Geoscience Reference
In-Depth Information
H
max
2
a
≈
2
.
6
.
(5.15)
This ratio satisfies definition
(5.12)
of a freak wave and is apparently the highest wave
that can be achieved due to modulational instability if measurement
(5.14)
describes the
breaking onset precisely enough. Estimates of the individual-wave steepness in this meas-
urement, with account for the frequency increase
(5.8)
and corresponding wavelength
shrinkage, give
Hk
43, very close to the breaking-onset limit
(5.4)
, and therefore
the estimate
(5.14)
can be regarded as a good approximation of what happens at the break-
ing point. Such an observation therefore means that freak waves due to this mechanism
can only be produced in wave fields/trains with background steepness close to
(5.13)
, not
much lower or higher (see also Babanin
et al.
, 2011b).
In
Banner
et al.
(
2000
) and
Babanin
et al.
(
2001
), a similar mean-background-steepness
threshold was established for dominant waves in a continuous wave spectrum. This was
done on the basis of two deep-water and a finite-depth data set. The deep-water sets
included the Black Sea data (
Babanin
(
1995
), see
Section 3.7
) and Lake Washington
observations (
Katsaros & Atakturk
,
1992
), and the finite-depth measurements were those
conducted at Lake George (
Young
et al.
(
2005
), see
Section 3.5
). The overall range of the
dominant frequencies involved as a result was very broad:
f
p
=
/
2
≈
0
.
0
.
2-0
.
4 Hz for the Black
Sea,
5 Hz for Lake George. Also,
two deep-water data points from the Southern Ocean were included with
f
p
<
f
p
>
0
.
5 Hz for Lake Washington, and
f
p
=
0
.
3-0
.
0
.
1Hz.The
ten-metre reference wind speed
U
10
ranged from 3 to 20m
/
s, and the dimensionless depth
of Lake George - from deep water down to values of
k
p
d
=
0
.
7(see
Young & Babanin
,
2006b
).
The Black Sea data are tabulated in
Table 5.1
. The experimental arrangement involved
visual surveillance of waves passing over a wave probe, with collocated breaking events
labelled electronically by an observer. With this data, it was possible to investigate the
distribution of breaking probability with respect to the distance from the spectral peak.
The first 12 records (
Table 5.1
) were obtained in 1993 from the research vessel “Profes-
sor Kolesnikov” (henceforth PK) operated by the Marine Hydrophysical Institute (MHI) in
Sebastopol.
The PK wave data were recorded using an accelerometer buoy, as described by
Babanin
et al.
(
1993
). Briefly, the buoy diameter was 0
.
58m and its operational bandwidth was
0
0 Hz, which easily covered the wave frequencies of interest. It was deployed around
100m from the ship to avoid any interference between the ship and the wind and wave
fields. Record lengths of 34 min to 68 min were acquired using a sampling frequency of
4 Hz. An observer watched the buoy from the vessel and triggered an electronic signal to
register the passage of a whitecap over the buoy. This signal was recorded synchronously
with the buoy data. The observer varied the duration of the electronic label according to the
geometrical size of the whitecap, providing an approximate indication of individual breaker
dimensions for future analysis. The observer was about 10m above sea level, allowing
a clear view of whitecaps with scales down to the size of the buoy. The environmental
data collected simultaneously included 10-minute averages of the 10m wind speed and
.
08-1
.
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