Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 117

Since, as was discussed above, from a practical point of view the model is basically
designed for dominant waves anyway, the uncertainty is not too essential and the limit
perhaps reflects well the critical level suitable for this kind of model.
Srokosz ( 1986 ) followed the approach of Snyder & Kennedy ( 1983 ), but offered an
alternative estimate of the breaking probability which is closer to the definitions used here
(i.e. Section 2.5 ). The statistics of Snyder & Kennedy ( 1983 )

“is essentially a spatial quantity representing the fraction of the area of the sea surface over which
breaking occurs, while B represents the proportion of crests that break at a given point”.

A very simple expression for B was proposed:

exp

2 g 2
2 m 4

− γ B = . (3.47)

In technical terms, Srokosz ( 1986 ) relied on the limiting acceleration at the wave crest
only, as opposed to Snyder & Kennedy ( 1983 ) who considered the entire wave surface
(in this regard, see Liu & Babanin , 2004 , and discussion in Section 3.7 above). Srokosz
concluded that the limiting fraction of the gravitational acceleration in (2.60) should be
0 4 g which was also consistent with his interpretation of the experimental data of Ochi &

Tsai ( 1983 ).
The relevance of inclusion/exclusion of high-frequency breaking, already discussed
above, is again highlighted in Srokosz ( 1986 ). The author points out that his estimate of
the acceleration variance m 4 depends on the choice of high-frequency cutoff. If, for the
Pierson-Moscowitz spectrum this cutoff is chosen as 2 f p , then B

.

10 − 8 , and the 6 f p - =

cutoff leads to B 002, i.e. five orders of magnitude difference in predicted breaking

rates when small-scale breaking is included.
To summarise the overview of probability methods and models, we have to conclude
that they of course do not deal with individual breaking events, like the other approaches
described in this chapter, but appear to be extremely capable in quantifying statistical char-
acteristics of breaking waves in the overall surface-wave field. This should not come as a
surprise as, unlike many or even most of the empirical breaking-detection techniques, they
refer to limiting surface properties based on fundamental physical grounds. In most cases
those are limiting steepness, orbital velocity or downward acceleration, or their derivatives
(see Section 2.9 ), which signify definite conditions such that beyond these conditions the
water surface cannot sustain itself and collapses. One can argue that the water surface may
become unstable even before it reaches these limiting conditions, but ultimately the wave
certainly cannot persist without breaking after. Therefore, although quantitative conclu-
sions of the probability models perhaps need revision, particularly those that try to predict
the dissipation as described above, such statistical models are very sound and promising in
the physical and theoretical sense.

= 0 .