Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 218

discussed in detail in Section 5.3.2 , the breaking rates at scales small relative to the peak
are affected by the induced breaking and their dependence on the local spectral density
is smeared. Rather, they should depend on the integral of the spectrum over longer scales
(e.g. (5.41) , by analogy with the dissipation function (5.40) ).
These scales include the spectral peak. If so, Figure 5.42 provides a reasonable explan-
ation of the observed wind effect in terms of the induced breaking. The two spectra that
exhibit higher breaking rates of short waves are the ones which correspond to much higher
dominant waves. For these two spectra the peak enhancement above the others is very
noticeable. This is particularly apparent in the linear scale (right), that is, the peak spectral
density of the 15m

/ s wind (crosses) is 1.5 times higher than the rest of the group, and for

the 20m s (circles) it is twice as high. If so, modulation of the short waves by the larger

dominant waves should be stronger and cause more frequent breaking in the corresponding
spectral range.
Therefore, the observed response of the breaking rates across the spectrum to the higher
wind speeds, under the virtually unchanged local spectral density, can in fact be a result
induced by larger dominant waves rather than by the wind directly. The cause of the high
dominant waves, however, still rests with the wind, which in this case managed to pump up
the spectral peak while the equilibrium level stayed unchanged. One way or another, wind
forcing is of course the major player in the dynamics of the fields of wind-generated waves
with a continuous wave spectrum, and its multiple roles in wave-breaking behaviour are
still in need of further understanding and quantifying (see also discussion of wind effects
on the breaking severity in Chapter 6 ).
To conclude this chapter, and to some extent related results of Chapter 4 , we would like
to say that the topic of breaking probability has enjoyed the close attention of the ocean-
wave community over the past two decades or so, and at the time of writing is still going
through a stage of active progress. Not only have some important physical features such as
breaking threshold, cumulative effect and limiting breaking steepness been formulated and
understood, they have been quantified too. It is instructive to notice that, while breaking
onset due to linear focusing was scrutinised much earlier than the details of onset because
of modulational instability, focusing-breaking probability is yet to be parameterised in
terms of the background wave-field conditions. Many other behaviours and characteris-
tics of breaking probability are still to be identified, appreciated and described. These are
first of all related to the breaking occurrence in spectral, and particularly in directional
environments.

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