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course of wave breaking. While one-phase models can simulate outcomes of this behaviour
quite realistically as described above, the two-phase models are in principle capable of
explicitly reproducing the dissipation process. So far, most of them have concentrated on
simulations of plunging breakers in shallow waters, which cases are apparently more chal-
lenging and more appealing from the point of view of verification and demonstration of
the method. And even then less attention was paid to the dissipation as such, among such
interesting phenomena of the breaking as capturing and fragmenting the air pocket, for-
mation of the coherent structures, splash-ups and other free-surface behaviours, transfer of
the momentum to the currents and of the energy to the turbulence and vorticity. Given all
these achievements, investigation of the breaking in progress, and particularly the spilling
breaking which is most abundant in field conditions, by such two-phase models is quite
feasible and for now should only be a matter of time and concentrated effort.
7.3 Measurements of the wave dissipation of spectral waves
Measurement of the wave dissipation of monochromatic waves, in a way, was discussed
with breaking-severity in Chapter 6 . Severity, combined with breaking probability
described in Chapter 5 , provides the dissipation estimate (see also Section 2.7 ).
Subdivision of the monochromatic cases and spectral cases, however, is quite superficial.
As mentioned throughout the topic, strictly sinusoidal linear water-surface waves do not
exist. At the very least, they immediately turn themselves into Stokes waves, and therefore
in the Fourier space will produce bound harmonics at higher frequencies/wavenumbers
(see e.g. Chalikov , 2011 ), which fact has implications for wave breaking as we shall see
below. If the waves are not infinitesimally small, they start interacting with background
turbulence and generate resonant sidebands, leading eventually to all sorts of nonlinear
interactions in the wave system and to spreading into a broader spectrum (see e.g. Yuen &
Lake , 1982 ,forareview).
Most essentially from the point of view of the present topic, however, is that the dissi-
pation impact of the breaking is never local in frequency-wavenumber space. Even in the
simplest artificial experiment, when a quasi-linear wave is produced by a wavemaker and
made to break mechanically (for instance, by means of a subsurface obstacle), the outcome
will be spectral - at the very least, the plunger will generate some propagating ripples of
frequencies higher with respect to the original breaker.
Spectral impacts of natural breaking are well documented in the literature (e.g. Melville ,
1982 ; Pierson et al. , 1992 ; Tulin & Waseda , 1999 ; Waseda & Tulin , 1999 ; Meza et al. ,
2000 ; Manasseh et al. , 2006 ; Young & Babanin , 2006a , among others). In this section, we
will describe such measurements conducted in the laboratory ( Section 7.3.1 ) and in the
field ( Section 7.3.3 ). Different causes may lead to the breaking, such as linear or non-
linear dispersion, modulational instability and strong wind forcing, and it appears that
the dynamics of the resulting dissipation and the spectral outcome of the breaking will
also be different. The wave breaks because it becomes too steep, and not because of lin-
ear focusing or nonlinear instability, but in a way it 'remembers' what made it that steep.
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