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In the context of the above estimates for the breaking-in-progress stage, this would mean
that the entire breaking process (excluding the residual stage) lasts for half of a wave period.
Bonmarin
(
1989
) also suggested the interesting analogy of plunging breaking with tur-
bulent flow: the overturning phase would compare with laminar flow, the breaking as such
to the transient stage and the afterbreaking to fully developed turbulence.
“If this comparison is adopted,
...
the experimental procedures and the theoretical and numerical
approaches have to be adapted to these three different phases”.
We should point out that the water motion in the overturning crest is far from being laminar
(e.g.
Gemmrich
,
2010
), but overall the suggested analogy is quite attractive and promising.
2.5 Breaking probability (frequency of occurrence)
Breaking probability, or as it is often called breaking rates or frequency of breaking
occurrence, is one of the most important statistical characteristics of wave fields that
contain breaking events. Since wave breaking is the main sink of energy in such fields,
but not every wave is breaking, the breaking probability, together with the breaking sever-
ity (
Section 2.7
), provide a means of statistical description of wave energy dissipation and
other dynamic impacts caused by breaking.
In order to achieve this description, an understanding of the distribution of breaking
probability, as well as breaking severity across the spectrum is needed. In other words, we
need to be able to predict how frequently waves of different scales will break and howmuch
energy they will lose in a breaking event. It is also most important to understand the physics
that controls breaking rates and severity, and to quantify and parameterise the dependence
of the breaking occurrence and severity on wave development and other environmental
characteristics. These will be the main topics of
Chapters 5
and
6
; here we will suggest the
main definitions.
Previous authors have used various characteristics and parameters to describe breaking
statistics or probabilities.
Wu
(
1979
) provided a summary of whitecap coverage statistics
based on field observations by
Monahan
(
1971
) and
Toba & Chaen
(
1973
) who analysed
photographs of the water surface.
Longuet-Higgins & Smith
(
1983
) detected 'jumps' in the
rate of change of the elevation signal related to the passage of breaking crests.
Weissman
et al.
(
1984
) analysed changes in spectral energy in the 18-32 Hz frequency band to detect
breaking events. In his Loch Ness measurements,
Thorpe
(
1992
) associated large time-
derivatives of the signal strength in sonograph records with the occurrence of breaking
wave crests.
Ding & Farmer
(
1994
) used an array of four hydrophones to detect and track
breaking waves and thus determine their duration, velocity and spacing in terms of 'active
acoustic coverage.'
Gemmrich & Farmer
(
1999
) detected breaking waves from a buoy on
the basis of air entrainment within breaking waves measured by changes in the electrical
conductivity of the water at fixed depths just below the surface.
More details on the measurement of breaking probability and statistics will be provided
in
Chapter 3
. It is evident that thresholds underlying most of these methods are empirical
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