Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 143

which correspond to the spectral peak and exhibit pronounced group-modulated structure
( Section 5.3.1 ), appears essentially different to that of waves which are relatively shorter
compared to the dominant waves and whose breaking may be induced by larger and longer
waves ( Section 5.3.2 ). In directional wave fields, the very existence of modulational insta-
bility is an issue. Since the real waves are directional, with the exception of swell which
has low steepness and does not break anyway, this issue is of significant importance for
wave breaking and will be discussed in Section 5.3.3 . Finally, wind-forcing effects will be
described in Section 5.3.4 .

5.1 Initially monochromatic waves

In Section 4.1 , numerical simulations were described of the breaking development within
initially monochromatic wave trains, conducted by means of CS models. Results of the
simulations were further used in a laboratory experiment to verify the model's ability to
predict the breaking onset and to parameterise the breaking probability for such waves
( Babanin et al. , 2007a , 2009a , 2010a ).
Following the logic of Section 4.1 , the current section is subdivided into a number of
subsections on laboratory measurements of the wave evolution to breaking, breaking onset,
wind influence, and breaking probability. Each subsection has a brief introduction on the
main and side topics discussed. Before these subsections, we will outline the issue of com-
paring numerical simulations and laboratory experiments, provide necessary definitions for
the modulational instability, and describe the ASIST wave tank and laboratory experiments
conducted in this tank. Examples of time series and modulational instability will be shown,
and a definition of the depth of the modulation, important for the breaking-severity issue
and used throughout the rest of the topic, will be given.
Although it has already been mentioned a number of times, it should be emphasised
again that comparisons of numerical simulations of nonlinear wave evolution with labora-
tory experiments can only be qualitative. Firstly, no matter how sophisticated the model is,
it is still a simplification of the physical environment and disregards or possibly suppresses
some natural features. One such feature is the three-dimensionality of wave motion. Even
in the quasi-two-dimensional environment of the wave tank, some directional features may
play an essential role. For example, Melville ( 1982 ) showed that for steepness

3, the
wave crests develop a crescent-shaped perturbation and this three-dimensional instability
manifests itself in a more complicated way compared to the strictly two-dimensional case.
This has a significant consequence for numerical simulations. The two-dimensional CS
model predicts immediate breaking onset for

> 0 .

29, whereas in the laboratory experi-
ments of Melville ( 1982 ) such waves become short-crested but can persist without breaking
for some time.
Another significant difference between the laboratory and the model is the continuous
nature of modes in the experimental environment, even if those modes are only minor back-
ground noise, and the discrete nature of numerical modes. It is important to understand
that at the initial stages of development, the necessary modulational modes should grow

> 0 .