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10
Conclusions. What else do we need to know
about wave breaking?
Wave breaking represents one of the most interesting and most challenging problems for
both fluid mechanics and physical oceanography. It is an intermittent random process, very
fast by comparison with other processes in the wave system. The distribution of wave
breaking on the water surface is not continuous, but its role in maintaining the energy
balance within the continuous wind-wave field is critical.
The challenges thus outlined make understanding of such wave breaking and even an
ability to describe its onset very difficult, and as a result knowledge of the physics of the
breaking, and even practical parameterisations of the phenonemon have been hindered for
decades. Recently, knowledge of the breaking phenomenon has significantly advanced, and
this topic is an attempt to summarise the facts into a consistent, even if still incomplete,
picture of the phenomenon.
If this picture were to be formulated into a few paragraphs of these conclusions, we
would like to say the following. The waves break because the water surface reaches some
limiting steepness. Apparently, the fluid interface has to have a limit beyond which it will
collapse. In the system of nonlinear water-surface waves subject to a variety of external
forcings and internal instabilities, there are a number of physical processes which can lead
to such a steepness. They are the modulational instability, linear (dispersive and directional)
and nonlinear (amplitude-dispersion) focusing, modulation of steepness of shorter waves
by longer waves, direct forcing by the wind (if very strong) or by the current, and wave-
bottom interactions, among others. It is not, however, these processes, for example, not the
modulational instability or the focusing which make the waves break; their importance is
only in bringing the wave steepness to the limit. In nonlinear wave fields with a continuous
frequency-directional spectrum, both the nonlinear evolution and the focusing are always
active, but if the result of their activity does not lead to the limiting steepness, the wave
subjected to such action will not break. The wave will only collapse if it is steep beyond
the limit. Breaking is a surface phenomenon and therefore subsurface and other accom-
panying features related to the breaking are simply indicators that the steepness limit is
being reached.
While the breaking as such is triggered by the limiting steepness regardless of the
mechanism which led to this steepness, in terms of the dynamics of the wave-energy dis-
sipation due to the breaking the wave appears to 'remember' what made it that steep. This
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