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Even at the peak, where the induced breaking is absent and the dimensional hypothesis
of
Duncan
(
1981
) can be expected to hold, the proportionality coefficient varies by many
orders of magnitude depending on the wave age and, for the same wave age, on the wind
speed. It is only in the range of the wind forcing conditions 1
.
5
<
U
10
/
c
p
<
2 that the
10
−
3
of
Melville & Matusov
(
2002
)formost
coefficient
b
br
is close to the value of 8
.
5
·
wind speeds.
For wind speeds
U
10
s, as waves develop, the coefficient
b
br
exhibits a redu-
cing trend, reaching down a value of the order of 10
−
3
<
20m
/
at full development (10
−
2
at
U
10
s in the figure, coefficient
b
br
exhibits significant growth towards full development, after reaching a minimum close to
the Melville-Matusov value.
Comparison of the dissipation function
(5.40)
with the dissipation function based on
phase speed
c
only
(7.58)
,isshownin
Figure 7.20
. For convenience of the comparison,
both functions were converted into wavenumber space, and the dissipation
(5.40)
was
weighted by
∼
20m
/
s). For very strong winds,
U
10
=
30m
/
3
. Computations were performed for Combi spectra
(7.46)
with
(
10
/
U
10
)
U
10
/
c
p
=
1
.
3 at wind speeds of
U
10
=
7
.
2m
/
s
,
9
.
8m
/
s and 13
.
6m
/
s. For the dissi-
10
−
5
10
−
3
and 8
10
−
3
were
pation
(7.58)
, a number of values of coefficient
b
br
=
2
·
,
1
·
.
5
·
employed.
As has already been pointed out by
Babanin & Young
(
2005
) and
Babanin
et al.
(
2007c
),
(7.58)
is expected to underestimate the dissipation at smaller scales away from the spectral
peak because, even if there was a universal constant value for the proportionality coefficient
b
br
, it would only be applicable to the inherent dissipation term
T
1
(7.51)
of the total
dissipation
(7.50)
, whereas the term
T
2
(7.52)
will tend to dominate at those scales. This is
clearly the case in the figure.
Figure 7.20 Comparison of the dissipation functions
(5.40)
and
(7.58)
, both converted into
wavenumber space. Dissipation
(5.40)
is weighted by
(
10
/
U
10
)
3
, computations are performed for
Combi spectra
(7.46)
at
U
10
/
c
p
=
1
.
3 for wind speeds
U
10
=
7
.
2m
/
s (line with dots), 9
.
8m
/
s
(line with crosses) and 13
.
6m
/
s (line with asterisks). For dissipation
(7.58)
, different values of coef-
ficient
b
br
=
2
·
10
−
5
(dashed line), 1
·
10
−
3
(plain line) and 8
.
5
·
10
−
3
(bold line) are used.
Figure is reproduced from
Babanin
et al.
(
2010c
) © American Meteorological Society. Reprinted
with permission
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