Definitions for wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 47

( 1983 ) (see their interpretation by Srokosz ( 1986 )) for broadband breaking and laboratory
studies of Hwang et al. ( 1989 ) showed that

is closer to 0.4, and some other field mea-
surements (e.g. Holthuijsen & Herbers , 1986 ; Liu & Babanin , 2004 ) further indicated that
the value of

γ

could be even lower.
For more breaking-onset properties and criteria, we refer the reader to a near-comprehen-
sive table of the possible wave-breaking threshold variables in Snyder & Kennedy ( 1983 ).
In this paper, in addition to those already mentioned here, such characteristics as vertical
velocity gradient, horizontal velocity divergence, surface curvature and vertical acceler-
ation gradient are included. Bonmarin ( 1989 ) used 37 geometric parameters or coeffi-
cients, and an additional 8 parameters in terms of potential energy, to characterise the
breaking wave.
This brief summary of breaking-onset indicatorswould be incompletewithoutmentioning
a set of criteria that came from numerical simulations of the evolution of nonlinear wave
groups with imposed modulation ( Banner & Tian , 1998 ; Song & Banner , 2002 ; Banner &
Peirson , 2007 ). In general terms, these criteria can be regarded as dynamic, i.e. the rate
of change of the local mean wave energy density/the rate of change of the momentum
flux averaged over half a wavelength/the local average mean energy flux to the energy
maximum in the wave group. Such criteria can hardly be employed in a practical sense and
even their verification in refined laboratory conditions proved intangible and inconclusive
(i.e. Section 4.2 in Babanin , 2009 ).
Overall, we would like to say that breaking-onset criteria have proved very useful and
successful in wave-breaking studies of all kinds, but once the physics of breaking is under-
stood better, their significance will diminish or even eventually become redundant, with
the definite exception of the Stokes steepness limit (2.47) and related geometric, kine-
matic and dynamic features (2.48) - (2.50) . As we will try to show later ( Chapters 4 , 5 ), it
appears that waves break, not because of some particular physical mechanism, but rather
because in the course of their evolution they reach this limiting steepness and the water sur-
face becomes unstable, regardless of the processes behind the steepness growth. The same
growth mechanism, if it does not bring the wave height up to the Stokes limit (or its modifi-
cation in the case of directional waves (see Toffol i et al. , 2010a ; Babanin et al. , 2011a , and
Section 5.3.3 )), will not make the wave break. Therefore, probably, no single criterion,
except the limiting steepness, can be a robust breaking predictor in all circumstances.
Mechanisms that can lead to such a steep wave occurrence can be few, with modulational
instability likely to be largely responsible for the breaking of dominant waves.

γ

2.10 Radiative transfer equation

The radiative transfer equation ( RTE ) plays an important role in the context of wave-
breaking and breaking-dissipation studies, their intentions and motivations. It will not be
explicitly used in this topic for derivations or modelling, but it will be referred to, and
therefore needs to be mentioned and described among the other relevant definitions relating
to the wave-breaking process.