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brought about by longer waves (e.g.
Donelan
,
2001
;
Babanin & Young
,
2005
;
Babanin
et al.
,
2007c
). Breaking of laboratory waves can also be made random if the waves are,
for example, wind-generated (e.g.
Xu
et al.
,
1986
;
Hwang
et al.
,
1989
), in which case the
physical mechanism leading to the breaking is one or a combination of the above.
Whatever laboratory practice is chosen, breaking severity can now be estimated. Rele-
vant differences between estimates due to different breaking mechanisms, however, appear
to be of a very essential nature (
Babanin
et al.
,
2009a
,
2010a
, see also
Section 7.3.2
) which
puts the notion of a roughly constant breaking strength in serious doubt. How applicable
this notion is in the field is another very important question. Field breaking is a combination
of the various mechanisms, although some may prove less frequent and less significant;
linear superposition is likely to be among the latter (
Babanin
et al.
,
2009a
,
2010a
,see
also
Chapter 10
). In any case, breaking severity seen in
Figure 2.3
, based on Black Sea
measurements, is very different from 50%. In this figure, waves which display whitecap-
ping, i.e. breaking waves, are shown squared for the spectral-peak frequency band. Their
steepness ranges from
=
=
.
=
.
03. If the ratio signifies a loss of
wave height in the course of breaking, then it amounts to nine times and translates into
energy loss
ak
0
27 down to
ak
0
2
after
E
after
E
before
=
=
0
.
012
(2.28)
2
before
or, according to
(2.23)
,
k
2
after
=
4
H
before
−
H
after
=
2
2
988
H
before
.
E
s
=
before
−
0
.
(2.29)
H
If, however, at breaking onset the steepness were even higher (i.e.
ak
44 as
measured by
Brown & Jensen
(
2001
) for linear-superposition breaking and by
Babanin
et al.
(
2007a
,
2010a
) for modulational-instability breaking), then the energy loss is even
greater:
=
2
k
=
0
.
H
before
−
H
after
=
995
H
before
.
E
s
=
0
.
(2.30)
Above,
E
before
,
before
,
H
before
are respectively the wave energy, wave steepness and wave
height immediately before breaking, and correspondingly
E
after
,
after
,
H
after
immediately
after breaking.
Estimates
(2.28)
-
(2.30)
should be treated with caution because the wavelength changes
somewhat in the course of breaking (e.g.
Babanin
et al.
,
2007a
,
2009a
,
2010a
) and therefore
the change of steepness
in
(2.28)
-
(2.30)
depends on the change of wavenumber
k
too, not
only on the reduction of the wave amplitude
a
. Besides, as mentioned above, the expression
for total wave energy in terms of wave height
(2.23)
is strictly valid for linear waves and can
be biased in the case of strongly nonlinear waves which the breakers are. Also, individual
waves change their height as they propagate through the group even without breaking.
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