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to dominate over the inherent breaking severity. This is a purely spectral effect which is
always present regardless of whether or not the dominant waves break.
Therefore, as far as the spectral impact of the breaking severity is concerned (i.e. spectral
distribution of the energy loss in a single breaking event), there appears to be a broad range
of possibilities, uncertainties and ambiguities. Depending on the physics leading up to
the wave breaking, energy may or may not be lost from the primary breaking wave. In all
scenarios, energy loss is endured across the entire spectrum, certainly at scales smaller than
that of the primary breaker. These smaller scales may be harmonics of the primary wave or
free waves (e.g. Meza et al. , 2000 ; Young & Babanin , 2006a ), but in any case their breaking
occurrence and breaking strength are strongly coupled with the breaking and severity of the
primary waves. Additionally, the wave energy is downshifted as a result of the breaking, at
least if the breaking is strong enough ( Babanin et al. , 2009a , 2010a ). This means that part
of the energy, that which is lost from the primary breaking scale, is not in fact removed
from the wave system. Finally, some scales in the wave spectrum, distant from the scale of
the primary breaker, may actually acquire energy as a result of breaking. These scales are
both below and above the scale of the breaker ( Pierson et al. , 1992 ). Overall, the (2.27) -
like notion of a fixed or even a reasonably approximate average value for the severity s is
a gross simplification or is simply inapplicable in a spectral environment.
In summary, we have provided four definitions for breaking severity (2.24) , (2.32) ,
(2.38) and (2.42) . While this may seem confusing and even discouraging, there is an appar-
ent order which should allow for measurement and quantifying of the breaking strength.
The basic definition of the energy lost by a single isolated breaker (2.24) , although the
most obvious, has perhaps the least practical significance and can only be employed in
refined conditions when breaking is due to superposition of linear or nonlinear modes, or
to a subsurface obstacle, mostly in the laboratory.
Equation (2.38) is the most general definition in spectral terms. It accounts for the
spectral impact of a breaking, which can include energy losses, energy gains and energy
exchange (shifting) between different wave scales in the spectrum. Since the spectrum,
however, is a resolution of waves, often nonlinear, into linear modes, the spectral distribu-
tion of breaking strength can signify both the actual energy lost by free shorter waves and
a reduction in nonlinearity of the primary waves (bound harmonics). Also, the attenuation
of the short waves in the wake of large breaking can occur without breaking, for example,
because of interactions of the short waves with intensive turbulence in the trace of the large
breaker (e.g. Banner et al. , 1989 ). In physical space, this loss will be attributed to the large
breaker, or to the group where this breaker occurred, and in the spectral sense it will be
placed at high frequencies/wavenumbers even though the waves at those scales may not
break. Obviously, the spectral definition of breaking severity (2.38) can be rewritten for
any spectral band f 1
f 2 if there are reasons to believe that the loss of energy is
restricted to this band, or if such a band is of dedicated interest:
<
f
<
s spectral
f 2
f 2
f 2
1
16 E s spectral (
f 1 ,
f 2 ) =
F before (
)
F after (
)
=
F before (
)
.
f
df
f
df
f
df
f 1
f 1
f 1
(2.44)
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