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1
1
2
1
0.5
0
1.5
0
0
−1
1
−1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
kH
kH
kH
S
k
1
1
1
1
0.5
0
0.5
0
0
−1
0
−1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
kH
kH
S
k
S
k
1
1
1
1
0
0
0
0
−1
−1
−1
−1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
kH
kH
S
k
S
k
1
1
2
2
0
0
1.5
1.5
−1
−1
1
1
−1
0
1
−1
0
1
1
1.5
2
1
1.5
2
A
s
A
s
f, Hz
f, Hz
Figure 5.15 As in
Figure 5.7
, with wind forcing. IMF
=
1
.
5Hz,IMS
=
0
.
30
,
U
/
c
=
3
.
9. Laboratory
statistics for the 20 steepest incipient breakers
negative, that is, the breakers do not tilt forward. Frequency remains a robust property and
stays in almost the same range of
f
19 IMF.
Therefore, while breaking is mainly a hydrodynamic process, wind, if present, does
influence incipient breaking. This is apparently achieved both through slowing down the
modulational-instability growth and directly. As was noticed in the numerical simulations,
this influence is small, but it is noticeable and diverse - from the shape-stabilising effect
when approaching breaking onset to the shape-randomising effect at the point of breaking.
=
1
.
11-1
.
5.1.4 Distance to the breaking
In this subsection, the probability of breaking of the monochromatic waves is analysed in
terms of the spatial extent of their evolution to the breaking occurrence. In this context,
differences between predicting the breaking within monochromatic wave trains and within
full-spectrum wave fields are discussed, as well as the issue of comparison of laboratory
breaking rates, which are based on deterministic detection of breaking onset, and statistical
field estimates for the progressive, rather than incipient breakers.
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