Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 186

In Banner et al. ( 2000 ) and later in Banner et al. ( 2002 ), attempts were made to draw
a dependence, similar to (5.24) through a selection of frequency bins at scales smaller
than the spectral peak. Filipot et al. ( 2008 , 2010 ) were interested in a different property,
breaking wave height distribution, for the same ultimate purpose of assigning breaking
probability and breaking dissipation to different scales of the wave spectrum. In these and
other studies on this topic mentioned earlier in this subsection, since there is no charac-
teristic bandwidth at these small scales, a selection of different f in (2.5) were applied

in order to define a characteristic spectral steepness in those spectral bins. Even then,

adjustments to the shape of the spectral windows and to the threshold values had to be
made. Since parameterisation (5.24) is quadratic in terms of the wave steepness, it should
be expected to be linear if expressed through some spectral-density measure.
In this regard, two issues must be clarified. The absence of the characteristic bandwidth
away from the spectral peak is not merely a technical question, this is a physical problem.
As mentioned above, the modulational-instability mechanism cannot be active in the broad-
banded process which the small-scale waves appear to be. Even if the induced-by-long-
waves breaking of short waves is disregarded, this means that the physics of the breaking
at the shorter scales is altered compared to the dominant waves. The induced breaking,
however, cannot be disregarded as it is already significant close to the spectral peak and
apparently becomes dominant at higher frequencies/wavenumbers.
Another possibility may be that the short waves, as well as the dominant waves, are
also represented by coherent wave groups, information about which is averaged out in
such a space-time mean characteristic as the wave spectrum. Within such trains, the usual
instability mechanisms would be working, but such a concept would be mere speculation
at the present stage of our knowledge.
The second issue is the actual count of waves falling within a spectral band, whatever
width for such a band is found to be relevant. In Manasseh et al. ( 2006 ), the bubble-
detection method described in Section 3.5 was applied to the Lake George wave-breaking
data in order to estimate the breaking probability at wave frequencies beyond the spec-
tral peak, and to obtain the distribution of breaking probability b T ( f ) (2.4) with wave

frequency. To do this, the number of waves at each frequency N was redefined. As dis-

cussed in Section 2.5 , if the waves are counted by the zero-crossings, the resulting count
N c (

( f )

f ) will be less than the nominal reference count N ( f ) given by (2.13) , because in real

seas, waves of periods different to 1 f will occupy some part of the record. The breaking

probability b T used by Manasseh et al. ( 2006 ) was defined as

/

n ( f )

b T ( f ) =

) ,

(5.28)

N c ( f

where N c ( is the number of waves actually counted by the zero-crossing analysis within

the bandwidth

f )

f = f c ± 0 . 1 f p , (5.29)