Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 421

severity, and whitecapping dissipation discussed above is one set of problems. Breaking
due to linear directional focusing is another issue, whereas the impact of wave direc-
tionality on the modulational instability is a completely different topic. Yet another topic
is the shortcrestedness of waves, particularly of nonlinear waves progressing to break-
ing. All these problems are due to an additional level of difficulty and complexity when
studying a three-dimensional as opposed to a two-dimensional phenomenon, whether
these are theoretical or experimental investigations. This additional level, however, should
be addressed as the directionality obviously provides a principal impact on the
physics of the wave breaking rather than a mere set of corrections to the existing
knowledge.
Some problems, such as the role of the modulational instability in the breaking of real-
istic oceanic waves, cannot be answered by means of two-dimensional studies in principle.
Such instability is a well-established and understood phenomenon for wave trains, but its
very existence in the directional fields has been questioned lately. In Section 5.3.3 ,how-
ever, it is argued that breaking due to modulational instability is active in directional wave
fields with typical magnitudes of wave steepness and directional spread.
If so, the relative role of wave focusing and of the modulational instability in the break-
ing of realistic waves observed in field conditions can now be compared. Indeed, as has
been discussed throughout the topic, it appears that in order to break all a wave needs is
to reach some limiting steepness. It should not really matter what process leads it to this
steepness, and potentially such processes are many. Broadly, however, it is the focusing and
the instability of nonlinear wave groups which have been the main competitors for leading
the waves to the no-return steepness in benign and moderate deep-water conditions. As
already mentioned above, the first mechanism, wave focusing, can be further subdivided
into frequency focusing, amplitude focusing and directional focusing.
The frequency focusing and amplitude focusing both exploit variation in the phase
speeds of waves: either because of different frequencies or due to different amplitudes
respectively. The frequency dispersion is quite large if the frequencies differ significantly
and seems like a good candidate to often provide superpositions of various waves in the
field with a continuous wave spectrum. The problem, however, is the fact that the drop
in spectral density (and the wave height) away from the peak is much more rapid than
changes in the phase speed, as a function of frequency. That is, the waves with close fre-
quencies/heights propagate with close speeds and are not likely to superpose, and the waves
which are likely to superpose have such different wave heights that addition of the smaller
ones to the primary wave does not alter the height of the latter appreciably. In a wave field
with a typical primary steepness of ak 1, superposition of very many such waves at a

single point would be needed in order to reach the limiting steepness of ak

= 0 .

= 0 . 44 which

becomes an event with quite a low probability.
The frequency dispersion has been one of the standard techniques of making waves
break in the laboratory, and correspondingly features of the breaking achieved this way
have been well investigated. Some of these features are similar to those of the modulational
type of breaking, some are not, as will be discussed below. What is surprising, however,
is the apparent lack, if not absence, of studies which would provide a parameterisation or