectra evolution in countercurrent with Vrn
0.25 at points with
different velocities v: 1 ~ 0.10; 2 ~ 0.15; 3 ~ 0.175; 4 ~ 0.20; 5 ~ 0.225
Numerical estimation results of non-linear energy transfer in the
rip spectrum.
In order to estimate numerically the non-linear energy
transfer in the rip spectrum in the form (5.33) the algorithm described in
Sect. 4.1 can be used. Numerical estimations of the non-linear energy transfer ( 4.1) are integrated over the directions for different stages of spectrum
development. The results for the following current points: v = 0.10; v = 0.15;
v = 0.175; v = 0.20; v = 0.225 are shown in Fig. 5.12.
The function value Cnl (see Fig. 5.12) is normalized in the following way:
Gnl(a) = Gn!(a) (S 3 (amax)a;;ax/gr
1 ,
(5.36)
where a= a/amax·
The form of the function Gnl is similar to the non-linear transfer functions
in the wind wave spectrum. A positive energy transfer is mainly observed at
frequencies smaller than the second spectrum maximum. There is a negative
function value, becoming positive again for larger frequencies. The function