Geoscience Reference
In-Depth Information
Aerodynamic and Quasi-laminar Resistances
In Eq.
8.2
, the aerodynamic resistance,
R
a
, represents the effects of diffusion by
turbulent processes in the surface layer. It mainly depends on the atmospheric
stability and surface roughness. For neutral atmospheric conditions, the expression
of
R
a
is
h
ln
z
.
z
0
h
i
1
.k
u
/
R
a
D
(8.5)
with
k
the von Karman constant (0.4);
u
*
the wind friction velocity; and
z
the
reference height for wind velocity,
z
0
the aerodynamic roughness length of the
surface, and
h
the stability function.
The quasi-laminar resistance,
R
b
, describes the transfer of particles through the
viscous layer taking into account both the Brownian diffusion of particles having
small diameters (<0.5 m) and the inertial impaction, more efficient for particles
with large diameters (>2 m):
1
u
Sc
2=3
R
b
D
10
3=St
(8.6)
C
The resistance to particle diffusion across the quasi-laminar layer to a solid surface
is proportional to the Schmidt number, Sc, to the power of
2/3, at least for viscous
flow at high Reynolds numbers, Re, over a fixed, smooth surface and is depending
on the Stokes number, St (Slinn et al.
1978
). However, a nonrigid surface (e.g.,
the ocean surface) will tend to slip in the direction of the mean wind so that the
characteristic air velocity in the diffusion layer is somewhat larger and the resulting
transfer coefficient for particles across the quasi-laminar layer to a free surface
should be proportional to Sc
0.5
(Slinn and Slinn
1980
).
Sc is the ratio between viscous and diffusion forces associated with the Brownian
diffusion:
air
D
1
Sc
D
(8.7)
g
with ยค
air
the kinematic viscosity of air (1.461 10
5
m
2
s
1
)and
D
g
the Brownian
diffusivity expressed according to Davies (
1966
):
D
g
D
2:38
10
7
=D
p
1
0:0548 exp
6:66D
p
=D
p
(8.8)
C
0:163=D
p
C
In Eq.
8.6
, St represents the particle susceptibility to inertial impaction. Indeed, the
large particles, due to their high inertia, are less able to follow the flow when it
changes direction to avoid obstacles on the surface (rocks, bushes, trees, etc.). It is
expressed as
.
u
/
2
V
s
g
air
St
D
(8.9)
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