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In-Depth Information
Donelan
(
1998
) did not provide an explicit quantitative dependence for the ratio
R
D
.
For practical purposes, in
Babanin
et al.
(
2010c
) his Figure 6 was segmented, digitised and
parameterised here as following:
⎧
⎨
12
U
10
U
10
c
p
≤
−
0
.
c
p
+
1
.
52
4
.
5
<
5
.
8
,
0031
U
10
U
10
c
p
≤
0
.
c
p
+
0
.
96
1
.
5
<
4
.
5
,
R
D
=
(7.48)
⎩
052
U
10
U
10
c
p
≤
−
0
.
c
p
+
1
.
043
0
.
83
<
1
.
5
,
U
10
c
p
≤
1
0
.
83
.
5, and parameter-
isation
(7.48)
also includes the range of very young dominant waves
U
10
/
The upper wind-forcing limit of
Donelan
(
1998
)was
U
10
/
c
p
=
4
.
8.
For this range of wave ages, the dissipation ratio
R
D
was determined on the basis of con-
sistency between the model results for the variance of the energy-density spectra and the
experimental data of
Babanin & Soloviev
(
1998a
). It was found that for very young waves
the dissipation ratio is relatively small compared to the ratio for mature waves. For very
young waves of
U
10
/
c
p
=
4
.
5-5
.
c
p
=
5
.
8, it was of the order of
R
D
=
0
.
82 (see Section 4.3 of
Tsagareli
(
2009
) for more details).
The segmented parameterisation
(7.48)
produces discontinuities of the derivatives and
such sharp transitions are undesirable in numerical modelling. Therefore, for application
within a spectral model, the relationship was further smoothed and used in the following
form
⎧
⎨
1
tanh
3
U
10
2
U
10
c
p
≤
0
.
97
−
0
.
07
·
+
c
p
−
5
.
2
<
5
.
8
,
1
tanh
5
U
10
1
U
10
c
p
≤
R
D
=
0
.
97
+
0
.
015
·
−
c
p
−
1
.
0
.
9
<
2
,
(7.49)
⎩
U
10
c
p
≤
.
≤
.
.
1
0
83
0
9
The dissipation term tested in
Babanin
et al.
(
2010c
) is that proposed by
Babanin &
Young
(
2005
) and
Young & Babanin
(
2006a
) and written out in
(5.40)
; it has already been
outlined in
Section 5.3.2
. In short, it consists of the inherent-dissipation term
T
1
(
f
)
and
the cumulative dissipation
T
2
(
f
)
:
S
ds
(
f
)
=
T
1
(
f
)
+
T
2
(
f
)
(7.50)
where
T
1
(
f
)
=−
a
1
ρ
w
gf
(
F
(
f
)
−
F
threshold
(
f
))
(7.51)
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