Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 410

concluded that the modulational instability can produce the freak waves if the background
mean steepness is close to ak

13.
The breaking threshold and the limiting steepness should be equally important to all the
breaking waves, but it appears that in the spectral fields these arguments become of sec-
ondary importance for waves relatively short with respect to dominant waves. The amount
of short waves breaking due to inherent reasons, i.e. due to the same reasons as the long
waves, is small compared to their induced breaking. The latter can be triggered by the
dominant breaking, or caused by modulation of the short waves with the carrying longer
waves which modifies the steepness of short waves, or both.
In any case, the experimental evidence shows that the induced breaking essentially
changes the breaking rates of shorter waves, and at spectral scales greater than some 3 f p
the induced breaking completely dominates over the inherent breaking, to such an extent
that the breaking probabilities at those frequencies should be disconnected from the local
spectral density and be determined by the integral of the spectrum over frequencies below,
including first of all the spectral peak. In passing, we will mention that this frequency
should also identify the transition from the

= 0 . 12-0 .

ω − 5 behaviour at the spectral equilib-
rium interval, as the latter associates with the purely breaking-defined spectrum tail (this is
discussed in detail in a different chapter in Section 8.2 ).
The induced breaking brings about the so-called cumulative effect, that is, at each higher
frequency the breaking is determined by all the waves with frequencies below. As with the
breaking-threshold feature mentioned above, the cumulative effect is a definite observa-
tional physical property which is missing in the present dissipation functions. That is, all
the operational models and the majority of the research spectral wave models currently
treat whitecapping dissipation at smaller scales in an unrealistic way.
Following the logic of the fully-nonlinear analytical and numerical investigations of the
breaking in quasi-monochromatic two-dimensional wave trains in Chapter 4 , Section 5.1
investigated the evolution of nonlinear waves to breaking, breaking onset and wind influ-
ences for such wave trains, and provides direct measurements of a great variety of proper-
ties of an imminent breaker. The wave-breaking probability is parameterised as the distance
to the breaking dependent on initially monochromatic steepness of the nonlinear trains.
Section 5.3 described the breaking of spectral waves, and its structure is necessarily
different to that of Section 5.1 . Some analogies between monochromatic wave trains and
spectral wave fields are applicable to the dominant waves in the spectrum which corre-
spond to the narrow-banded spectral peak and therefore exhibit the characteristic features
of modulated wave groups. For these waves, parameterisation in terms of background mean
wave steepness is possible, in a way similar to that above based on the IMS.
The analogies clearly do not work at smaller scales away from the spectral peak. Here,
depending on how far the scale is from the peak, breaking of short waves is induced by the
longer waves one way or another. Wind-forcing effects on the spectral distribution of the
breaking are also discussed.
Particularly challenging is understanding the directional distribution of the breaking
probability. In the context of directionality, Section 5.3.3 also contains a new important

ω − 4 to