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0.04
0.02
0
−0.02
−0.04
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0.04
0.02
0
−0.02
−0.04
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, sec
Figure 5.1 Time series of surface elevations
η
measured at the first wave probe. (top panel) Waves
of
U
/
c
=
0andIMF
=
1
.
6 Hz for different IMS: 0.31 (solid line), 0.25 (dashed line), 0.23 (dotted
line). (bottom panel) Waves of IMS
=
0
.
23 and IMF
=
1
.
6 Hz under different wind forcing:
U
/
c
=
0
(solid line),
U
/
c
=
.
4 (dashed line),
U
/
c
=
1
11 (dotted line)
at the first and the second
wave probes are shown. All the waves in these time series are generated with the same
initial monochromatic frequency IMF
In
Figures 5.1
and
5.2
, time series of surface elevations
η
=
.
1
6 Hz, but with different initial steepness IMS
and wind forcing
U
c
, as indicated.
At the first probe (
Figure 5.1
), 4
/
55m from the wavemaker, the waves are still near-
monochromatic, with only marginal modulation due to developing instabilities and perhaps
some parasitic modes present in the tank (i.e. non-potential parts of the oscillations gen-
erated by the paddle, seiches etc.). The latter, if present, are part of the background noise
from which the necessary modulational modes will grow in
Figure 5.2
, as dictated by
M
I
(5.1)
(see e.g.
Reid
,
1992
;
Babanin
et al.
,
2007a
,
2010a
).
The top subplot of
Figure 5.1
has zero wind forcing. Waves with three different
IMS
.
31 (solid line), 0.25 (dashed line) and 0.23 (dotted line) are shown. Differences
other than those due to the initial wave height are hardly distinguishable.
In the bottom subplot, waves of IMS
=
0
.
23 are plotted with no wind forcing (solid
line, for cross-reference with the top panel),
U
=
0
.
/
c
=
1
.
4 (dashed line) and a very strong
wind of
U
/
c
=
11 (dotted line). The effect of the wind on the profile of the mechanically
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