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found
b
br
varying by up to four orders of magnitude, which therefore makes dissipation
formulations based on such a coefficient quite unreliable.
Besides, the connection between dissipation in a breaking wave with its phase speed
is clearly not applicable in the case of induced breaking (i.e. the breaking of short waves
caused and carried by the large waves as in
Sections 5.3.2
and
7.3.4
). Therefore, it is only
the inherent term of dissipation
(7.51)
which should be considered in
(7.59)
for comparison
purposes. Thus, a dissipation formulation of the type shown in
(7.58)
is applicable at the
spectral peak region or below, where the cumulative effect is negligible.
Therefore, to reduce the uncertainty, values of coefficient
b
br
were compared at the spec-
tral peak. The spectral dissipation function
S
ds
(
(5.40)
was computed for the modelled
Combi spectrum
(7.46)
of mature waves with
U
10
/
f
)
c
p
=
1
.
3 and at the wind speeds of
U
10
=
s (i.e. same as in
Melville & Matusov
(
2002
)), and compared
with the dissipation
(7.58)
-
(7.59)
. Reasonable agreement was achieved at
b
br
7
.
2
,
9
.
8 and 13
.
6m
/
≈
.
0
01 (see
10
−
3
used by
Melville &
=
.
·
Figure 7.19
). This quantity is close to the value
b
br
8
5
Matusov
(
2002
).
In
Figure 7.19
, the parameter
b
br
of
(7.58)
is plotted as a function of inverse wave age
U
10
/
c
p
, obtained from the dissipation function
(5.40)
at the spectral peak of Combi spec-
trum
(7.46)
for different wind speeds:
U
10
=
7
.
2m
/
s (plain line), 9
.
8m
/
s (line with dots),
13
.
6m
/
s (line with asterisks), 15m
/
s (line with circles), 20m
/
s (line with crosses) and
30m
s (line with diamonds). The straight line signifies the value obtained in
Melville &
Matusov
(
2002
).
/
Figure 7.19 Dependence of the parameter
b
br
in
(7.58)
on the sea state
U
10
/
c
p
, based on the dis-
sipation function
(5.40)
, computed at the spectral peak of Combi spectra
(7.46)
for different wind
speeds:
U
10
=
7
.
2m
/
s (plain line), 9
.
8m
/
s (line with dots), 13
.
6m
/
s (line with asterisks), 15m
/
s
(line with circles), 20m
/
s (line with crosses) and 30m
/
s (line with diamonds). The straight solid
line is the value obtained in
Melville & Matusov
(
2002
). Figure is reproduced from
Babanin
et al.
(
2010c
) © American Meteorological Society. Reprinted with permission
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