Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 156

In the third row, the skewness of the wave preceding the breaker is even less scattered:
S k =−

12 (first panel). Remarkably, it is essentially negative, i.e. rear trough of
the preceding wave is always deeper than its crest. The asymmetry A s =

0 . 55-0 .

0to1 . 33 is never

negative (a couple of large A s = 33 values are off scale in the second panel and not

shown), that is, this wave is tilted backwards. There is no correlation of the skewness
and asymmetry of this preceding wave with those of the near-breaker (last two panels
of the third row, first panel of the bottom row). Thus the three waves surrounding the
breaking event tend to exhibit some quasi-universal form, but variations of their shape
are not correlated with each other, which means that these shape distortions are random.
Therefore, it is not the mean characteristics of the observed shapes, but rather their limiting
values that should asymptote the universal form parameters. These were analysed for the
highest breakers in Figure 5.6 .
The last two subplots in the bottom right corner show the local frequency of the follow-
ing f f and preceding f p waves versus the frequency of the breaker f b .IMF

1 .

8Hzis
shown with two solid lines. The local frequency was found to be a robust characteristic for
the incipient breaker above, and we can expect a reasonable correlation of these properties.
Although f f and f p are more scattered than f b , the correlation is present. In the last panel,
all the data points are in the second quadrant and thus the preceding wave is decreasing in
length along with the incipient breaker. In the second last panel, the points are on average
in the fourth quadrant. Therefore, while the incipient breaker is decreasing in length, the
following wave is actually longer than its initial value defined by IMF

= 1 .

18 Hz. Since
we know that double-breaking will likely occur, i.e. this following wave will break shortly
after the current breaker, then it should now be shrinking rapidly. Both the preceding and
the following waves are quite steep, but the preceding wave is less steep than the following
wave (see also Figures 5.8 , 5.9 ), and therefore the observed opposite deviations of their fre-
quency with respect to IMF

= 0 .

= .

18 Hz are more complicated than just second-order effects
in the dispersion relationship (2.14) . Thus, some very active physics must be involved in
the short-time-scale evolution of this set of very nonlinear waves.
Figure 5.8 provides further similar detailed analysis of the shape of the wave follow-
ing the incipient breaker. Note that this wave will break shortly after the current incipi-
ent breaker and therefore, whatever its properties are now, they are progressing towards
breaking. In the figure, kH

0

, S k , A s , f are properties of the currently analysed wave.

57 is on average about half the steepness of the incipient
breaker (first subplot). Since this wave is still the second largest in the modulated group,
this fact highlights how much higher is the incipient breaker. The ranges of skewness
S k =

The steepness 2 = 0 . 28-0 .

33 have been mentioned above; here
they do not appear to correlate with the steepness (first and second plots) or with each
other (fourth plot).
There is a 94% correlation between the steepness and local frequency (third subplot),
and the frequency grows as steepness increases. Whilst this following wave is on average
longer than IMF, it crosses the IMF values at approximately 2

0 . 32-0 . 70 and asymmetry A s =− 0 . 29 to 0 .

= 0 . 5 and continues to

decrease: