Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 423

breaking due to amplitude focusing but is opposite to the frequency-focusing dissipation
outcomes. The fact that doubling the wind input brings about modulational wave breaking
four times as fast is consistent with field experiments on wind input.
In experiments described in Section 5.3.3 , the directional wave fields were created by
two-dimensional waves coming from different directions. In the resulting three-dimensional
pattern, the waves are often called short-crested, because of their appearance, but in fact
they are a superposition of long-crested waves. This is the typical Fourier approach, expli-
citly or implicitly prevailing in ocean wave studies of any kind.
The term short-crestedness is often used as a counterpart for directionality, but this
causes great confusion. Wave trains can be perfectly two-dimensional (unidirectional), but
still apparently short-crested - for example, steep waves in wave flumes (see also discus-
sion in Section 3.4 ).
As a result, the same Fourier spectrum can potentially be measured in very different
directional wave fields: those created by the superposition of long-crested waves, and those
due to quasi-two-dimensional short-crested short-lived wave groups (wavelets) coming
from different directions. Those groups can be coming to the measurement point one at
a time, but would produce a directional spectrum if the measurements are conducted long
enough. If such groups remain coherent at the time scale of a few dozens of periods of dom-
inant waves, then the basic two-dimensional Benjamin-Feir-like modulational-instability
mechanism will be active. In the wave fields with a typical background steepness ak

1,
this will lead to the breaking without a need for any further superpositions or explanations
like those offered in Section 5.3.3 in terms of the directional modulational index.
Evidence for such coherent wave groups is available among remote-sensing studies of
surface ocean waves. If such a structure of the wave fields is confirmed, this could prove
an exciting novel development for the entire set of analytical and statistical approaches in
wave dynamics, not just for wave breaking.
The answer to the question of whether it is the modulational instability or something
else that causes the dominant waves to break is not just a subject of scientific curiosity.
This answer has the most serious implications for the topic of wave-energy dissipation, as
the spectral signatures of the dissipation brought about by different physical mechanisms
are different. In this regard, if the short-crested short-lived wavelet structure is a reality,
then such instability may even be applicable to the short-scale wave trains. In the present
continuous-wave-train Fourier perception of wave fields, such waves at the spectrum tail
do not have a characteristic bandwidth and therefore are not expected to have a group
structure leading to such instabilities and breaking.
Hand-in-hand with the question about the role of the modulational instability comes the
non-dissipative question of the downshifting of the wave energy due to wave breaking. For
decades, such downshifting was attributed to the resonant nonlinear interactions, and if
the modulational-breaking does bring it about in oceanic wave fields, many features of the
wave evolution may need to be reconsidered, as well as those of the wave modelling.
Another issue, related, at least partially, to the breaking is the question of the aero-
dynamic surface roughness due to small-scale waves and of the sea drag. Progress in

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