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w
m
þ w
m
u
k
z
þ
z
0
z
0
z
L
z
0
L
u
ð
z
Þ
¼
In
;
ð
5
:
20
Þ
where z
0
is the linear size of surface roughness,
ʨ
m
are universal functions of
similarity calculated, for instance, in Paulsen (1970). Based on these calculations,
the wind speed is estimated with the formula (
5.20
)atz
z
B
and is assumed to be
equal to u(z)=u(z
B
) for all heights z > z
B
, where z
B
= max{0.1z
i
,|L|.
Practical application of the Gauss-type models has many aspects appearing,
depending on the multitude of the factors of the natural-anthropogenic environment.
This includes an effect of buoyancy of aerosol particles in the atmosphere,
intermittent atmospheric layers, and many others. Raaschou-Nielsen et al. (2000)
proposed to calculate the h
ef
parameters using the following formulas:
≤
H
ef
¼ h
s
þ D
h
;
where
1
=
3
; D
h
in
¼ 1
F
u
V
p
g
T
e
2
=
3
D
h
f
¼ min
D
h
in
; D
h
f
:
6
u
;
F ¼
ð
T
e
T
a
Þ;
Here F is the buoyancy
fl
ux, h
s
is the stack height, V is the
fl
flux volume, T
e
is the
temperature of the
flux emitted from the stack, T
a
is the air temperature.
The height of the aerosol jet due to the effect of its buoyancy is calculated with
the formula:
fl
8
<
3
uu
2
h
s
D
1
:
1
þ
;
neutral conditions
;
h
f
T
a
q
c
p
2
=
5
3
u
3
=
5
D
h
f
¼
Yg
4
:
;
convection
;
:
us
1
=
3
F
2
:
6
;
stability
;
where s ¼ g
=
T
a
ð
Þ@h
a
=@
z. Here
@h
a
=@
z is the potential air temperature gradient at
the stack
s level.
A multitude of possible situations with the use of the Gauss-type model is
determined by locality topology, the presence of the boundaries of the sea-land
type, mountains, and others. A consideration of a concrete situation enables one to
simplify the formulas and raise their reliability. In particular, Wang and
Christiansen (1986) considered such situations at the lake-land boundary. At the
water-land boundary the air
'
fl
flux is continuously adjusting itself to the wind
eld
con
guration forming into jets, corresponding to mechanical and temperature
conditions. Under conditions of a persistent coastal heat layer the gradient of
aerosol concentration can be stable, which depends on the distance of the source
from the shore. Here the following formula is valid:
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