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used to measure the spectra in four locations such that the breaking happened between two
of them.
The authors developed a special technique to separate free waves from the bound har-
monics, and compared spectra of free-wave components before and after the breaking. One
of their main conclusions was that
“the energy loss was almost exclusively from wave components at frequencies higher than the spec-
tral peak frequency. Although the energy density of the wave components of frequencies near the
peak frequency is the largest, they do not significantly lose or gain energy after the breaking”.
Interestingly, Meza et al. ( 2000 ) also observed the spectral downshifting as a result of
the breaking. They subdivided their spectrum into a low-frequency band of f
/
f p =
0
.
65-1
and a high-frequency band of f
5. The two bands were clearly separated in terms
of the power-spectrum outcome, with the former gaining the energy and the latter losing it.
The quantitative estimates varied a lot depending on the type of the breaking (spilling or
plunging) and the mean initial steepness, with the average energy gain by the longer waves
being 12% (median 8.5%), that is some 10%.
Thus, the two laboratory experiments, where the breaking was created by different
physical mechanisms, produced quite different results not so much quantitatively as quali-
tatively - in terms of their spectral impact. These important differences and their implica-
tions will be discussed in the next subsection.
/
f p =
1-3
.
7.3.2 Difference in the spectral distribution of dissipation due to different types
of breaking mechanisms
The current subsection is effectively a continuation of Section 7.3.1 above, but because
of its significance for further discussions, we have separated it out. Indeed, the breaking-
dissipation differences observed in the experiments of Tulin & Waseda ( 1999 ) and Meza
et al. ( 2000 ) can be further used for identifying physical mechanisms of the breaking
based on indirect observational features. These include field conditions where direct meas-
urements of the breaking are particularly difficult due to its intermittent, random and
destructive nature, and therefore the indirect methods are a more effective and feasible
way of research. This will be demonstrated in Section 7.3.3 below dedicated to field
measurements of the wave-energy dissipation.
In summary, when measuring the spectral consequences of the breaking caused by mod-
ulational instability, Tulin & Waseda ( 1999 ) found that the energy is lost from the carrier
wave, the most energetic in the wave train. For the breaking produced as a result of linear
focusing, Meza et al. ( 2000 ) revealed quite an opposite picture: hardly any energy goes
from the most energetic waves, and the observed dissipation is maintained by the energy
loss incurred by high-frequency free waves.
Some technical issues have to be mentioned which would need further investigations.
In the case of Tulin & Waseda ( 1999 ), the initial condition was a line spectrum, whereas
Meza et al. ( 2000 ) worked with a continuous spectrum. Neither, however, was similar to
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