Environmental Engineering Reference
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0.023 m
0.167 m
0.696 m
0.0 0.3 0.6 0.9
1.2 1.5 1.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.00
0.05
0.10
0.15
0.20
<C>/ θ
Fig. 1. Normalized mean concentration. Black points, Coppin et al. (1986) data. Diamonds,
model results. The number at the top of each plot refers to the distance from the source
3. The Lagrangian Stochastic Model
We assume that the evolution of the centroid velocity is a Markov process (Luhar
et al., 2000), hence the plume meandering motion can be described by:
dx m = Uz ( dt
dz m = w m dt
dw m = a m ( t , w m , z m ) dt + b m
(2)
t , z ( dW ()
where Uz () is the mean wind vertical profile. The Langevin equation diffusion
parameter b m = 2 w 2 T m , where T m is the Lagrangian time-scale. The drift
coefficient a m can be derived using a quadratic functional form (Franzese, 2003;
Mortarini et al., 2009):
a m = Α m w 2 + Β m w m + Δ m
(3)
with Α m , Β m and Δ m depending on the first fourth moments of the velocity
PDF. An energy filter based on the partition of the turbulent kinetik energy is
 
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