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Figure 5.39 Total dissipation in the wave water column
T
a
(5.73)
versus measured total wind input
I
a
(denoted as
T
and
I
, respectively). Parameterisation
(5.69)
is used for integrating
D
a
in
(5.67)
.
Figure is reproduced from
Babanin
et al.
(
2005
)
Figure 5.40
shows the total dissipation
T
a
(5.73)
plotted versus the total input
I
a
, while
dissipation
D
a
(5.67)
was estimated on the basis of the wall-layer distribution for
dis
(5.68)
as was suggested by a number of authors mentioned above. Dissipation for the
light-wind points now matches the wind input quite well, whereas the dissipation at winds
U
10
>
s is greatly underestimated.
An obvious conclusion to be drawn is that the volumetric rate of total turbulent kinetic
energy dissipation
7
.
5m
/
z
−
1
law
(5.68)
for waves generated
dis
is distributed according to the
∼
z
−
2
(i.e. similar to predictions of
(5.69)
) for waves under stronger
winds. Since the inverse-quadratic dissipation has always been associated with wave break-
ing, such a conclusion is consistent with observations that the breaking does not occur for
waves forced by light winds of
U
10
≤
∼
by light winds and as
s.
Finally, to provide better agreement between the dissipation and the energy input of the
strong-wind points in the top panel, the scale for
H
in
(5.69)
had to be adjusted. To obtain
the
H
5-7m
/
6
H
s
scale in
(5.69)
,
Terray
et al.
(
1996
) had to rely on an inferred wind-input
rate.
Babanin
et al.
(
2005
) used the total wind input
I
a
measured, and the comparisons
led to a conclusion that the constant-dissipation layer does not reach below
H
=
0
.
=
0
.
4
H
s
.
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