Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 174

Figure 5.18 Observed dominant wave-breaking probability b T (2.3) versus the dominant wave steep-
ness (5.17) for two diverse field sites (a) Black Sea data (*), (b) Lake Washington data (+). The
legend shows the correlation coefficient based on a linear fit. Figure is reproduced from Banner et al.
( 2000 ) © American Meteorological Society. Reprinted with permission

on the basis of numerical simulations and laboratory experiments, once this is converted
to an equivalent root-mean-square measure. Therefore, a link between the modulational-
instability mechanism of two-dimensional wave trains and breaking in three-dimensional
wave fields can be expected.
The finite-depth Lake George breaking probability is tabulated in Table 5.2 and plotted
in Figure 5.22 a. As can be seen in this figure, the Lake George data are consistent with the
peak threshold observed for deep-water data in Figure 5.18 . Therefore, the value of

peak threshold = 0 . 055 (5.19)

can be adopted as a universal wave-breaking threshold for dominant spectral waves, appli-
cable both in deep water and in finite depths.
Thus, the presence of a wave-breaking threshold is established both for monochro-
matic wave trains and spectral waves. The threshold represents some characteristic mean
steepness value. Whether this is a uniform two-dimensional wave train or a spectral three-
dimensional directional wave field, this characteristic value signifies whether evolution of
the train will result in a breaking event or events, or not. In the spectral sense, the threshold
as described here is established for dominant waves.
For shorter waves of the spectral tail, such a threshold is impossible to define unam-
biguously, in terms of a characteristic steepness similar to (5.17) - (5.18) , because there
is no characteristic bandwidth at the broad-banded spectral tail (see also discussion in
Section 2.5 ). A breaking threshold, however, does exist at the smaller scales too, as the
wave-breaking dissipation clearly exhibits thresholded behaviour in terms of the spectral