Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 236

of breaking in propagating wave groups. This wave-group argument, however, is strictly
valid at the spectral peak only. The peak of the wind-generated spectrum is finite-width
but narrow, which allows us to explain both the existence and properties of linear groups
of dominant waves (e.g. Longuet-Higgins , 1984 ) and the development and instability of
nonlinear wave groups in a narrow-banded environment (i.e. Zakharov , 1966 , 1967 ; Ben-
jamin & Feir , 1967 ). The tail of the spectrum is not narrow-banded and does not have a
characteristic bandwidth in principle, and therefore the nature and very existence of the
short-scale groups is unclear and questionable.
Thus, the quasi-saturated argument may be appropriate if it is at the spectrum tail,
whereas the local-in-wavenumber-space dissipation is pertinent at the spectral peak, that is
both reasons are not applicable at the same time. Furthermore, the quasi-saturated concept
of equilibrium interval has been subject to various doubts, but even if it exists, the Phillips
saturation level is not constant and depends on environmental conditions (e.g. Babanin &
Soloviev , 1998a ). Also, none of the source terms that shape the spectral balance are known
explicitly and accurately enough to provide a reliable determination of the dissipation as a
residual sink term. And finally, as discussed in Sections 5.3.2 , 6.2 and throughout the topic,
there is a growing understanding that dominant waves and the breaking of dominant waves
affect waves and their dissipation at smaller scales ( Longuet-Higgins & Stewart , 1960 ;
Phillips , 1963 ; Banner et al. , 1989 ; Meza et al. , 2000 ; Donelan , 2001 ; Young & Babanin ,
2006a ; Donelan et al. , 2010 ). If so, the dissipation in the saturation interval should consist
of both functions local and non-local in wavenumber space. Therefore, the quasi-saturated
models, with all the limitations outlined above, would still be only part of the story.
The whitecapping model was introduced by Hasselmann ( 1974 ) and, with a variety of
empirical modifications (see e.g. Ardhuin et al. , 2007 , for an overview), is the dissipa-
tion theory most frequently utilised in wave-forecast models, or at least most frequently
referred to. This model relies on the distribution of well-developed whitecaps situated
on the forward faces of breaking waves. According to Hasselmann ( 1974 ), once there is
an established random distribution of such whitecaps, it does not matter what caused the
waves to break: the whitecaps on the forward slopes exert downward pressure on upward-
moving water and therefore conduct negative work on the wave. In a way, this mechanism
is similar to the physics of wind-to-wave input which is determined by the downward pres-
sure on the rear wave faces, just with the opposite sign. This dissipation model is a linear
function of the wave spectrum, i.e. n 1in (7.1) .

Two main assumptions of the whitecap model are that the dissipation, even if it is
strongly nonlinear locally, is weak in the mean, and that the whitecaps and the underlying
waves are in geometric similarity. Both assumptions are not strictly accurate. For example,
Babanin et al. ( 2001 ) investigated wave fields with over 10% dominant breaking rates, and
Young & Babanin ( 2006a ) examined a 60% dominant-breaking case. It is hardly that the
weak-in-the-mean approach is still applicable in such circumstances, which are apparently
a regular feature of wind seas.
The geometric similarity is also a questionable approximation for real unsteady break-
ers. The whitecapping commences at some point on the incipient breaking crest and then

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