Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 409

the topic. Instead, a new section on Lagrangian fully nonlinear methods of wave-breaking
numerical simulations was added.
Chapters 5 and 6 are the core of the topic, discussing wave-breaking probability and
severity. Here, knowledge of the first four chapters is used, that is, understanding of the
breaking concept, of the definitions, of the breaking measurements and of fully-nonlinear
wave behaviour. The structure of Chapter 5 is essentially altered compared to the earlier
review.
The breaking probability was discussed for the monochromatic (or rather quasi-
monochromatic, since the unstable sidebands will grow from the background noise if they
were not imposed initially) wave trains in Section 5.1 and for waves with a continuous
spectrum in Section 5.3 . Section 5.2 is dedicated to the important feature of the wave-
breaking threshold in terms of the background mean wave steepness. It is not to be confused
with the limiting steepness of individual waves which signifies the breaking onset.
The threshold behaviour means that the breaking in the wave train/field does not happen
unless the mean steepness is above some certain level. Once it is above this level, then
the breaking rates/probabilities are determined by the magnitude of excess of mean back-
ground steepness over the level. In the case of a continuous-spectrum environment, there
is a threshold value for the spectral density at each spectral scale.
The significance of the threshold aspect of wave breaking, which is a certain observa-
tional and experimental feature, should not be underestimated. At present, for example,
none of the operational wave-forecast models account for the threshold behaviour in their
dissipation functions, although dedicated developments in this regard are already under
way. This means that the models implicitly employ the physics which is not adequate in
some circumstances and will predict an active whitecapping dissipation in environments
where the waves do not actually break (for example, swell).
It should be emphasised that wave trains/fields falling below the breaking threshold (i.e.
such conditions where the breaking does not happen) do not, however, represent some
different kind of nonlinear behaviour compared to those waves above the threshold. All
the nonlinear features of the below-threshold wave fields should be the same, just of a
lesser magnitude of course, with allowance for the smaller steepness/nonlinearity. What is
different is that individual waves in the course of such impaired nonlinear evolution do not
reach a limiting steepness beyond which the water surface collapses.
This limiting steepness of Hk 44, which follows both from the fully nonlinear

numerical simulations of the breaking onset as a transient wave condition, and from the
experiments, is remarkably close to the well-known 150-year old Stokes limit. The waves
at the breaking onset, however, as they are simulated and observed, do not look like the
stationary point-crested Stokes waves and rather exhibit the characteristic features of the
crest instabilities (that is the crest is leaning forward while the wave is still symmetric) and
other transient dynamic properties. In this regard, it is not obvious whether the agreement is
coincidental or based on fundamental limitations for the water surface in the gravity field.
In the context of this limiting breaking-onset steepness, modulational instability and
background mean wave-train steepness, the issue of freak waves is discussed. It is

/ 2 ≈ 0 .