Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 411

result on the efficiency of modulational instability in the directional wave fields. Here, the
directional modulation index was introduced, by analogy with the Benjamin-Feir index for
two-dimensional wave trains, which describes the balance between steepness and direc-
tional spread. It is shown that for the magnitudes of this index typical for the oceanic
waves, the modulational instability remains active.
Section 5.3.4 discussed another breaking threshold, the wind speed below which the
wave breaking does not happen. Estimates of this range from 3m s and the dis-

crepancy may be due to natural rather than observational-accuracy reasons. Transition from
no-breaking to breaking is important across the entire range of the air-sea features, that is
in the context of wave evolution, of the near-surface underwater turbulence and of the sea
drag (see also Section 9.1.1 ).
If the results of Chapters 4 and 5 are combined, the most important conclusions are the
breaking threshold in terms of the background statistical wave steepness, which is applica-
ble both to the wave trains and wave fields, the limiting value of individual wave steepness,
which identifies a breaking onset for this wave, and the induced-breaking effect for short
waves modulated by longer ones. The directional behaviour of the breaking probability is
not trivial and very intriguing, but is also very unclear at the present stage. Wind-forcing
impacts, both for the breaking probability in wave trains and in the fields, are marginal and
even negligible unless the winds are very strong.
Due to rather incomplete knowledge on the wave-breaking severity, Chapter 6 dedicated
to this topic was relatively short. It incorporated two sections which describe the breaking
strength of waves in modulated wave trains and in waves with a continuous spectrum,
respectively. Again, as with the many topics mentioned above and below, important updates
to this subject have happened recently which were introduced in the chapter, in addition to
the material of the respective sections in the review.
The breaking severity appears to vary in a very broad range, virtually between 0% and
100% energy loss in an individual breaking event. The most important finding in this regard
is the role of the wind which appears to control the rate of development of the modulational
instability. While wind influence has always been mentioned as marginal as far as the
breaking onset and breaking probability are concerned, it emerges as being of primary
significance for the breaking strength.
As shown in laboratory experiments with modulated wave trains, the larger wind forc-
ing increases the breaking probability, but decreases the breaking severity, to the point of
practically cancelling the breaking as such. It appears, however, that the wind achieves this
effect not directly, but rather by means of gradually affecting the instability growth in non-
linear wave groups. Slowing down of this instability, because of the wind, is indicated by
the depth of the wave-group modulations in the course of wave-train evolution. As a result,
the modulation depth of wind-forced trains is much smaller compared to those unforced,
and this appears to lead to the different energetics of the breaking once it happens.
In Section 6.1 , a laboratory experiment was described, where dependence on the depth of
the modulation was isolated: that is variation of this depth was achieved by purely hydrody-
namic means, without involving the wind. The dependence indicates a robust trend between

/ sto8m /