Non-dissipative effects of breaking on the wave field - Breaking and Dissipation of Ocean Surface Waves - page 349

Thus, to summarise the entire chapter, we described three effects in the wave sys-
tem which relate to or, rather, are defined by the wave breaking and extend beyond the
usual physical-oceanography applications of the breaking such as whitecapping dissipa-
tion. More effects which extend beyond such applications will be attended to or outlined in
the next chapter, 9 , dedicated to the atmospheric boundary layer and the upper ocean. Here,
we only concentrated on those directly pertinent to the field of surface waves themselves.
Section 8.1 describes downshifting of the spectral wave energy in the course of wave
breaking brought about by the modulational instability. Customarily, such downshifting in
the wave system is attributed to the weak nonlinear interactions, but the instability-caused
breaking can certainly contribute to this feature, if not dominate it. Indeed, as discussed in
this section, the breaking happens at a much shorter time scale than the resonant four-wave
interactions. The theory of the downshifting for two-dimensional waves, which is able
to describe qualitatively and quantitatively evolution of the nonlinear groups, including
breaking and post-breaking periods, is described in the section. So, eventually, it comes
down to the question of whether the modulational instability is active in realistic directional
(i.e. three-dimensional) wave fields, and the recent experimental progress on this topic is
quite positive.
The next section, 8.2 , attends to the oldest known other-than-dissipation effect due to
wave breaking, i.e. the role of breaking in maintaining the level of the spectrum tail. Not
only the breaking defines the shape of the wave spectrum at small scales, i.e. its well-known
f − 5 behaviour, it also holds a major responsibility for the magnitude of the spectral power
in this frequency band. For younger waves, the tail level is approximately constant, and it
is achieved through the breaking varying its severity in response to changing wind-forcing
magnitude. For mature waves, starting from a wave age defined in the section, the level
starts decreasing towards the full-development value. The wave breaking controls this by
altering the breaking-occurrence rates. This wave age also potentially signifies change in
the wind-input regime (see Stiassnie , 2010 ), and within the spectrum this dimensionless
frequency defines the transition from the f − 4 to f − 5 interval, from inherent breaking to
induced breaking (see Section 8.2 ).
In controlling the shape and level of the spectral tail, the breaking has to compete with
another mechanism, nonlinear fluxes across the spectrum owing to energy input by the
wind. This leads, except in very strongly-forced wind-wave fields, to the co-existence of
the f − 4 and f − 5 subintervals above the spectral peak. In Section 8.2 , the expression for
the transitional frequency between these subintervals is obtained.
And the final section of this chapter, the current section, is dedicated to the energy-input
rather than energy-dissipation capacity of the breaking. It is demonstrated, based on field
measurements, that the energy flux over the breaking waves doubles. This fact can lead to
a significant altering of the wind-input energy rates in the case of a substantial amount of
breaking in a wave field, and the parameterisation of the respective wave-growth rates is
described.