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type which relys on the turbulence damping by suspended droplets.
Troitskaya & Rybushk-
ina
(
2008
) attribute this suppression of the turbulence to the role of the strong wind which
stimulates transfer of the air-turbulence energy near the water surface into the energy of
pressure waves in the air.
An additional factor which leads to reduction of the aerodynamic drag in the
Troitskaya
& Rybushkina
(
2008
) model is smoothing of the sea surface under extreme wind forcing,
i.e. removing or reducing the magnitude of short waves which support a significant part of
the drag. In this regard, the qualitative consequences of this model are similar to those in
the rain-like model of
Andreas
(
2004
) or the full-flow separation models of
Donelan
et al.
(
2004
,
2006
) and
Kudryavtsev & Makin
(
2007
).
Another model was proposed by
Soloviev & Lukas
(
2010
). This most original approach
can hardly be classified into any of the above-mentioned schemes, as it allows for and
relies on the existence of almost all the features of the other models mentioned above,
that is the two-phase layer near the surface filled with spray and bubbles, as well as on
the air-flow separation due to wave breaking. This breaking, however, is a micro-breaking
of capillary parasitic waves riding the front face of dominant waves (see e.g.
Cox
,
1958
;
Crapper
,
1970
;
Ebuchi
et al.
,
1987
;
Longuet-Higgins
,
1995
, about such parasitic modes),
rather than the breaking of gravitational waves mostly discussed in this topic, and it is
caused by Kelvin-Helmholtz (KH) instability.
Following
Koga
(
1981
),
Soloviev & Lukas
(
2010
) assume that KH instability happens
and disrupts the water surface when the wind-drift current velocity
U
s
exceeds the minimal
phase speed of capillary waves
c
min
=
0
.
232m
/
s. This condition is characterised by what
they call the 'Koga Number'
K
:
U
s
c
min
=
u
∗
K
=
1
/
4
.
(9.15)
(
g
σρ
w
/ρ
a
)
KH instability occurs if
K
>
K
critical
(9.16)
where the critical Koga Number ranges from
K
critical
=
1to
K
critical
=
0
.
26, which values
correspond to
U
10
≈
10-30.
That is, sporadic flow separation due to KH microbreaking can happen at wind speeds
as low as
U
10
s. Note that this is approximately the wind speed where the spo-
radic full flow separation was found in field experiments of
Donelan
et al.
(
2006
). These
latter authors, however, provided a different explanation of their observation: i.e. centrifu-
gal acceleration of the flow over the crest of steep waves was exceeding that due to the
pressure gradient which forces the flow to stay attached to the surface.
One way or another, once the flow separation is a permanent feature at wind speeds in
excess of
U
10
=
=
10m
/
s, it leads to what
Soloviev & Lukas
(
2010
) call a 'transition layer'
filled with spray and bubbles. Once created, this layer experiences a shear stress which
leads to another type of KH instability. This instability leads to entraining the water and
air parcels and to thickening the transition layer. The thickness reaches some equilibrium
level when this mixing is balanced by the gravitational force which acts on the droplets
30m
/
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