Geoscience Reference
In-Depth Information
0.05
0
−0.05
0
10
20
30
40
50
60
70
0.5
0
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
1
0
−1
0
2
0
4
0
6
0
8
0
1
0
0
1
2
0
2
0
−2
0
20
40
60
80
100
120
2.5
2
1.5
0
20
40
60
80
100
120
no. of subsequent waves
Figure 5.3 Segment of a time series with IMF
=
1
.
8Hz
,
IMS
=
0
.
30,
U
/
c
=
0. a) Surface elevation
η
. b) Rear-face steepness
(1.1)
. c) Skewness
S
k
(
1.2
, rear trough depth is used). d) Asymmetry
A
s
(1.3)
. e) Frequency. IMF
=
1
.
8 Hz is shown by the solid line. The waves propagate from right to left.
Figure is reproduced from
Babanin
et al.
(
2007a
) by permission of American Geophysical Union
considering the waves shown propagating from right to left, as indicated by the arrow in
the figure.
The top panel in
Figure 5.3
shows the measured water surface elevation
as a func-
tion of time (horizontal axis). Interpreting this as a wave moving from right to left shows
that, within each wave group, the maximum value of the water-surface elevation gradually
decreases and then suddenly increases until a point, where breaking occurs. The saw-tooth
shape of the wave envelope once again indicates modulational instability as the mechanism
behind this behaviour of the nonlinear wave train (e.g.
Shemer & Dorfman
,
2008
). The
point of breaking was located immediately after the probe at a distance of 10
η
1m
from the wave maker. Each successive wave passing the wave gauge was analysed to deter-
mine its steepness, skewness, asymmetry and frequency, which are shown in the four panels
of
Figure 5.3
.
The major features seen in the numerical model are confirmed by the laboratory data.
The incipient breaking waves are the steepest waves in the wave train, with the steepness
oscillating in a periodic fashion. Skewness and asymmetry also oscillate, but behave in a
less ordered fashion. However, at the point of breaking skewness is positive (i.e. peaked up)
.
73
±
0
.
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