Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 419

velocities in breaking field waves, the elusive property which serves as a breaking criterion
for many theoretical approaches.
The issue of the breaking onset in finite depths, and particularly in shallow waters is
quite a different one (e.g. Miche , 1944 ). While the waves should certainly collapse if they
reach the limiting steepness, how much could such a limit be modified when the effect of
the bottom is crucial? The transient wave is a dynamic phenomenon and the wave may
collapse because the velocity field cannot be sustained (for example, the orbital velocity is
higher than the phase speed), and whether this occurs at the same limiting steepness in, for
example, very shallow environments is not that obvious.
Breaking probability in such very shallow environments also deserves special consider-
ation. In Section 5.3 , adjustment of the deep-water breaking-probability dependence was
done for finite-depth conditions and it worked at the Lake George field site, but the analysis
showed that, while affected by the bottom proximity, the majority of waves were still break-
ing due to inherent reasons. How should the breaking probability be described in shallow
non-dispersive waters, where deep-water nonlinear mechanisms, including the modula-
tional instability, are deactivated? Would the dependences be the same for flat and sloped
bottoms, or for different slope angles?
A very separate issue is waves on currents with horizontal velocity gradients both follow-
ing and adverse currents. In the latter circumstance the waves can be blocked and breaking
occurs at the blocking point (e.g. Chawla & Kirby , 2002 ). Will such an external forcing
modify the breaking onset? What is the rate of penetration and reflection of energy of non-
linear wave trains in such circumstances? This needs to be understood in order to estimate
the wave dissipation correctly.
A particularly interesting question is the end of the wave breaking (see also Section 2.2
about the subsiding stage of wave breaking). We now understand why the breaking starts,
but why does it stop? The severity of the breaking can be anything, from almost 0% to
100%, so the fraction of energy lost does not signal the end of breaking. An interesting
insight was produced by two-phase modelling, discussed in Section 7.2 . At least for some
spilling breakers, the wave breaks until the energy is reduced back to the steepness level
which defined the no-breaking threshold in the wave system. This is not so for plunging
breakers which do not stop breaking at such a threshold. And this issue is very impor-
tant for understanding, describing and parameterising the wave-energy dissipation. Since
a wave can completely disappear in the course of the wave breaking, this means that there
is no lower-steepness limit which signifies the end of breaking, and the stop-trigger here is
perhaps some dynamic property.
Since phase-resolving wave modelling is mentioned at this point of the discussion, the
modelling issue raised above in the descriptive part of the Conclusions has to be reiter-
ated. Two-phase models can explicitly simulate the breaking process, and they are well
developed analytically and numerically, and broadly used in engineering applications. The
main problem of their transfer into physical-oceanography studies in general, and wave
breaking in particular, is their high computational cost. Such a cost makes long-term sim-
ulation of the nonlinear wave evolution by two-phase models unfeasible, but this can be