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For the spectrum tail, the induced breaking, due to various influences of the large waves,
dominates (see
Section 5.3.2
). The transition between the prevalence of induced breaking
over the inherent breaking happens at approximately the same relative frequency
ω
0
∼
3
ω
p
(see discussions in
Sections 2.7
and
5.3.2
) as the transition
ω
t
in this section (see also
(7.46)
). This means that most of the breaking which we see to control the
f
−
5
interval is
induced, and whatever the wind does to stimulate this breaking is done mostly indirectly
through altering the long-wave conditions in the field.
On the other hand, this induced breaking for younger waves reacts to the changing wind-
forcing conditions by adjusting the breaking strength, whereas the breaking rates as such
do not necessarily change (see also
Section 5.3.2
and current section, above). This is for
U
10
/
45, as was already discussed in this
section, the induced breaking is likely to simply alter the rate of occurrence because of the
wave age.
Why and how the dominant waves do that to the induced breaking of the short waves
is yet to be understood, but one way or another, at both sides of the
U
10
/
c
p
>
1
.
45. For the mature waves of
U
10
/
c
p
<
1
.
45 wave
age, the extent of the
f
−
4
interval starts shrinking. This shortening leads to complete dis-
appearing of this dynamic spectral range for younger waves, but for the mature waves
such an interval controlled by the nonlinear fluxes always exists. Even at full develop-
ment,
c
p
≈
1
.
ω
t
=
1
.
6-2
.
1
ω
p
depending on the wind speed (bottom panel of
Figure 8.1
). Transi-
tional frequency 1
.
6
ω
p
, however, which occurs at full development at wind speed
U
10
=
40m
/
s is very close to the spectral peak whose half-width is approximately 1
.
3-1
.
5
ω
p
.
Therefore, at very strong winds, the width of the
f
−
4
interval, even when it exists, is
quite short.
To conclude this section, we would also briefly mention that wave breaking can make
other, perhaps even somewhat unexpected contributions to the spectrum tail.
Willemsen
(
2002
), for example, showed by means of the deterministic modelling of directional waves
that the power of the dissipation function, if altered, influences the asymptotic wave tail.
Breaking of large waves can actually generate short waves and ripples (e.g.
Pierson
et al.
,
1992
;
Hwang
,
2007
, see also
Section 2.7
). Such a contribution is interesting, but is perhaps
small and is yet to be quantified. Control of the level of the
f
−
5
interval, which is achieved
both through the breaking frequency and strength, and its competition with the nonlinear
fluxes for the shape of the spectrum tail, is, however, a very important role of the breaking
in wave fields with a continuous spectrum.
8.3 Wind-input enhancement due to wave breaking
The third subsection in this chapter dedicated to non-dissipative effects of wave breaking
indeed deals with the phenomenon which is not associated with dissipation in any way (or,
rather in any direct way, since any additional input in the balanced wave system ultimately
leads to an additional dissipation in some part of the wave spectrum, see
Section 9.2.1
below). This section is about the energy input to the wave system due to the breaking. This
energy, of course, comes from the usual source, that is from the wind, but the input rates
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