Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 179

Figure 5.22 Lake George dominant wave-breaking probability b T versus (a) steepness peak (5.17) ,
(b) bottom-interaction parameter H s / d , (c) shear-stress parameter (5.21) , and (d) non-dimensional
peak frequency γ (5.20) . The legend shows the correlation coefficient based on a linear best fit. Figure
is reproduced from Babanin et al. ( 2001 ) by permission of American Geophysical Union

Also, the existence of a shear threshold is not as evident as with the steepness. These
indicate the secondary role of vertical shear as outlined above.
For the finite-depth Lake George data set, these marginal influences, as well as the pri-
mary dependence on peak (5.17) , are demonstrated in Figure 5.22 a, c and d. Since waves

observed at Lake George were affected by bottom proximity, ratio H s / d wasalsousedas

a parameter to characterise finite-depth effects on the wave-breaking statistics (denoted as
H

h in Figure 5.22 b). In the final parameterisation (5.24) , the secondary properties were
introduced as perturbation terms of the form 1

/

+ γ, 1 + and 1 + H s / d , which makes their

effect negligible when the parameters are small. For example, H s / d reduces to zero when

the water becomes deep or when the waves vanish, and in such circumstances the parameter
will have no effect on the overall dependence of breaking probability b T on steepness peak .

We note that extrapolations of the expression (5.24) into conditions when d

are very large have to be done with caution as such extrapolations would take the depen-
dence beyond the range of actual experimental data used to obtain the parameterisation.

γ, or H s /