Geoscience Reference
In-Depth Information
Kudryavtsev
(
2006
) found that the spume, if injected into the air at the level of breaking-
wave crests, can slow down the turbulence mixing, and thus lead to acceleration of the
wind speed and reduction of the sea drag as observed in the field. Outcomes of the model
depended essentially on the assumed size of the droplets, and that needed further reanaly-
sis. Also reanalysis was needed for situations when the density of the droplet-air mixture
was becoming large and therefore a non-Boussinesq approximation of the momentum
balance for such flow would have to be employed.
These revisions were done by
Kudryavtsev & Makin
(
2007
,
2009
,
2010
). One essential
outcome of this series of research studies was a conclusion that the second dynamic effect
of the spume, that is the attenuation of the turbulence due to density stratification produced
by the suspended droplets, dominates. The momentum effect is still present, but in terms
of its influence it can be disregarded by comparison with the other.
The governing equations for conservation of mass and momentum in
Kudryavtsev &
Makin
(
2010
) are written as
∂
∂
z
(
s
w
−
as
)
=
V
s
(9.8)
and
∂
∂
u
w
)
=
z
(ρ
0
.
(9.9)
The model is two-dimensional, and
u
here is the
x
-component of the horizontal-velocity
oscillations. The Reynolds terms in
(9.8)
and
(9.9
)
are t
he
vertical turbulent kinematic
fluxes of the droplets and momentum, respectively;
s
and
are the mean droplet concen-
tration and two-phase-fluid density, correspondingly, and
V
s
is the volume source of the
spume - the total volume of spume created per unit of time and per unit of volume of air.
Equation (9.9)
is the constant-momentum flux
equation (9.1)
, but for WBL with density
ρ
ρ
, and it turns into
(3.7)
far enough from the surface layer filled with spray:
u
w
=
ρ
a
u
2
ρ
a
u
w
+
ρ
s
(
z
)
∗
.
(9.10)
Here,
ρ
=
ρ
w
−
ρ
a
, and closer to the surface the difference with
(3.7)
is due to the
second term on the left-hand side which describes the contribution of the droplets into the
momentum balance.
(9.10)
can be rewritten in terms of what
Kudryavtsev & Makin
(
2010
) call 'local friction
velocity'
v
∗
:
∗
=
ρ
a
u
∗
2
u
2
v
∗
=
s
.
(9.11)
ρ
1
+
(ρ/ρ
a
)
10
−
3
, which it
can be, the stress is halved. That is the spray-stress impact may be very significant.
Thus, to conclude and briefly summarise this section, we can say that there is a general
consensus that the effects of spray are important across a broad range of applications and
processes in the atmosphere, from being a condensation seed in meteorological phenomena
to altering the dynamics of the lower boundary layer in the air-sea-interaction physics.
10
3
, and if
s
The ratio at the bottom of
(9.11)
is of the order
ρ /ρ
a
∼
∼
Search WWH ::
Custom Search