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In-Depth Information
10
0
10
−10
10
−1
10
0
10
1
10
0
10
−10
10
−1
10
0
10
1
1
0.5
0
10
−1
10
0
10
1
100
0
−100
10
−1
10
0
10
1
frequency
Figure 4.6 Numerical simulations (see
Figure 4.5
). Dimensionless wave period is 1. Co-spectra of
running skewness and asymmetry for waves of IMS
=
0
.
13
,
U
/
c
=
10
.
0, 19 wave periods to break-
ing. (top panel) Skewness spectrum. (second top panel) Asymmetry spectrum. (second bottom panel)
Coherence spectrum. (bottom panel) Phase spectrum (in degrees), positive phase means asymmetry
is leading. Dashed line shows 90
◦
phase shift
Figure 4.7
shows a composite set of fetch-versus-steepness dependences for different
values of wind forcing
U
11. The fetch is expressed in dimensionless terms of
number of wavelengths to breaking at a particular IMS
/
c
=
1
−
ak
.
As shown in
Babanin
et al.
(
2007a
), a wave with no superimposed wind forcing and
IMS
=
1 will never break, even though it will exhibit oscillations of steepness, asym-
metry and skewness similar to those shown in
Figures 4.1
,
4.2
and
4.5
. The evolution of
such waves is not plotted in the figure, and in fact we do not plot IMS
<
0
.
17 because such
development to breaking is too slow for the purpose of demonstration. The upper limit of
steepness included is IMS
<
0
.
3 will break immediately, within
one wavelength/period. Between these two limits, the dimensionless distance to breaking
decreases with increasing IMS.
Figure 4.7
allows the estimation, based on numerical simulations with the CS model,
of when a two-dimensional wave breaks. For example, it will take a wave of IMS
=
0
.
28 as waves with IMS
>
0
.
=
0
.
24
six wavelengths to reach the point of breaking under
U
/
c
=
8
.
5, and 11 wavelengths
under
U
/
c
=
8
.
0, and 11 wavelengths under
U
/
c
=
7
.
5. If wind forcing is reduced
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