Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 172

The surface-elevation time series with labelled individual breaking events were analysed
to determine individual breaker properties and breaking statistics. The accelerometer data
series from the PK cruise were segmented to reduce the effects of low-frequency trends
and integrated twice prior to analysis. With shorter waves riding on longer ones, occasional
confusion could occur as to which wave scale was actually breaking, but since dimensional
information on the individual whitecaps was available from the label length, it is believed
that uncertainties of this type were not essential.
The Lake Washington data set described by Katsaros & Atakturk ( 1992 ) represents a
short-wave extreme of natural deep-water wind-waves. These short fetch-limited waves
were generated by light winds. For this data set, U 10 ranged from 3

. 4m / sto6 . 8m / s,

with peak wave frequencies f p = 0 . 55 Hz to 0 . 75 Hz and wave-development stages of

U 10 / 5 to 2.5. The waves were measured by means of a wire wave gauge, with

breaking events recorded by a video camera observing the wave gauge. A detailed analysis
provided the number of plunging, spilling and micro-scale breakers for each of the sixty-
six 17-minute-long records. For the breaking-probability analysis, available plunging and
spilling breaker statistics were combined to quantify the breaking waves in the spectral
peak band.
The finite-depth wave-breaking data were obtained at the experimental site at Lake
George near Canberra in south-eastern Australia ( Figure 3.6 ) during October-December
1997. These data were described in detail in Section 3.5 (see also Table 5.2 ). The two
Southern Ocean data points were processed from the videos taken from a low-flying plane,
i.e. in the spatial domain, and were added to extend the probability study to very long
waves, see Banner et al. ( 2000 ).
As mentioned above, Banner et al. ( 2000 ) and Babanin et al. ( 2001 ) concentrated on the
breaking statistics of dominant waves. These statistics were investigated and the dominant-
breaking probability was parameterised in terms of average spectral-peak steepness. The
significant wave steepness given by

c p = 1 .

H s k p
2

significant = (5.16)

and contains some contribution from the higher-frequency components, which is irrele-
vant from the point of view of the evolution of dominant-wave groups to the breaking.
Therefore, the significant steepness of the spectral peak was introduced:

H p k p
2

peak = , (5.17)

where

4 1 . 3 f p
0

df 1 / 2 H p = F ( f ) , (5.18)

. 7 f p

i.e. the dominant waves were assumed to have frequencies within ± 30% vicinity of the

spectral peak (see (2.6) and discussion in Section 2.5 ). Intrinsically, peak is an appropri-

ate parameter as it provides a direct measure of the nonlinearity of the dominant waves.