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negative correlations with some phases of other waves in the wave train: for example, if a
wave crest was breaking, there was a tendency for successive crests to also break.
Some of the outcomes, however, indicate the limitations of the method. Thus, it was
concluded that the whitecaps should travel with a speed appropriate to their scale. Such
a finding is of course perfectly consistent with the expected behaviour of waves breaking
due to inherent reasons, but not of induced breaking, i.e. breaking of short waves forced
near crests of dominant waves. Obviously, one cannot blame the model for not reproducing
what it was never designed to reproduce, but this fact outlines important constraints of such
models. Since the induced breaking is expected to dominate at small scales (see
Chapter 5
),
this means that in practical terms the
Snyder & Kennedy
(
1983
) approach is restricted to
some range of frequencies around and above the spectral peak.
Snyder & Kennedy
(
1983
)
in fact had a self-imposed cutoff of some 5
f
p
-10
f
p
, due to divergence of the integral of
the acceleration spectrum which they relied on. The lower bound of this cutoff is actually
in reasonable agreement with the limits that indicate dominance of the induced breaking
(
Babanin & Young
,
2005
;
Babanin
et al.
,
2007c
).
To bypass the integration of probability densities for the acceleration, the technique was
further tested bymeans of Monte Carlo simulations of the vertical accelerations (
Kennedy&
Snyder
,
1983
). An additional interesting finding of this statistical study was that
“the propagation velocity of the whitecap was typically 45% of the phase velocity associated with
the frequency of peak energy”
(see also references to
Smith
et al.
(
1996
) and
Stevens
et al.
(
1999
)in
Section 3.6
).
Kennedy
& Snyder
(
1983
) further conjectured that
“while this velocity is close to the group velocity, the similarity between the two velocities is probably
coincidental, as there appears to be no reason to believe that group velocity is a pertinent param-
eter. The low velocity of the whitecaps probably reflects the importance of higher frequency wave
components to the breaking process”.
Both the conclusion and the conjecture now find experimental support (e.g.
Gemmrich
et al.
,
2008
).
Snyder
et al.
(
1983
), the final paper in the series of
Snyder & Kennedy
(
1983
) and
Kennedy & Snyder
(
1983
), was intended to provide experimental support to the proba-
bilistic model and its rich set of interesting and important conclusions, and to estimate
experimentally the key parameter of the model, i.e. threshold value of the downward accel-
eration. A field experiment was conducted in order to measure the statistical geometric
properties of whitecaps, by means of synchronised photographing of the breaking waves
and recording them with an array of wave probes. Many theoretical findings of the statis-
tical model were confirmed, with the most important conclusion being that the threshold
acceleration should correspond to the theoretical limit for monochromatic Stokes waves
(2.50)
, i.e. 0
.
5 g. The authors cautiously warned that
“this conclusion is less than definite because our analysis is limited to wave components with
frequencies less than twice the frequency of the spectral peak”.
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