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dependence of the enhancement on the breaking severity was evident, a possible depen-
dence of the breaking enhancement on wave steepness was also investigated. Individual
waves were identified by their zero-crossings and their windward (rear) face steepness was
calculated as
H
L
rear
=
(8.25)
where
H
is the rear crest-to-trough height and
L
is the rear crest-to-trough length (see also
Section 2.9
).
L
was determined from the time series as
t
L
T
λ
L
=
(8.26)
where
t
L
is the rear crest-to-trough duration of the wave of period
T
. The wavelength
λ
was approximated from the period
T
on the basis of linear wave theory.
Contributions of the individual waves to the local mean energy flux
p
∂
∂
t
were then esti-
mated. The energy flux to each individual wave was normalised by its rear-face steepness.
To calculate the enhancement
G
for individual waves, this energy flux was divided by
the mean energy flux for the entire record, normalised by the significant wave steepness
defined as
H
s
λ
p
/
s
=
2
where
λ
p
is the length of waves at the spectral peak:
E
ind
E
mean
s
rear
.
G
=
(8.27)
The influence of normalising by wave height was also examined. The results were, how-
ever, not sensitive to this choice.
Next, the individual waves were segregated into groups according to their steepness. The
waves were separated into breaking, non-breaking and non-segregated categories, and then
grouped according to their rear-face steepness. The energy-flux enhancement for each of
these groups was estimated and averaged. This was done for dominant waves from all the
available records. In total, this analysis included 6347 individual waves, 1132 of which
were breaking.
The energy-flux enhancement is plotted as a function of the steepness for the full ensem-
ble in
Figure 8.6
a. The result of this analysis demonstrates that the enhancement does not
depend noticeably on the steepness. Thus, once an individual wave of a certain steepness
breaks, the mean flux over that wave increases by approximately a factor of 2 compared to
the flux over a non-breaking wave of the same steepness.
A further statistic derived from grouping and then counting the waves, according to
their steepness and breaking/non-breaking characteristics, is shown in
Figure 8.6
b. A semi-
logarithmic scale was used because the number of waves with large steepness decreases by
two orders of magnitude. The distribution according to steepness of Lake George waves
has a maximum in the steepness range 0.05-0.1 (2689 waves), and the number of waves
rapidly drops towards higher steepness. It is interesting, however, that a significant number
(54) of very steep waves, even as steep as 0.25-0.3, were detected.
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