Geoscience Reference
In-Depth Information
50
40
a)
30
20
10
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.3
b)
0.25
0.2
0.15
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
ε
Figure 5.35 a) As in
Figure 5.17
(the filled-circle wind-forced data points are omitted). b) Black Sea.
As in
Figure 2.3
. Figure is reproduced from
Babanin
et al.
(
2010a
) by permission
That is, with caution we will try to apply our modulational-instability results to the field
data. Another problem, of the technical kind, still prevents direct comparisons of breaking
rates obtained by means of
(5.10)
and field observations. Relationship
(5.10)
predicts the
probability of incipient breaking, whereas in the field it is impossible to directly measure
whether a wave is an incipient breaker or not. What is usually measured are quantities
which result from the breaking process whose probability is significantly higher than the
probability of breaking onset (e.g.
Liu & Babanin
,
2004
, see also
Sections 2.4
and
5.1.4
).
Qualitative comparisons of laboratory and field breaking-probability dependences were
made in
Babanin
et al.
(
2007a
) and featured well. Here, the
Babanin
et al.
(
2007a
) depen-
dence, already shown in
Figure 5.17
, is reproduced in the top panel of
Figure 5.35
for
comparison with the bottom panel which is the reproduced
Figure 2.3
. In this bottom panel,
we plot the frequency (inverse period) of individual dominant waves (from frequency range
of
f
3
f
p
) versus the steepness of these individual waves. This is done for a Black
Sea record with
f
p
=
f
p
±
0
.
25 Hz (Rec. 244 of
Table 5.1
)usedby
Babanin
et al.
(
2001
)to
obtain field breaking rates in the same frequency band.
If there were no shrinking of the wavelength prior to breaking, as described in
Section 5.1.1
, at each steepness the distribution of the frequencies around
f
p
=
=
0
.
0
.
25 Hz
would be approximately even. This is so for waves of
<
≈
0
.
12. For steeper waves,
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