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strongly forced and highly nonlinear wind-waves, the wind-wave energy transfer, which
depends on the mean wind speed, and the wave asymmetry are correlated, and they both
oscillate with the same period. Thus, the connection of magnitude of the asymmetry with
the wind speed observed by Leikin et al. ( 1995 ) can be explained through the mechanism
of air-sea coupling.
The waves, however, have to become nonlinear first, and this comes through the gradual
growth of the wave steepness as a result of wind action. According to Agnon et al. ( 2005 ),
the steepness
and skewness S k also exhibit oscillations correlated with the wind speed,
but no direct connection of
and S k was observed by Leikin et al. ( 1995 ).
This discrepancy can be explained by the growth of wave-breaking occurrence that
accompanies increasing wind speeds. In nonlinear wave trains, steepness, skewness and
asymmetry all oscillate due to modulational instability ( Babanin et al. , 2009a , 2010a ). The
mean value of A s remains close to zero unless a wave breaks. The wave always breaks
when it starts leaning forward, i.e. its steepness and skewness are maximal and the asym-
metry A s
0 and at this stage
the oscillations of the asymmetry are interrupted. Therefore, if many wave-breaking events
take place within a wave record, the average asymmetry over such a record will deviate
towards negative values, whereas maximal values of
0. In the course of breaking such a wave exhibits A s
<
and S k are not affected (see also
Section 5.3.3 and Eqs. (7.18) - (7.19) ).
It is also instructive to notice that values of asymmetry A s in Leikin et al. ( 1995 ) tend to
saturate at u /
c p ≥∼
1
.
2 (their Figure 1a). Since the phase speeds of the laboratory waves
measured were c p ≤∼
1m/s, this translates into the saturation at wind speeds
U 10
34m
/
s
(3.26)
which is consistent with recent observations both in the field ( Powell et al. , 2003 ; Jarosz
et al. , 2007 ) and the laboratory ( Donelan et al. , 2004 ) for the saturation of sea drag (3.8)
at wind speed (9.12) , and for the change of regime of gas transfer (9.50) . Kudryavtsev &
Makin ( 2007 ) investigated the former case and explicitly connected it to wave breaking.
Returning back to the issue of contact measurements of wave breaking, two good exam-
ples of trial-and-error methods are papers by Weissman et al. ( 1984 ) and Stolte ( 1992 ).
As mentioned in Section 3.2 , both studies used visual observations in order to develop an
ad hoc breaking criterion and further process wave-breaking records automatically.
Weissman et al. ( 1984 ) were measuring the surface elevations with very thin wire probes
and were detecting the breaking waves based on spectral energy in the 18-32 Hz frequency
band. A wave was regarded as breaking if the energy density exceeded some threshold
level in the vicinity of the crest of a respective wave group. The technique was applied in a
fetch-limited field experiment, and the breaking statistics at
s wind was considered.
Again, it was found that the mean steepness of breaking waves is well below the Stokes
criterion (2.47) . While temporal coverage of the breaking was only 1
6m
/
2%, the relative high-
frequency energy in those events was ten times that, i.e. 12%. Such a difference may bear
significant implications for interpretations of radar and other remote-sensing techniques
that rely on short-scale waves.
.
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