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were obtained from the time series of surface elevation by means of a Hilbert transform
(see
Section 3.7
).
Breaking regions were found to be geometrically similar, with the duration of their per-
sistence and spatial extent being proportional to the scale of breaking waves. This observa-
tion gave good experimental support to the dissipation theory by
Hasselmann
(
1974
) which
has formed the basis for dissipation terms employed in spectral models up to now, and
has only started to be challenged recently, in the light of new experimental evidence (see
Chapter 7
).
Interesting observations were made with respect to the breaking phase, which challenged
the unambiguity of the breaking criteria themselves. According to the authors,
“
...
based on the geometric criterion, the breaking inception is on the downwind side of the wave
crest, while the kinematic criterion indicates inception on the upwind side. This delicate difference,
although restricted to a narrow region of
10
◦
of the wave crest demonstrates that the breaking
phenomena described by these two criteria, as well as by other threshold variables, are not exactly
the same”.
±
Depending on the wind speed, a trend was observed for the breaking to move closer to the
crest at higher wind speeds. Since for higher wind speeds
Babanin
et al.
(
2009a
,
2010a
)
observed depleted severity, it may be that the phase of the wave-breaking region relative to
the wave crest is linked to the breaking strength.
The probability of breaking, breaking duration and breaking length were investigated
in terms of wind speed. Repeated breaking within wave groups was also found to corre-
late with the wind, but the probability of a repetition in these laboratory observations was
quite low compared to field observations (e.g.
Donelan
et al.
,
1972
;
Holthuijsen & Herbers
,
1986
;
Babanin
,
1995
). Such a probability was about 20% at 16m
/
s wind and only around
10% at 7m
s. Current understanding of repeated breaking indicates that it is primarily due
to the behaviour of nonlinear wave groups, i.e. hydrodynamics, rather than the wind. The
strong wind, however, can influence wave grouping (through slowing down growth of the
modulational instability) and correspondingly the breaking and reduce the breaking sever-
ity, and thus decrease or even diminish the probability of multiple subsequent breaking
(
Babanin
et al.
,
2009a
,
2010a
;
Galchenko
et al.
,
2010
). For laboratory waves, which are
always young, wind forcing is usually quite strong even at moderate wind speeds and thus
could have affected the observed statistics of repeated breaking.
Estimates of breaking severity, because they are rare, are most instructive.
Hwang
et al.
(
1989
) evaluated the loss of potential energy in terms of ratio
/
H
/
H
before
where
H
=
H
before
−
H
after
. They found that it is
H
H
before
=
H
after
H
before
=
1
−
30%
±
3%
.
(3.23)
If translated into energy, this gives
H
after
=
−
H
before
≈
.
s
1
50%
(3.24)
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