Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 168

exist. Besides, the waves will be three-dimensional, and the modulational mechanism will
be combined with wind forcing, current shear, superposition of dispersive spectral waves,
and modulation due to linear wave groups, among other relevant features. However, the
above analysis suggests that should waves reach some critical steepness then they will
ultimately break. It does not matter whether this limiting steepness occurred due to sus-
tained wind forcing, wave-group modulation or other means, as long as the limiting value is
reached.
Clearly, the breaking process is associated with individual waves, and hence a local
measure of the steepness of each wave is the desired quantity. For applications (e.g. in
a wave-prediction model), such time-domain information is impractical and a spectral or
average value of the steepness of the wave field is the only possible quantity available.
A further complication in comparing available field data with predictions of the current
parameterisation results from the fact that the relationship (5.10) predicts the probability
of incipient breaking, whereas in the field it is impossible to directly measure whether a
wave is an incipient breaker or not. At best, we can measure quantities that result from the
breaking process. Common measures of this type include the acoustic signature of breaking
waves or surface whitecap coverage. Although these quantities are indirect measures, they
are related to the breaking process. However, a breaking wave emits an acoustic signature
and forms whitecaps over a substantial part of its period, and therefore the probability of
encountering such sound or whitecaps would be higher than the probability of breaking
onset (see Section 2.4 above).
Given the uncertainties, comparison of the present parameterisation of the breaking
probability (5.10) with field data can only be qualitative at this stage, as the quantities
being compared are not identical. This is done in Figure 5.17 (bottom), but will be dis-
cussed in detail in Section 5.3 after the probability dependences for spectral waves are
introduced in Section 5.2 .
5.2 Wave-breaking threshold
Before discussing the breaking probability in spectral environments ( Section 5.3 ), here we
would like to formulate and quantify the wave-breaking threshold, below which break-
ing does not happen in a wave train or a wave field, in terms of wave steepness. While
applicable in any wave-breaking scenario, the threshold has to be introduced differently
in monochromatic wave trains, where it is the steepness of individual waves, and in the
spectral wave field where the information on the steepness of individual waves is usually
not available. Essentially, the meaning of this threshold will be discussed and its difference
from the breaking criterion that signifies breaking onset (5.4) will be explained. Examples
from the deep-water (Black Sea) and finite-depth (Lake George) field sites will be used
and respective data will be described in detail (see also Sections 3.7 and 3.5 for general
descriptions of the two field experiments, correspondingly).
In the numerical simulations of Section 4.1 and the laboratory experiments of
Section 5.1 , breaking threshold was established in terms of the initial monochromatic