1.300.90
0.50 r0.10 f-0.10
r-0.50
r-0.90
f-1.30
f-1.70 f0
4.1 Non-Linear Energy Transfer in Wind Wave Spectrum
91
a)
) A ""' """
~
- - 1
_,.2
X
3
I
I
I
I
I
I
I
I
0.16
0.32
0.48
0.8'>
0.80
0.96 Ci, Hz
Fig. 4.4. (a) Non-linear transfer function for the JONSWAP spectrum with 1 = 7:
1 - according to results (Hasselmann and Hasselmann, 1981); 2 - by the given
algorithm; 3 - calculated points (Fig. 4.4(b) see next page)
Thus, it can be concluded that this algorithm obtains sufficiently stable results of calculating the non-linear energy transfer integral with limited
computing time.
It should be noted that an explicitly analytical separation of the singularities ofintegrands (4.7), (4.8) in the form (4.9) and (4.11), as well as selection
of the corresponding quadrature formulas and use of the most accurate numerical integration methods are a successful "finding" for the numerical integration algorithm. Probably, this is the main difference of this approach in
comparison with those proposed by Polnikov (1988), Hasselmann and Hasselmann (1981), Masuda (1981), Komatsu and Masuda (1996). They preferred
"struggling" against the integrand singularities and performed integration
using less efficient methods.