Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 260

discussions in Sections 7.3.1 and 7.3.2 , this fact points to the modulational instability as a
likely cause for the breakings which took place here. Secondly, this result underlines the
cumulative effect to be discussed in Section 7.3.4 below.
It has to be emphasised here that, even though the short waves do also break as discussed
in Section 5.3.2 , the observed broadband difference of the two spectra is due to the domi-
nant breaking only. The inherent breaking of short waves, which would naturally occur (if
it would) in the absence of background dominant breaking, would not be detected by the
segmenting method. Such breaking will take place randomly on a time scale shorter than
the segment length. As a result, such smaller-scale breaking will happen in all segments
and the resulting differences in the energy between the segments will not identify breaking
at this scale - as though the segments were selected randomly. Therefore, any differences
in the high-frequency parts of the spectra are linked to the dominant breaking, rather than
to any other processes occurring at the higher frequencies.
It should be pointed out that the observed spectral difference is effectively the indi-
cator for spectral dissipation, rather than for the breaking probability only, regardless of
what an actual physical cause is for such high-frequency dissipation: i.e. whether this is
an enhanced level of high-frequency breaking, or an enhanced level of turbulent viscosity
dissipation at high frequencies, or both. This is equally true with respect to the directional
spectra and directional distribution of the dissipation discussed below. Figures 7.3 and 7.4 ,
therefore, demonstrate the cumulative effect for the wave-energy dissipation, similar to the
cumulative effect for the wave breaking shown in Section 5.3.2 .
The conjecture that the difference/dissipation between the observed spectra in
Figures 7.3 and 7.4 is due to dominant breaking required quantitative verification. Mea-
surements of the total dissipation in the water column beneath the surface waves were used
for this purpose. Estimates obtained by means of such measurements are not necessarily
more accurate than the estimates obtained in Young & Babanin ( 2006a ) by the segmenting
method, but the first approach is quite well established and provided a good reference value
for the new results.
The total dissipation per unit of surface, which is the usual measure of the wave-energy
properties including, for example, radiative transfer equation (2.61) , can be estimated
directly by measuring the volumetric dissipation rate

dis ( z ) in the water and then inte-

grating over the water-column depth z . If measurement of dis is only available at a single

distance from the surface, this can be used as a reference point, and for the integration a
parameterised depth-dependence would need to be adopted.
Field measurements of the profiles were discussed in detail in Section 5.3.4 ,

and the respective parameterisation was suggested there (5.74) . For the strong-wind Lake
George case employed here, the inverse-quadratic dissipation profile of (5.74) was used.
During the wave record analysed in our segmenting exercise, ADV measurements synchro-
nised with the wave and sound recordings were carried out at a distance of 20 cm from the
surface at the location of the wave array. The ADV velocity spectra of incipient-breaking
and post-breaking periods are shown in Figure 7.5 . The orbital velocities of waves around
the peak, unlike the peak spectral densities of the power spectra in Figures 7.3 and 7.4 ,do

dis ( z )