Geoscience Reference
In-Depth Information
attempt to illustrate the ongoing experimental effort on the phenomenon which has been
resisting such investigations and still remains difficult to approach experimentally.
The field study by Thorpe & Humphries ( 1980 ) used a breaker detection scheme based
on the jump of the surface slope associated with the leading edge of the breaking region.
Following the tradition of whitecap observations, they were seeking a correlation between
wind speed and breaking probability. The data clearly indicated such a dependence, but no
quantitative relationship was provided.
A similar breaking detection technique was developed by Longuet-Higgins & Smith
( 1983 ) who suggested a physical-limiter criterion; this was followed by many studies based
on this criterion. The authors reasoned that
“if a breaking wave passes the recorder, we expect a sudden jump in surface elevation”
which has to be detectable because of large values of the time t derivative of surface eleva-
tion
t . To detect the jumps, a wire wave probe was deployed on a specially designed
buoy. The buoy was tested first in the laboratory and then applied in the field to look for
the derivative
∂η/∂
= η
c η
R
t =
x =
c tan
θ
(3.21)
where the discretisation
is determined by the sampling frequency of the time series, and
the limit is defined by the maximal possible inclination of the surface (2.56) . The authors
argued that if lower values of R are set as the criterion for the jump-detection circuit,
breaking in progress will be identified, but caution should be exercised not to have the
circuit respond to steep, but non-breaking waves.
Longuet-Higgins & Smith ( 1983 ) applied their technique in the field, and measurements
were conducted for wind speeds from 1m
s. At the maximal wind speed, the
breaking rates found were of the order of 1% which is consistent with later field obser-
vations (e.g. Babanin et al. , 2001 ). Interestingly, however, they found that histograms of
measured surface jumps in breaking waves did not depend on the actual selection of the
critical value for R (provided, of course, it was high enough). Measured values of R often
exceeded what would signify the value in the maximal theoretical ratio of
R
c =
/
sto14m
/
0
.
586
(3.22)
which follows from (3.21) and (2.56) .
Detection of the surface-elevation jumps in accordance with the technique defined by
(3.21) - (3.22) was employed for wind-generated waves by Xu et al. ( 1986 ) and Caulliez
( 2002 ) in the laboratory. Xu et al. ( 1986 ) measured the probability of breaking occurrence,
breaking height and breaking duration, their dependence on the wind and their intercon-
nections. The data disintegrated into two distinct groups, the dominant breakers and the
second group
“probably associated with either the breaking of small waves riding on long waves or other profile
irregularities”.
 
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