Definitions for wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 37

In the case of a spectrum being estimated over a single wave group, or in circumstances
where breaking occurs in every wave group as in dedicated laboratory experiments (e.g.
Babanin et al. , 2009a , 2010a ),

s spectral = s group . (2.40)

Otherwise,

n group
N group s group .

s spectral = (2.41)

In the case of field waves, because wave groups at scales other than the spectral peak can-
not be identified, definitions (2.40) - (2.41) are only relevant for the breaking of dominant
waves.
Apart from the mere energy loss, downshift of the spectral energy also occurred in
Figure 6.1 , and the peak frequency moved from 2 Hz to less than 1

8 Hz. Both the spectral
downshift in the course of breaking (e.g. Tulin & Waseda , 1999 ) and the spectral distri-
bution of the energy loss due to a breaking (e.g. Pierson et al. , 1992 ; Meza et al. , 2000 )
have been reported in a number of other studies. The latter two papers, however, provide
an account on the spectral pattern of breaking severity which is quite different both to
Figure 6.1 (i.e. Babanin et al. , 2009a , 2010a ) and to each other.
Meza et al. ( 2000 ), who studied the dissipation of energy of laboratory two-dimensional
waves by means of frequency dispersion, found that the energy is lost almost entirely from
the higher frequencies, whereas the spectral peak remained unchanged after breaking.
Pierson et al. ( 1992 ), who stimulated the laboratory breaking through amplitude disper-
sion, obtained the opposite result: that is, most of the energy is lost from the primary wave.
This main conclusion is similar to that of Babanin et al. ( 2009a , 2010a ), but the spectral
breaking impact in their experiment is still different. In the experiments by Pierson et al.
( 1992 ), while the dominant wave loses energy, some components of the spectrum actually
gain energy. This outcome is quite physical because breaking is known to be associated
with the generation of short waves, whether by means of the production of parasitic cap-
illary waves on the front face of the breaker (e.g. Crapper , 1970 ; Ebuchi et al. , 1987 )or
because of a plunging jet impacting the surface (e.g. Hwang , 2007 ).
This brings us to another issue relevant to breaking severity in a spectral environment.
It is well known that field waves do not necessarily break at the spectral peak (domi-
nant breaking), but in fact breaking occurs frequently or even more frequently at smaller
scales (e.g. Babanin , 1995 ; Banner et al. , 2002 ; Melville & Matusov , 2002 ; Babanin &
Young , 2005 ; Hwang , 2007 ; Mironov & Dulov , 2008 ; Babanin et al. , 2007c ). Here, by
smaller scales we mean frequencies/wavenumbers of the spectrum tail, away from the
spectral peak, that is, waves that are relatively shorter than the dominant waves rather than
just short waves in terms of some dimensional limit of length. As discussed above, such
waves do not form groups, at least not in the narrow-banded wave-group sense. Therefore,
the problem of breaking severity distributed across the group is not relevant for them.

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