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It should also be pointed out at this stage that the
T
∗
property of
Figure 8.4
a, taken at
b
t
=
5, should not be interpreted as the breaking rate. First of all, as noted above, waves
falling below the threshold may or may not break and thus may or may not contribute
to the rate. Secondly,
T
∗
is related to a relative duration of breaking 'ringing' (over the
wave period) rather than to a number of breakers, the former being an unknown function of
environmental properties such as breaking severity, wind speed, perhaps water temperature
and others (see e.g.
Bortkovskii
,
1997
, and
Section 3.1
for further discussions). And finally,
if
T
∗
is attempted to compare breaking rates for different records, the spectral distribution
of breaking events may become an issue. For example, if for
U
10
2
.
s it is mostly
peak waves that are breaking and for the other records these are waves above the spectral
peak, there will be different duration
T
∗
for the same breaking rate.
Had a threshold level
b
t
above 2.5 been adopted, it would have significantly reduced the
breaking occurrence-rate statistics. As may be seen in
Figure 8.4
b, the number of breaking
waves with higher steepness decreases dramatically as the breaking threshold is increased.
Thus, the threshold level of 2.5 is a purely empirical level and may only be applicable to
this particular experimental setup with the prevailing mean water depth. In deeper water, a
different value of
b
t
could have been needed to detect the breakers reliably if the acoustic-
induced pressure above the background noise is reduced for the deep-water breakers.
It should be mentioned that other methods of deriving the breaking-detection threshold
were attempted in the search for a universal high-frequency pressure property which would
characterise the breaking. In particular, the rms level (averaged over the local wave period)
of the high-frequency pressure fluctuations was considered as an indicator of the average
breaking intensity over a local wave. It was expected that, if the rms background level of
fluctuations at these frequencies in the certain absence of breaking (during light winds, for
example) is subtracted, the remaining property would unambiguously identify the break-
ing. The background level was obtained from the high-frequency-noise histograms where it
should have a high probability. It was found that the extreme values of the high-frequency-
noise rms histograms clearly depend on the wind speed, i.e. (in arbitrary units) 2.4 for
U
10
=
6
.
6m
/
s. Mean values of the
noise also depend on the wind. Apparently, the background ambient noise at different wind
speeds changes due to the presence of small-scale breakers and the detection threshold
would have to be determined for each wave record individually.
It is instructive to highlight some consequences of
Figure 8.4
that are further related to
the topics other than the wave-breaking wind-input enhancement.
Figure 8.4
c shows qual-
itatively the dependence of the enhancement effect on the breaking severity, since higher
thresholds imply that only more severe breakers are detected. It is apparent that the con-
tribution to the ratio
E
in
Figure 8.4
c increases for more severe breaking events, implying
a dependence of the enhancement on the breaking severity. Another interesting feature is
that the enhancement effect itself increases for stronger winds (record 10 of
Table 8.1
), but
reduces for the fully separated case (record 8 of
Table 8.1
was classified as fully separated
in
Donelan
et al.
(
2006
)). Hence, there are some additional dependences underlying the
mean value of O(100%) enhancement indicated in this section.
=
6
.
6m
/
s, 13.1 for
U
10
=
8
.
1m
/
s , 35.8 for
U
10
=
11
.
9m
/
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