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and asymmetry is small (i.e. only slightly tilted forward), that is the asymmetry phase is
approximately shifted by a quarter of the oscillation period. A feature which was not deter-
mined from the numerical model is that there is also a modulation in the frequency (inverse
period) of the individual waves. At the point of breaking the frequency increases rapidly,
further increasing the steepness and hastening the onset of breaking (see also
Bonmarin
,
1989
).
5.1.2 Measurement of the breaking onset; limiting steepness at breaking
Measurement of the physical properties of breaking onset due to modulational instability
is a most intriguing task. Whilst the properties of waves breaking due to focusing the
coalescing packets have been described in detail previously (e.g.
Rapp & Melville
,
1990
),
physical characteristics of breaking resulting from nonlinear wave evolution have rarely
been measured. This is despite the fact that a great number of geometric, kinematic and
dynamic criteria have been proposed for the breaking over the years and were expecting
verification (e.g.
Longuet-Higgins
,
1969a
;
Holthuijsen & Herbers
,
1986
;
Caulliez
,
2002
).
In this subsection, the steepness, skewness, asymmetry and inverse period of the incip-
ient breaker, and the waves following and preceding it will be investigated in great detail.
Connections and correlations between these properties of these waves will be analysed,
both statistically and asymptotically.
As the location of the breaker can be controlled by varying the IMS at the wavemaker, the
waves were made to break immediately after a wave probe and thus the properties of incipi-
ent breakers could have been measured directly.
Figure 5.4
shows the four steepest incipient
breakers. A slight variation of the recorded height of the breakers is visible here and was
also the case in
Figure 5.3
. There are two reasons for this variation in height. Firstly, there is
some low-frequency modulation of the wave-group amplitude which can be either natural
or an artifact of the tank. Secondly, there was a
10 cm variation of the observed break-
ing location. This variation in the breaking position could have been due to a non-integer
number of waves in the modulation. These reasons were not investigated in detail as they
did not influence our main results. In any scenario, transition of the wave to the incipient-
breaking stage is very rapid and difficult to capture precisely. Therefore, we chose the
highest breakers for examination, as those are apparently the closest to breaking onset.
Typical features of waves just prior to breaking can now be analysed. The nearly break-
ing wave is the highest and most skewed, but is almost symmetric. The two waves imme-
diately preceding and following the breaker are asymmetric: the preceding wave is tilted
backwards (positive asymmetry) and the following wave is tilted forwards (negative asym-
metry). The preceding wave is smaller than the following wave, and, at least in these
observations, the preceding trough is shallower. This may be a key feature to distinguish
linear-focusing breaking onset from modulational-instability breaking, as the former is not
expected to exhibit uneven front and rear troughs. Thus, the boat that climbed the front
face of the breaker, would then fall into the very deep trough followed by an even steeper
wave front.
±
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