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0.05
0
time, sec
−0.05
0
5
10
15
20
25
30
35
40
0.5
time, sec
0
0
1
0
2
0
3
0
4
0
5
0
6
0
1
0
−1
0
1
0
2
0
3
0
4
0
5
0
6
0
2
0
−2
0
10
20
30
40
50
6
0
1.8
1.6
1.4
1.2
0
10
20
30
40
50
60
no. of subsequent waves
Figure 5.13 As in
Figure 5.3
, with wind forcing. Segment of time series with IMF
=
1
.
5Hz
,
IMS
=
0
.
30
,
U
/
c
=
3
.
9. (top panel) Surface elevation
η
. (second top panel) Rear-face steepness
. (middle
panel) Skewness
S
k
(rear trough depth is used). (second bottom panel) Asymmetry
A
s
. (bottom
panel). Frequency (inverse period). IMF
=
.
1
5 is shown with solid line
probe 2 where data are recorded. With the wind superimposed, the waves of IMF
=
1
.
8Hz,
IMS
30 would break before this probe (see discussion in
Section 4.1
and
Figure 4.2
).
In
Figure 5.3
, the modulation depth
(5.3)
is
R
=
0
.
=
4 whereas in the current
Figure 5.13
it
is
R
9, i.e. the difference in the modulation depth is 1.4 times. Thus, we observe the
expected feature of smearing of the modulation by the wind (see
Trulsen & Dysthe
,
1992
).
This smearing is reflected in all other nonlinear properties shown in the figure. Steep-
ness (second panel), skewness (third panel) and asymmetry (fourth panel) are intentionally
plotted at the same vertical scale as those in
Figure 5.3
even though their range of oscil-
lations is now noticeably reduced. Because of the IMF change, the scale of the frequency
plot (bottom) could not be left the same, but scale limits were kept proportional to those in
Figure 5.3
. Reduction of the local frequency oscillations, moderated by the wind, is also
apparent.
The major features of breaking onset in the presence of wind forcing are shown in
Figures 5.14
,
5.15
and
5.16
. Visually, the breakers in
Figure 5.14
did not qualitatively
change compared to those in
Figure 5.5
with no wind. Quantitative properties, however,
were altered by the wind.
=
2
.
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