Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 216

goes up. This was demonstrated by Babanin et al. ( 2007c ) and this effect can be seen in
Figure 5.27 of Section 5.3.2 .
In the top panel of this figure, the peculiarity of the wave-breaking-probability behaviour
at strong winds is demonstrated. According to (5.10) , (5.24) and (5.40) , the breaking prob-
ability and the dissipation function are expected to be determined by the wave spectrum,
at least near the spectral peak. As concluded above, the wind influence on wave break-
ing and energy attenuation is indirect: the wind changes the wave spectrum first, and this
change brings about alterations of the breaking as a consequence. In Figure 5.27 (top) the
breaking distributions merge together for moderate winds and are clearly enhanced for the
two stronger-wind cases, across the entire spectral band. Therefore, we could expect that
if the wave spectra solely define the breaking/dissipation, the spectra for the last two cases
should also be enhanced as a result of the stronger wind forcing.
This is, however, not the case. Figure 5.42 shows the full spectra in log-log scale in
the left panel, and in the right panel these spectra are plotted in expanded linear scale in
the frequency range of f 8 f p -3 f p . The wave spectra do merge as expected for the

moderate winds, but at strong winds of U 10 >

= 0 .

s a further increase of the wind speed
and the wind input does not cause noticeable changes of the wave spectrum either, except
at the peak. The excessive wind input, or at least a significant part of it, appears to be
dissipated locally through the enhanced breaking.
Alternatively, the excessive input could have been handled by the nonlinear interactions
( S in term in (2.61) ) and converted into the growth of the spectral peak. To add an uncer-
tainty, however, we must point out that in the scenarios studied here the peak waves were
strongly forced, with U 10 /

14m /

5, respectively (records 6 and 5 of Table 5.2 ),
and thus extensively received the energy for their growth directly from the wind.

c p = 2 . 5 and 6 .

Figure 5.42 Wave spectra for the records shown in Figure 5.27 . (left) Full spectra in log-log scale.
(right) Spectra in f = 0 . 8 f p − 3 f p range in linear scale. Figure is reproduced from Babanin et al.
( 2007c ) (public domain site http://www.waveworkshop.org/ sponsored by Environment Canada, the
U.S. Army Engineer Research and Development Center's Coastal and Hydraulics Laboratory, and
the WMO/IOC Joint Technical Commission for Oceanography and Marine Meteorology)