Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 176

Therefore, in Section 5.3.1 , we start from parameterising the spectral-peak breaking
probability first, following Banner et al. ( 2000 ) and Babanin et al. ( 2001 ), and will then
attempt the analogy with monochromatic wave trains ( Figure 5.17 ) for these dominant
waves of continuous-spectrum wave fields. In Section 5.3.2 , the breaking probability of
relatively short waves (i.e. short with respect to the waves at the spectral peak) will be
discussed.

5.3.1 Breaking probability of dominant waves

As defined in Section 2.5 , the breaking probability b T (2.3) for spectral dominant waves
will be considered as the mean passage rate past a fixed point of dominant wave-breaking
events per dominant wave period. The dominant waves are taken within the spectral band of
0 3 f p (2.6) , which contains spectral components determining the group structure

of the dominant wave field. Measurements of b T require averaging over a large number
of wave groups since the breaking process is characterised by long-period intermittencies
(e.g. Donelan et al. , 1972 ; Holthuijsen & Herbers , 1986 ; Babanin , 1995 ; Babanin et al. ,
2010a ).
As discussed in Chapter 3 , wave breaking properties such as breaking probability, white-
cap area coverage etc. had been assumed to have a primary dependence on the wind
speed U , the dependence ranging from linear up to the fourth power according to dif-
ferent authors. In Figure 5.19 , the breaking probabilities for two deep-water data sets are
plotted against the wind speed U 10 . These are the Black Sea data ( Table 5.1 , first panel) and
Lake Washington data ( Katsaros & Atakturk , 1992 , second panel) (see also Section 5.2 for
more details on these data). It is seen in these panels of Figure 5.19 a and b, that in isolation
the Black Sea data and the Lake Washington data do correlate rather well with U 10 . When
these two data sets are plotted together in Figure 5.19 c, however, they have distinctly dif-
ferent offsets. The two additional data points obtained from analysis of the Southern Ocean
video records show yet another dependence on U 10 . Therefore, it is an obvious conclusion
that it is not possible to establish a common dependence of the dominant wave-breaking
probability on U 10 . While for individual data sets such a dependence can be a good fit to
the data, there is no universal direct dependence of the wave-breaking probability on the
wind speed.
In Figure 5.20 , the breaking probability is plotted against another plausible wind-forcing
parameter, the inverse wave age U 10 /

. 7 f p to 1 .

πγ

c p denoted as 2 in this figure:

U 10 f p
g

1
2

U 10
c p .

γ = f p = = (5.20)

π

Here, it is seen that the individual data sets have similar offsets, but exhibit quite different
rates of change of breaking probability as a function of wave age. Therefore, wind forcing
does not appear to be a universal breaking-probability property either, although it provides
a relevant secondary parameter as will be seen below.