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rapidly increases until breaking occurs. Apparently, the same considerations are applicable
to physical waves too.
At present, the concepts of incipient breaking and breaking onset are poorly defined
and even ambiguous. Traditionally, the initial phases of a breaker-in-progress are treated
as incipient breaking. As an example, let us consider how 'near-breaking' was defined by
Caulliez
(
2002
). In this paper, surface elevations were recorded, differentiated, and the
wave was regarded as a 'near-breaker' if its slope exceeded 0.586 any time between two
subsequent zero-downcrossings. This criterion is an estimate of the highest slope that a
Stokes wave can reach (
Longuet-Higgins & Fox
,
1977
). But if this slope is exceeded, then
the wave is not about to break - it is already breaking. This is not an incipient breaker, but
represents breaking in progress. The features and physics of breaking-in-progress, how-
ever, may be very different to that of incipient breaking (
Section 2.2
). Thus, investigation of
geometric, kinematic, dynamic and other properties of breaking-in-progress, such as white-
capping, void fraction, acoustic noise emitted by bubbles etc., will be of little assistance if
we are seeking to understand the causes of breaking and breaking onset.
In this topic, as in
Babanin
et al.
(
2007a
,
2009a
,
2010a
), we suggest that breaking onset
is defined as an instantaneous state of wave dynamics where a wave has already reached
its limiting-stability state, but has not yet started the irreversible breaking process charac-
terised by rapid dissipation of wave energy. That is, breaking onset is the ultimate point
at which the wave dynamics caused by initial instabilities is still valid. This definition
allows identification of the onset and, once the location of breaking onset can be pre-
dicted, allows measurement of the physical properties of such waves. The state of breaking
onset is instantaneous, unlike the stages of incipient breaking and breaking in progress (see
Sections 2.2
and
2.4
). The latter can be further subdivided into stages with different prop-
erties and different dynamics (
Rapp & Melville
,
1990
;
Liu & Babanin
,
2004
).
2.2 Breaking in progress
Beyond the point of onset, breaking occurs very rapidly, lasting only a fraction of the
wave period (
Bonmarin
,
1989
;
Rapp & Melville
,
1990
;
Babanin
et al.
,
2010a
), but the
wave may lose more than a half of its height (
Liu & Babanin
,
2004
). This is a highly
nonlinear mechanism, conceptually very different from the processes leading to breaking
onset, and should be considered separately. As mentioned in
Chapter 1
, while the collapse
is driven, to a greater extent, by gravity and inertia of the moving water mass and, to a
lesser extent, by hydrodynamic forces, breaking onset occurs mostly due to the dynam-
ics of wave motion in the water. Waves are known to break even in the total absence of
wind forcing, provided that hydrodynamic conditions are appropriate (e.g.
Melville
,
1982
;
Rapp & Melville
,
1990
;
Brown & Jensen
,
2001
;
Babanin
et al.
,
2007a
,
2009a
,
2010a
).
Therefore, processes leading to wave breaking, i.e. the stage of incipient breaking, can be
simplified by studying only the water side of surface behaviour, whereas for breaking in
progress, the air-sea interaction part, such as whitecapping (e.g.
Guan
et al.
,
2007
), void
fraction (e.g.
Gemmrich & Farmer
,
2004
), work against buoyancy forces (e.g.
Melville
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