Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 259

Figure 7.4 (Top panel) Mean power spectrum of incipient-breaking (solid line) and post-breaking
(dashed line) waves. (Bottom panel) Ratio of the spectra shown in top panel. Figure is reproduced
from Young & Babanin ( 2006a ) © American Meteorological Society. Reprinted with permission

that is

b T =− 5 A s . (7.19)

The spectral difference is quantified in the bottom subplot of Figure 7.4 , where the ratio
of the two spectra is plotted as a function of frequency f . The top subplot duplicates
Figure 7.3 to make comparisons easier. Clearly, the loss of spectral density, following the
breaking of dominant waves, is spread across almost the entire frequency range. Although
there is considerable noise, the longer wave scales appear more affected by the dominant
breaking than the shorter scales of f 5 f p . It is possible that these shorter scales recover

from the breaking impact at a time scale of a few tens of dominant periods (shorter than
the averaging period of the spectra shown here). It is also possible that the broadband
impact of the dominant breaking becomes less effective at high frequencies. The strongest
attenuation is observed for waves in the 3 f p -5 f p range.
The mean energy loss across the full measured spectrum is approximately 20%. This
is an important observation which will be mentioned in different aspects and discussed
many times below. Firstly, this does mean that the dominant wave scales, the spectral peak,
do lose substantial energy in the course of the dominant breaking. In the context of the

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