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Figure 7.5 Mean velocity spectrum of
incipient-breaking
(solid line) and
post-breaking
(dashed line)
waves. The Kolmogorov interval slope of
f
−
5
/
3
is shown. The text demonstrates values of respective
total dissipation rates
D
a
(
5.67
, denoted as
D
in this figure) and the integral of spectral dissipation
seen in
Figure 7.3
. 95% confidence limits are shown with the vertical straight segments. Figure is
reproduced from
Young & Babanin
(
2006a
)
©
American Meteorological Society. Reprinted with
permission
not appear to differ significantly. The levels of the Kolmogorov intervals at higher frequen-
cies of the two spectra, however, are essentially different. At these frequencies and at the
20 cm depth, the turbulent velocities apparently dominate the orbital velocities. The dif-
ference between Kolmogorov intervals can be attributed to the loss of energy from across
the wave spectrum seen in
Figures 7.3
and
7.4
. The total dissipation estimated from the
velocity spectra in
Figure 7.4
and the wave spectra in
Figure 7.3
should match:
F
df
(
f
)
p
−
F
(
f
)
i
D
a
i
−
D
a
p
=
g
·
(7.20)
t
f
where
t
is the time difference between the mean time points of subsequent breaking and
non-breaking segments and the overline represents the ensemble average. Here, the spectral
dissipation term is multiplied by
g
:
·
(
)
F
f
S
ds
(
)
=
f
g
(7.21)
t
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