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Therefore, we should conclude that wind influence on wave breaking in spectral environ-
ments accepts additional roles compared to its effects in the case of wind-forced uniform or
modulated wave trains. The latter are obviously applicable to the trains of dominant waves
and inherent breaking of shorter waves, but important new features of the wind-breaking
connection are revealed at smaller scales in the spectrum.
At light-to-moderate winds, the spectrum responds to the growing wind forcing
U
10
/
c
p
by increasing the level of its saturation interval
α
(2.7)
up to a certain magnitude only:
8
f
1
.
24
p
f
p
≤
10
−
2
.
03
·
for
0
.
23,
α
=
(5.75)
f
p
>
10
−
3
.
·
13
2
for
0
.
23
(
Babanin & Soloviev
,
1998a
). Here,
fU
10
g
1
2
U
10
c
p
f
=
=
(5.76)
π
is a dimensionless frequency. While the level
is growing and when the spectral densities
overcome the threshold value of
(5.36)
, the waves across the spectrum start to break and
the rate of breaking should be increasing in response to the growing level and the induced-
breaking effects, see
Section 5.3.2
,
Figure 5.29
and associated discussions.
Once the equilibrium limit of
α
identified in
(5.75)
is reached, however, the level of the
spectrum tail stops growing. As usual in the physics of air-sea interactions, this conclu-
sion is far from comprehensive. The scatter with respect to the constant-
α
level in
(5.75)
,
according to the data shown in
Babanin & Soloviev
(
1998a
), does exist, and this scatter is
hardly random.
Babanin & Makin
(
2008
), for example, listed more than 15 factors other
than the wave age which can contribute to the dependences and scatter of the sea drag
(3.8)
and therefore of the equilibrium level
α
. There is experimental evidence that the tem-
perature of the water, which affects the spectral density of short waves and aerodynamic
roughness
z
0
in
(3.19)
, can be another factor to influence level
α
under what would seem
otherwise the same wind-forcing and dynamic conditions (
Brown
,
1986
;
Pierson
et al.
,
1986
;
Bortkovskii
,
1997
).
As seen in
Figure 5.27
, the wave-breaking rates across the spectrum in such conditions
remain approximately constant also, but only until the wind speed achieves some new limit.
In the Lake George scenario shown, when the wind speed exceeds this limit of
α
U
10
limit
≈
14m
/
s
,
(5.77)
it appears that further growth of the wind forcing results in abrupt changes of the breaking
probability across the spectrum's equilibrium interval. Here, it is interesting to note that
transition of the wave-growth regime at
f
p
23 in the measurements of
Babanin &
Soloviev
(
1998a
) parameterised by
(5.75)
, is predicted theoretically by
Stiassnie
(
2010
)
based on considering the fetch-limited wave growth due to
Miles'
(
1957
) and
Phillips'
(
1957
) wind-input mechanisms, and predicted exactly at the same wave age.
It should be remembered, however, that connections of the spectral density and the
breaking probabilities above are indicative, but are far from being unambiguous. As was
=
0
.
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