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extreme, in the laboratory experiments of
Babanin
et al.
(
2011a
), the directional focusing
did not happen for very narrow (i.e. near unidirectional) spectra of
A
>
2
.
25 (
A
>
9
.
4for
WDM-estimated spectra).
Therefore, the breaking due to directional focusing and other types of focusing on that
matter could not be expected as a frequent occurrence in realistic wave fields and thus
linear focusing is hardly expected to be the main cause of wave breaking in directional
fields. Indirectly, this conjecture is also supported by the wavelet directional method of
Donelan
et al.
(
1996
). The main assumption of WDM is that at any given time there is only
one wavelet of a particular frequency present at the measurement point. If not, the WDM
reading fails at that particular instant. The level of the noise in the directional spectra
produced by WDM would be an indicator of how often wavelets coming from different
directions superpose. The answer is - not that often. Noise in the WDM-estimated field
directional spectra is remarkably low (i.e.
Donelan
et al.
,
1996
;
Young
,
2010
).
On the other hand, the other possible cause of wave breaking, modulational instability,
is likely to be active in wave fields with typical directional-spread/wave-steepness prop-
erties as discussed above. It has to be emphasised again that this fact does not cancel the
possibility of linear or amplitude focusing of course, but places instability breaking as a
likely more-frequent cause of wave-breaking onset in a directional wave field.
5.3.4 Wind-forcing effects, and breaking threshold in terms of wind speed
If the wind forcing is superimposed, it can play multiple roles in affecting wave-breaking
probability. We would like to start, however, not from these roles, but from another wind-
related effect principal to wave breaking: breaking threshold in terms of the wind speed (see
also
Section 3.1
). That is, similarly to the threshold of the breaking occurrence imposed by
the wave-steepness/spectral-density (
Section 5.2
), there is a wind-speed threshold below
which no breaking will happen in a wave field.
As has been discussed starting from
Chapter 1
, dissipation is an important and inevitable
balance holder in the wave system, but in order to start breaking the waves have to grow
beyond some average steepness. It is known that not every wind forcing can provide such
conditions (e.g.
Donelan
,
1978
). In
Babanin
et al.
(
2005
), this threshold was investigated
quantitatively for the breaking of dominant waves by simultaneously measuring the volu-
metric energy-dissipation rate in the water column and the energy flux from the wind to
the waves in the air.
The volumetric rate of total turbulent kinetic energy dissipation
dis
can be obtained from
the Kolmogorov inertial subrange of the velocity spectrum in water (e.g.
Terray
et al.
,
1996
;
Veron & Melville
,
1999
). If the velocity spectrum
V
(
f
)
exhibits a
5
3
f
−
V
(
f
)
∼
(5.65)
Kolmogorov interval, the level of this interval depends on the dissipation
dis
:
1
3
8
2
/
3
u
orb
rms
2
7
dis
9
110
2
3
3
f
−
V
(
f
)
=
(5.66)
α
π
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