Geoscience Reference
In-Depth Information
Table 3.1 Summary of the Lake George data used. U 10 is
the wind speed at 10 m height, k p is the peak wavenumber,
a
4 is the standard deviation wave amplitude, d is the
water depth.
=
H s /
Record no.
U 10 , m/s
k p , rad/m
a , m
d , m
4
6.6
7.2
0.013
0.31
8
11.9
2.3
0.039
0.32
9
12.0
2.1
0.034
0.29
10
8.1
3.1
0.019
0.33
11
10.6
2.2
0.020
0.32
14
7.1
5.6
0.015
0.27
15
7.3
2.5
0.016
0.28
An example of such a wave record with the bottom-pressure-indicated breaking events
marked as vertical bars is shown in the upper panel of Figure 3.13 . Data records used
by Liu & Babanin ( 2004 ) were taken during the last stage of the Lake George study
when the lake became very shallow (see Table 3.1 ). Therefore, these records, if com-
pared to the deep Black Sea, represent the other end of wave development - bottom-
limited and strongly wind-forced waves, under winds of U 10 /
c p =
4
.
7-7
.
5, with peak
frequencies f p =
0
.
53-1
.
32 Hz (wavelengths
λ p =
0
.
9-3m), and significant wave height
H s of about 0
1m.
In Liu & Babanin ( 2004 ), the determination of the limiting fraction
.
in deep water
was based both on direct measurements of surface acceleration in the breaking waves
( Figure 3.15 ) and on comparisons of the ability of the measurements and the wavelet
breaking-detection technique to provide the same breaking statistics. The feasibility of
the approach was then verified by means of predicting the shallow water
γ
γ
on the basis of
knowledge of the deep-water limiting fraction. A reality check was also discussed.
It has always been obvious from general reasoning that once the wave collapse is in
progress, downward acceleration of the water particles on the breaking crest will be
determined by a ratio
in connection with the centrifugal acceleration of the particle and
gravitational acceleration g . The exact measure of
γ
, however, remained elusive. As was
mentioned earlier in this section, in studies which may already be regarded as classical
(i.e. Longuet-Higgins et al. , 1963 ; Snyder et al. , 1983 ) it has been enacted generally as
γ =
γ
.
5, although indirect inference of the acceleration based on laboratory ( Hwang et al. ,
1989 ) and field measurements ( Holthuijsen & Herbers , 1986 ; Srokosz , 1986 ) indicates that
the value of
0
should be 0.4 or even lower.
In the Black Sea, some of the breaking waves were measured by an accelerometer, and
therefore direct estimates of maximal acceleration
γ
α breaking , which is the a downward acceler-
ation in waves detected as those breaking ((see (2.50) , (2.59) , (2.60) ), for such a wave are
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