Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 263

dominant waves. What also matters here is that the dominant orbital velocities are the same
between the segments, and therefore the bottom friction is the same for the breaking and
non-breaking wave trains which is essential for the estimates made.
The second set of field measurements of the spectral distribution of wave-breaking dissi-
pation, mentioned in the beginning of this section, is based on the bubble-detection method
of Manasseh et al. ( 2006 ). This method was described in detail in Section 3.5 and its appli-
cation to measuring, across the wave spectrum, the breaking probabilities in Section 5.3.2 ,
and the breaking severity combined with the breaking probability (i.e. dissipation), in
Section 6.2 .
Since measurements of the spectral dissipation by this method have thus already been
described in the topic, we refer the reader to the above-mentioned sections. In short, the
conclusions are that it is only at the spectral peak that the dissipation intensity can be
related to the density of the wave power spectrum. As in the estimates done by means
of the spectrogram method above, major loss of energy is observed from the peak. In the
context of the discussions of Section 7.3.2 , this observation, again, points to modulational
instability as the likely course for the breaking here.
Neither below nor above the peak does the wave spectrum seem to correlate with the
dissipation at those spectral scales. Below the spectral peak, in the finite-depth Lake George
conditions development of the longer waves is arrested by the bottom-induced breaking
(see Section 3.5 ; Young et al. , 2005 ; Young & Babanin , 2006b ), and this is the most likely
reason for divergence of the wave-spectrum and dissipation-spectrum intensities. Above
the peak, this divergence is another demonstration of the cumulative effect which is the
subject of the next section.

7.3.4 Cumulative effect

Section 7.3.2 is essentially a separated out summary of the most important outcomes of
Section 7.3.1 , dedicated to the laboratory measurements of the dissipation and similarly,
the current section concentrates on the most important conclusion of the previous field-
measurement Section 7.3.3 . The significance of the cumulative effect for applications
which involve spectral distributions of the wave-energy dissipation is hard to overestimate,
and yet to date it is missing in the operational forecast models and is only starting to make
its way into research models.
The cumulative effect is due to breaking and/or dissipation of short waves being influ-
enced or even directly induced by longer waves. That is, as was shown in Section 7.3.3 (and
Young & Babanin , 2006a ), when the dominant waves of frequency

f p break, the energy
is lost not only from the waves of this frequency, but from the entire spectrum range of
f

∼

f p . So if the waves of frequency 2 f p will be breaking due to inherent reasons (rather
than being induced by f

>

2 f p breakings as just described above), they will not affect
the dissipation at the peak f p , but will cause a further associated dissipation at scales of
f

<

2 f p , and so on. Thus, dissipation of waves at a higher frequency, for example, 3 f p ,
will be induced every time waves in the range f

>

< 3 f p are breaking, and the higher the