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At typical oceanic winds of U 10
10m
/
s and typical wave age U 10 /
c p
1
.
2, (8.22)
produces the transition at
ω p which is close, even though slightly below the val-
ues of Forristall ( 1981 ) and Evans & Kibblewhite ( 1990 ) mentioned above. If dependence
(8.20) is used, then for U 10
ω t
2
.
2
35 Hz which is
exactly what the corresponding line in the top subplot of Figure 8.1 indicates.
The highest transitional frequency
10m
/
s and
ω t
=
2
.
2
ω p it gives f p
=
0
.
ω t , for individual cases over the five wind speeds, is
in the range of
ω p . The lowest transitional frequency is usually an asymp-
totic hypothetical value below the peak (
ω t
1
.
8-2
.
7
ω t p ) which fact basically means that in those
circumstances the f 5 interval will extend all the way to the spectral peak, i.e. there will
be no f 4 subinterval.
Such condition (i.e. no f 4 subinterval) is never reached for wind speeds U 10 =
s
(top subplot), that is at such wind the spectrum will always have the two subintervals. At all
the other wind speeds, for wind forcing stronger than U 10 /
10m
/
2, there will be only
the f 5 spectrum tail, and therefore no condition where the spectrum shape is controlled
by the nonlinear fluxes (8.18) will take place.
In accordance with (5.75) , the maximal transitional frequency
c p
3
.
9-7
.
ω t will occur at
U 10 /
c p
1
.
45
.
(8.23)
Both for the younger waves and more mature waves, it draws closer to the peak. This
demonstrates the relative significance of the breaking and the nonlinear fluxes in formation
of the spectrum at the respective wave-development stages.
In this regard, it can be expected that the f 5 tail comes closer to the peak at strong wind
forcing, and the f 4 tail may even eventually disappear at such forcing. The fact that this
is also a trend when the waves are maturing towards full development at U 10 /
c p less than
(8.23) , however, is somewhat counter-intuitive. This is, apparently, due to the reduction of
α
in (8.15) . Such reduction, however, is a consistent feature of the observations, not only of
the parameterisation (5.75) by Babanin & Soloviev ( 1998a ), but also those by Hasselmann
et al. ( 1973 ), Donelan et al. ( 1985 ), Bandou et al. ( 1986 ) and Evans & Kibblewhite ( 1990 ).
Moreover, (8.23) corresponds exactly to the transition of the regime of
α
behaviour in the
dependence (5.75) of Babanin & Soloviev ( 1998a ).
How can this be explained in terms of the competition between the wave-breaking
and the weak-turbulence mechanisms for the control over the saturation interval? At this
stage we can only offer a tentative reasoning rather than an explanation based on direct
experimental facts or theoretical grounds.
First of all, even if it may seem so, the competition is not between the external wind
forcing and nonlinear internal fluxes, it is between the breaking/dissipation and such fluxes.
Even though the forcing is large at the upper end of the equilibrium interval in
Figure 8.1 , the wind does not make the waves break directly, except in the hurricane-
like conditions mentioned above and described in Section 7.3.5 . Breaking happens either
due to hydrodynamic reasons, i.e. wave superposition or modulational instability, or is
induced.
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