A Random Displacement Model (RDM) and a Langevin Equation Model (LEM) are used to simulate point releases in a complex flow around a building. The flow field is generated by a three-dimensional finite element model that uses the standard
k- model to parameterize the turbulence. The RDM- and LEM-calculated concentration fields are compared, with particular emphasis on the structure in regions with high turbulence and/or recirculation. RDM and LEM results are similar qualitatively, but RDM tends to predict lower concentration levels. In part this is due to the higher early-time diffusion. However, the expected convergence at later times is prevented by the interaction of the diffusion with the strongly inhomogeneous mean flow.Notation
a
i
coefficient in the Langevin equation
-
b
ij
coefficient in the Langevin equation
-
C
0
the universal constant associated with the Lagrangian structure function
-
H
building height (22.5 m)
-
K
eddy viscosity
-
K
k
eddy viscosity used in the definition of the off-diagonal Reynolds stresses
-
k
turbulent kinetic energy
- LEM
Langevin Equation Model
-
p
1
local unit vector in the
xy-plane, orthogonal to
s
-
p
2
local unit vector, orthogonal to both
s and
p
1
- RDM
Random Displacement Model
-
s
local unit vector in the streamline direction
-
T
local decorrelation time (Lagrangian time scale)
-
U
magnitude of the local Eulerian mean wind velocity
-
u
s
total velocity in the streamline direction
-
u
1
velocity component in the
xy-plane, orthogonal to the streamline direction
-
u
2
velocity component orthogonal to both
u
s and
u
1
-
i
mean Eulerian wind velocity
-
W
i
stochastic vector-valued Wiener process
-
x
unit vector in
x-direction
-
y
unit vector in
y-direction
-
z
unit vector in
z-direction
-
angle between the
xy-plane and the mean wind streamline
-
angle between the projection in the
xy-plane of the streamline and the
x-axis
-
ij
the Kronecker delta function
-
rate of turbulence dissipation
-
i/g
a
the part of
a
i that contains mean wind and turbulence gradients
-
ij
inverse of a Reynolds stress tensor component
-
ij
shorthand for a quantity that defines a part of
i/g
a
-
i
shorthand for a quantity that defines a part of
i/g
a
-
ij
Reynolds stress tensor component
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