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Theweak breakers are characterised by a broader distribution of the bubble sizes below the
surface, with the distribution having a relatively larger fraction of bigger bubbles if compared
withthestrongerbreakers,whichobservationisconsistentwiththeabove-mentionednegative
correlation of the breaker speed and surface bubble-sizes. In time, bubble-size distributions
narrowdown and their median value shifts toward smaller bubble radii. This is due to smaller
bubbles being injected deeper and surfacing slower because of weaker buoyancy forces.
Ultimately, the mean bubble size becomes that of the minimal bubbles originally generated.
The rate of decreasing of such mean bubble sizes is greater for weaker breakers, apparently
due to the fact that they produce fewer large bubbles and inject them down to a smaller depth
(see, however, model of
Garrett
et al.
,
2000
, in this regard).
According to
Bezzabotnov
et al.
(
1986
), the typical behaviour for all the observed under-
water bubble distributions is a rapid and nonlinear reduction of the void fraction
N
V
in
time: at 10 cm below the surface, this air-volume concentration drops 4-6 times 1 s after
the breaking and falls to a mere 1-5% of its original magnitude during the following 2 s
for weak breakers, and over a further 5 s for moderate-strength and 8 s for strong breaking
events.
Bezzabotnov
et al.
(
1986
) classified the breaking strength not in terms of the wave
properties, but in terms of the wind speed
U
10
which classification produces some ambi-
guity as to what actual breaking severities are compared:
U
10
=
10-13m
/
s corresponds to
weak, 14-16m
s to severe breaking. In principle, some rela-
tion between wind speeds and the properties of the waves observed in field experiments
of
Bezzabotnov
et al.
(
1986
) can be figured out by using their parameterised dependence
between orbital velocities in the breakers and
U
10
:
/
s to moderate and 17-19m
/
10
−
4
U
2
.
67
10
u
orb
=
3
.
7
·
+
0
.
13
(9.46)
where all the velocities are in m/s.
For the weak breaking, quantitative time dependence is suggested:
N
V
(
t
)
=
N
V
0
exp
(
−
t
/
t
0
)
(9.47)
where
N
V
0
7 s is the damping constant.
Overall, if all the data of
Bezzabotnov
et al.
(
1986
), corresponding to the different winds
and various water bodies, are put together, the dependence of
N
V
on wind speed can be
approximated as follows:
is the initial air-volume concentration and
t
0
≈
0
.
N
V
(
t
)
=
0
.
007
U
10
−
0
.
042
(9.48)
where
N
V
is dimensionless (cm
3
of the bubble air per cm
3
of the total water-bubble
volume) and
U
10
is in m/s.
An interesting observationwas that at wind speeds
U
10
>
17m/s, at themeasurement level
of 10 cm below the surface, small bubbles of diameter less than 0
5mm are always present.
While quantitatively the volume concentration of this background void fraction,
N
V
∼
.
1%
of the concentration in the active whitecapping, is quite small, qualitatively this wind speed
indicates a transition to a new phase of air-sea interaction in extreme-wind conditions, when
0
.
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