4 Study of Physical Mechanisms
Forming the Wind Wave Energy Spectrum
in Deep Water
Introduction. As has been noted, the study of different physical mechanisms
forming the wind wave spectrum is one of the central problems associated
with wave simulation. The source function in the right-hand side of the wave
energy balance equation reflects the formal representation of these mechanisms. At present there are many papers devoted to this problem. The most
detailed description can be found, for example, in the latest monographs published in Russia (Problems of Research and Mathematical Modeling of Wind
Sea, 1995) and in some other countries (Komen et al., 1994; Massel, 1996;
Young, 1999). There is no need to present all these results in detail, but the
most important aspects should be considered.
It is assumed in most wind wave models (Davidan et al., 1985; Problems
of Research and Mathematical Modeling of Wind Sea, 1995; Komen et al.,
1994; Ocean Wave Modeling, 1985) that the source function Gin deep water
includes additively three main components: Gin - wind wave energy input,
Gds - wave energy dissipation and Gnl - non-linear energy transfer within
the wave spectrum, caused by a four-wave resonance interaction between the
spectral components.
It is reasonable to consider the theoretical and practical importance of
the problem once more.
4.1 Non-Linear Energy Transfer
in Wind Wave Spectrum
4.1.1 Problem Review
The problem of non-linear energy transfer in the wind wave spectrum was
formulated by K. Hasselmann (1960, 1962, 1963, 1965, 1966) and V. Zakharov
(1968) in the 1960s. As a result of non-linear interaction, the wave spectrum
evolution equation can be written as follows:
a~;k) =Iff T(k,kt,k2,k3) 8(k+kl-k2 -k3) 8(a+al-0"2 -a3)
x {N2N3 (N + N1)- N1N (N2 + N3)} dk1 dk2 dk3,
(4.1)