218
Air Pollution and Turbulence: Modeling and Applications
differential equations expressing the conservation of the momentum fl ux, buoyancy
fl ux, and volume fl ux. As an example, we will briefl y review the approach considered
in the TAPM LSDM (Hurley, 2005).
An equivalent approach was also proposed by Webster and Thomson (2002)
and is included in the NAME LSDM (Maryon et al., 1999). Among many other
NAME applications, the modeling study of a very large oil depot fi re in England is
of peculiar interest (Webster et al., 2006).
The TAPM approach is based on the model proposed by Glendening et al. (1984),
as simplifi ed by Hurley and Manins (1995). The equations of conservation of plume
volume G, buoyancy and momentum fl uxes, F b and F m , and the plume particle
trajectory are written as follows:
(
)
=
α
+ β
+ γ
2
1 / 2
d
2
d
a
p
G
R W
U W
u E
t
(8.45a)
d
1
d
2.25
b
m
a
p
F
F
s
U
W
t
u
⎛
⎞
= −
+
⎜
⎟
⎝
⎠
(8.45b)
d
d
m
b
F
F
t
=
(8.45c)
d
d
p
x
u
t
=
(8.45d)
d
d
p
y
v
t
=
(8.45e)
=
d
d
p
z
W
t
(8.45f)
where
2
a
p
s
T
G
u R
T
=
(8.46a)
2
a
m
p
s
T
F
u RW
T
=
(8.46b)
m
F
W
G
=
(8.46c)
(
)
2
s
a
b
p
s
T T
F u R g
T
−
=
(8.46d)
© 2010 by Taylor and Francis Group, LLC