3.2 Estimation of spectral front propagation
In wave spectrum the evolution of two effects can be observed: a relatively slow growth of spectra in the forcing
range and a fast "front propagation" to area of high wave numbers. It is a self-accelerating process. In paper (Komen
et al., 1994), this concept is used to explain high frequency spectrum formation and the migration of the spectral peak
towards lower frequencies.
A formation of the stationary spectra occures within a finite time interval. At the same time the wave energy
propagation to high frequency range is observed. The speed of this propagation can be estimated as a shift of the
spectral frequency front into high wave numbers (Fig. 2). The spectral frequency front is defined as a high frequency
("cut-off frequency"), with spectral density value being one order smaller in comparison with the limited spectrum
solution for a given frequency within the range ω f
< ω < ω p . The same effect is described in paper (Donelan et
al., 1985).
ω front
16
1
2
12
8
4
t(sec)
0
8000
12000
16000
20000
T ime (s )
Fig.2
Propagation of spectral frequency front ωfront into high frequency range
1 - data approximation (16), 2 numerical data;
According to theoretical estimations ( akharov et. al, 1992), the front propagation is approximated using a self-
Z
similar solution of the equation (1):
(
)
S (ω, t) ≅ (t0 - t )4 3 R ω(t0 - t )1 3
(15)
Hence, the "cut-off frequency" is increased explosively: