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This is a feature that is becoming familiar and has already been mentioned a few times
before - two-phase behaviour of wave breaking in a spectral environment (see Chapters 5
and 6 for more details). Xu et al. ( 1986 ) described statistics and dependences for the
two groups separately. For the dominant breakers, they found an average steepness of
ak
c exceed-
ing the limit (3.22) ; this is most likely the steepness of waves already breaking rather than
a criterion for incipient breaking, as it was interpreted.
Caulliez ( 2002 ) found that breaking waves detected in the wave records this way exhibit
a self-similar shape with very strong negative asymmetry of A s
=
0
.
375. This will be discussed later, since the detection was based on ratio R
/
5 (1.3) .Like Longuet-
Higgins & Smith ( 1983 ) and Xu et al. ( 1986 ), Caulliez ( 2002 ) also observed the ratio
R
0
.
c (3.22) exceeding the maximal theoretical value of 0.586. On average, the measured
maximal slopes of wavefronts were 45 which is
/
“much larger than 30 , the value predicted for the highest Stokes wave” (i.e. 2.56 ).
Longuet-Higgins & Smith ( 1983 ), Xu et al. ( 1986 ) and Caulliez ( 2002 ) interpreted the
fact that they found c
586 as measuring 'the waves that are just about to break', 'not
actually breaking', 'near-breaking', or in other words incipient breaking or breaking onset
(see Section 2.1 ). Here, we would disagree with the interpretation. If
>
0
.
θ critical (2.56) defines
the maximal possible inclination of the surface for steady waves, then inclination angles
of
θ>θ critical should signify the surface that is unstable and is already breaking. As the
review of pictures of breaking waves in Chapter 1 shows, local inclination of the surface
in the course of breaking can reach almost any angle and perhaps even 90 in a vertically
plunging jet. The fact that histograms measured by Longuet-Higgins & Smith ( 1983 )did
not depend on the critical value for R supports such a conjecture: raising the level of R
did not remove the breakers in progress and did not eventually limit the statistics to only
the incipient breakers because the breakers in progress exhibited surface steepness, locally,
higher than the limiting Stokes-wave steepness.
Therefore, the techniques developed by Longuet-Higgins & Smith ( 1983 ), Xu et al.
( 1986 ) and Caulliez ( 2002 ) appear to be an excellent practical tool to identify and mea-
sure properties and statistics of breaking in progress, rather than those for breaking onset.
This supposition is further supported by the experimental results of Babanin et al. ( 2007a ,
2009a , 2010a ) who found that at the breaking onset a wave is nearly symmetric with respect
to the vertical, but it inevitably starts leaning forward (develops a progressing negative
asymmetry (1.3) ) as it begins and continues to break, in accordance with measurements of
the breaking-wave shape by Caulliez ( 2002 ).
Another example of using physical limiters to detect breaking events is a laboratory
study on wind-generated waves by Hwang et al. ( 1989 ). The authors employed two limiting
criteria for the water waves in order to detect breaking, i.e. a geometric criterion (2.56) and
a kinematic criterion (2.49) , in a comprehensive study intended to investigate breaking
probability, breaking duration and lengthscale, breaking phase with respect to the wave
shape, breaking severity and the probability of multiple subsequent breaking within one
wave group. The instantaneous local values for the surface slope and the orbital velocity
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