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Figure 7.12 Spectral dissipation function
S
ds
(
f
)
(7.50)
(bold line) with the two terms
T
1
(f)
(7.51)
(line with dots) and
T
2
(f)
(7.51)
(line with asterisks), with coefficients
a
1
=
a
2
=
0
.
0065. Compu-
tations were performed for a Combi spectrum with
f
p
=
0
.
13 Hz,
U
10
/
c
p
=
2
.
7,
U
10
=
10m
/
s.
Figure is reproduced from
Babanin
et al.
(
2010c
)
©
American Meteorological Society. Reprinted
with permission
determining the saturation level, as well as the relative contributions of the two different
types of dissipation. Therefore, to achieve the correct level of wave dissipation in the
model, it is necessary to calibrate these coefficients carefully.
Because of the two-phase behaviour of the spectral dissipation, i.e. combination of terms
both depending on the wave spectrum
F
(
f
)
directly and depending on the integral of
(
)
, the induced-dissipation term
T
2
(
)
(7.52)
is zero below the peak, and thus the entire
dissipation in this region was attributed to the inherent breaking in order to estimate the
coefficient
a
1
(note that this is an upper estimate of the dissipation because the nonlinear
transfer could have contributed towards spectrum growth below the peak too). As the waves
approach full development, the dissipation
T
1
(
F
f
f
0
in such conditions. Once the coefficient
a
1
is then calibrated, the quantitative dependence
for
a
2
can be obtained based on the constraint
(7.47)
.
The behaviour of the coefficients
a
1
and
a
2
obtained this way is shown in
Figure 7.13
(designated as
a
and
b
, respectively) as a function of the wave-development stage
U
10
/
f
)
becomes negligible, and therefore
a
1
→
c
p
.
The magnitude of these coefficients is compared with the experimental value
a
exp
=
0
.
0065
estimated by
Young & Babanin
(
2006a
).
As shown in
Figure 7.13
, values of both coefficients decrease as waves develop, and
the rate of decrease accelerates as the waves approach full development. This trend, in
particular, indicates a reduction of the relative contribution of the dominant waves into
wave-energy dissipation, as the wave system develops.
For young waves (
U
10
/
2), the coefficients
a
1
and
a
2
differ by an order of mag-
nitude,
a
1
being larger. Regardless of this, as can be seen in
Figure 7.14
, the cumulative
term, the magnitude of which is effectively determined by the coefficient
a
2
, dominates the
dissipation at smaller scales of the wave spectrum (that is the tail of the dissipation function
c
p
>
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