Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 184

The fetch, apparently, becomes shorter as the breaking rates of larger waves go up which
would be under conditions of strong wind forcing, finite depths and, most essentially, the
surf zone where this second effect should dominate over the above-mentioned modulation
of short waves.
The quoted observational description is helpful in many regards. First of all, while it is
mentioned in definite terms that the short waves are eliminated, it is not said explicitly that
these microwaves actually break too. In principle, they can be dissipated without breaking,
because of interaction, for example, with the turbulent wake of the large breaker (e.g.
Banner et al. , 1989 ). In this regard, it is difficult if not impossible to separate small-scale
breaking and small-scale wave-energy dissipation.
In the context of such dissipation, parasitic capillary waves should also be mentioned
( Crapper , 1970 ; Perlin et al. , 1993 ; Longuet-Higgins , 1995 ; Fedorov et al. , 1998 ). These
high-frequency waves are generated by steep waves and actively dissipate wave energy at
the respective scales, or may in fact make the large waves break (i.e. Crapper , 1970 ), but
the dynamics of this dissipation is determined, again, by their interaction with the longer
waves rather than by their local steepness alone.
The quote above also points out that, in the presence of frequent large breaking, for
the short waves the induced breaking/dissipation dominates. Indeed, the small-scale waves
only exist between the large breakers and their breaking/dissipation is determined by their
effective fetch between such breakers, regardless of the physics which would inherently
drive them to breaking. This is the so-called cumulative effect, very important for the
spectral dissipation of wind-waves (see also Section 7.3.4 ). This effect signifies the fact
that the breaking/dissipation of short waves of a certain small scale above the peak in
the wave spectrum is determined by the integral of the wave spectrum below this scale,
rather than by the value of the spectral density at this particular frequency/wavenumber
( Babanin & Young , 2005 ; Manasseh et al. , 2006 ; Young & Babanin , 2006a ; Babanin et al. ,
2007c ).
Quantitative observations, and particularly parameterisation of the breaking probability
of short spectral waves are not very many. This is primarily due to difficulties of detecting
small breaking and of separating the dominant breaking and small breaking, particularly
as the latter is often correlated or even linked to the large breaking as mentioned above.
One of the first clear experimental evidences of the spectral distribution of breaking
events was provided by Gemmrich & Farmer ( 1999 ) in terms of rate of occurrence of
breaking events with different phase speeds. Banner et al. ( 2000 ) showed results on the
frequency distribution of the breaking probability based on information gathered in the
Black Sea data set. A total of 2121 individual breakers of the 13 records listed in Table 5.1
were analysed. The sampling frequency of 4 Hz allowed us to compile frequency dis-
tributions for the breakers as histograms over the range from f p to twice the peak fre-
quency 2 f p . Binning of breaking-event probabilities was carried out for ± 15% constant-

percentage wavenumber bands centred on k p , 1 . 35 k p , 1 . 83 k p , 2 . 48 k p and 3 . 35 k p , thereby

covering the wavenumber range k p to 4 k p or, equivalently, the frequency range

f p to 2 f p .