Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 158

the value of steepness observed for this incipient breaker. This result should be interpreted
as confirmation of the fact that the wave following our breaker is in a state of transition
towards its own breaking onset.
In the second row of plots and the last plot of the third row, the steepness, skewness and
asymmetry of the waves preceding and following the breaker are all plotted versus each
other. They all appear uncorrelated, in contrast to the steepness, skewness and asymmetry
of the breaker and steepness of the following wave (respectively, first and second subplots
of the third row and the last subplot at the bottom). There is also no correlation between
the frequencies of the preceding and the following waves (first bottom subplot). Thus, we
conclude that perturbations/distortions of the shape of the wave following the breaker do
not correlate with distortions of the other two waves in the set that corresponds to the 20
steepest breakers. There is only strong correlation between shape changes within the wave
itself, i.e. its steepness and frequency, which indicates its state of transition to limiting
breaking steepness.
In Figure 5.9 , these properties are analysed for the wave preceding the breaker. Since
many cross-correlations have already been analysed, this figure only has three rows of
plots. This wave will not break imminently, but is a part of the obviously inter-connected
double-breaking and appears to 'disappear' after the double-breaking (see Figure 6.2 ).
Therefore, some of its properties and cross-properties are different to those obtained for
the breaker and pre-breaker.
The wave is still steep, although its steepness 2 49 is lower compared to

the other two waves (first panel). Unlike them, it is negatively skewed (trough is deeper
than crest, first plot) and tilted backwards (positive asymmetry, second plot). It is very
short, even if compared with the incipient breaker, but its local frequency is more scattered:
f p =

= 0 . 27 − 0 .

27. There is no noticeable correlation between these properties of the wave
itself, or between its steepness, skewness and asymmetry and those of the breaker (bottom
three plots) and the wave following the breaker (first three plots in the second row). It
is only in the last subplot of the middle row that a marginal correlation (68%) may be
identified between the steepness of this wave and the skewness of the incipient breaker.
As discussed above, this skewness is transient and is expected to asymptote to some value
at the point of breaking (see Figure 5.6 ). This correlation may be an indication of some
interaction between the breaker and the wave preceding it which will very soon lead to
dissipation of the preceding wave ( Figure 6.2 ). The issue of the interaction between the
breaker and preceding wave, however, may be of significance and may even hold a key
to the downshifting observed in Figures 6.1 - 6.2 . Babanin et al. ( 2011a ) describe their
visual observation of instability breaking in a directional wave tank as a breaking wave,
whose length had apparently shrunk prior to the breaking onset, rapidly accelerated in
the course of breaking as its wavelength was bouncing back, increasing to the point of
catching up and merging with the preceding individual wave. This issue needs further
investigation.
In Figures 5.10 - 5.12 asymptotic, rather than statistical properties of the incipient breaker
are considered. Three subplots in the top row of Figure 5.10 were zoomed in and scrutinised

1 . 92 − 2 .