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winds. Some observations (i.e.
Munk
,
1947
) were quantified as the number of foam patches
per unit area thus allowing their relation to the breaking probability (see
Section 2.5
). The
majority of the results were expressed as a percentage of the whitecap coverage of the sur-
face, which property depends on a combination of the breaking probability, the breaking
strength and lifetime of the whitecap foam. The first two properties combined relate to
the overall dissipation due to wave breaking
(2.20)
, where contributions of the breaking
rates (
Section 2.5
) and breaking strength (
Section 2.7
), however, cannot be separated. The
whitecapping lifetime depends on environmental conditions, such as water temperature,
salinity and surfactants, and technically speaking it is not a characteristic of wave break-
ing. Therefore, the whitecap coverage bears essential uncertainties if treated as a property
of wave breaking or a quantitative feature of wave energy dissipation.
Parameterisation of breaking dependences, including the whitecap surface coverage, in
terms of the surface-wind speed is of course a reasonable approach as the waves are gener-
ated by the wind and many characteristic properties of the wave field ultimately correlate
with the wind. Because of the very large density difference between the air and the water,
however, the wind impact on breaking is mostly indirect. That is, the wind slowly pumps
energy into the waves, which gradually grow under the wind action, and as their steepness
increases, the hydrodynamic mechanisms (rather than wind forcing) lead some waves to
break. This will be discussed in detail in
Chapters 5
and
6
. Here, we will mention that the
capacity of the wind to stimulate or even affect the breaking onset as such is marginal,
unless the wind forcing is very strong (i.e.
U
10, see
Babanin
et al.
,
2009a
,
2010a
),
and the physics of wave-breaking parameterisations should be expressed in terms of the
wave, rather than the wind properties (e.g.
Babanin
,
1995
;
Felizardo & Melville
,
1995
;
Banner
et al.
,
2000
;
Babanin
et al.
,
2001
).
The last two studies used Black Sea (
Section 3.7
) and Lake George (
Section 3.5
) field
data, combined with measurements from a small shallow lake and data points from the
Southern Ocean, which together made up a very diverse data set, which argued that relating
the breaking probability to the wind speed provided a reasonable correlation within each
individual data set, but when the diverse data were combined, these correlations essen-
tially degraded. In the combined data set, with a broad range of dominant wave lengths
(10-300m) and wind speeds (5-20m
/
c
>
s), there was no correlation between the break-
ing rates and the wind speed, whereas the dependence of the breaking probability on the
properties of the wave field remained.
Keeping this understanding in mind, it is interesting to revisit the early results. They
clearly exhibited many features of wave-breaking behaviour that are being 'rediscovered'
years later, and they set many standards to follow. For example,
Munk
(
1947
) concluded
that there was no breaking at wind speeds
U
/
<
6m
/
s and
Gathman & Trent
(
1968
) found
no whitecaps at
U
s. Similarly,
Blanchard
(
1963
) demonstrated a significant
increase in whitecap coverage at
U
<
3
.
1m
/
s and
Monahan
(
1969
) observed that the frac-
tional coverage was very small, less than 0.1% for light winds, and only started to grow
and depend on the surface wind at
U
>
3m
/
s. Such results are consistent with later obser-
vations (e.g.
Donelan & Pierson
,
1987
;
Bortkovskii
,
1997
,
1998
;
Babanin
et al.
,
2005
,see
>
4m
/
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