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A further complication in comparing field spectral data with predictions of the param-
eterisation (5.10) results from the fact that the latter predicts the probability of incipient
breaking, whereas in the field we can only measure quantities that result from the breaking
process. Therefore, the probability of encountering such breaking in progress is higher than
the probability of breaking onset (see Liu & Babanin , 2004 , and Chapter 2 ). These diffi-
culties and uncertainties have been mentioned on a number occasions above, most notably
in Section 5.1.4 .
Given the uncertainties, comparison of the parameterisation (5.10) with field data can
only be qualitative, as the quantities being compared are not identical. In order to conduct
the comparison, the Black Sea data set of Babanin et al. ( 2001 ) was considered. Based
on visual observations of whitecapping, this data set provides information on the prob-
ability of breaking b T of dominant waves (see Table 5.1 ). Dominant waves are defined
in the spectral sense as those having frequencies near the spectral peak frequency f p ,
i.e. f
3 f p (2.6) . In the present context, b T can be approximately related to the
non-dimensional distance to breaking N by
=
f p ±
0
.
b T
1
/
N
.
(5.26)
b T as a function of the peak spectral steepness (5.17) .
An approximation to the data shown in the figure, consistent with the functional form of
relationship (5.24) between N and IMS is
1
b T =−
Figure 5.17 (bottom) shows 1
/
10 atanh
(
13
.
3
( peak
0
.
13
)) +
17
,
for 0
.
055
peak
0
.
205
.
(5.27)
The lower limit (no breaking if
055) is obtained from the experimental data
( Banner et al. , 2000 ; Babanin et al. , 2001 ) and the upper limit (
peak <
0
.
205) is obtained
by extrapolating the parameterisation developed in Babanin et al. ( 2001 ) to the 100%
breaking condition.
Thus, we conclude that the distance before breaking occurs, which is related to the break-
ing probability, is a function of the background mean wave steepness in the wave train/field.
In the latter case, this concept/analogy can only be applied to the dominant waves. Another
potential method of estimating the breaking rates of dominant waves, based on measure-
ments of ensemble-average asymmetry (1.3) in the wave trains, without having to actually
detect the breaking events, will be discussed in Section 7.3.3 (see parameterisation (7.19) ).
Breaking of relatively short waves, i.e. waves of scales smaller than the dominant waves,
is a separate topic in many regards and will be discussed in Section 5.3.3 .
peak =
0
.
5.3.2 Breaking probability of small-scale waves
Breaking of waves shorter than those at the spectral peak is altered in a number of ways and
at smaller scales is perhaps driven by physics different to that of dominant-wave breaking.
Therefore, this subsection of the spectral-breaking section is important and is necessarily
large, and needs a summary overview to begin with.
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