248
Air Pollution and Turbulence: Modeling and Applications
9.3.4 BOUNDARY CONDITIONS FOR THE ADVECTIVE TERMS
We assume, for every time step, zero gradient boundary conditions and zero outfl ow
boundary conditions, that is,
⎧ =
⎪
=
⎨
⎪
=
⎩
0
0, ,
0
for
1
0
h
h
k i
P
j
C
(9.24)
1, ,
0
for
0
h
Nx
x
h
Nx k i
P
j N
C +
⎧
=
⎪
=
⎨
⎪
=
⎩
(9.25)
Analogous conditions are applied in the y and z-directions.
9.3.5 BOUNDARY CONDITIONS FOR THE DIFFUSION TERMS
We assume, for every time step, zero outfl ow boundary conditions, that is,
+
+
=
=
=
1
1
2
0, ,
0, ,
for
1
0
h
h
k i
k i
j
C
C
(9.26)
+
+
+
+
=
=
=
1
1
2
1, ,
1, ,
for
0
h
h
Nx k i
x
Nx k i
j N C
C
(9.27)
Analogous conditions are applied in the y-direction. For diffusion in the z-direction,
the boundary conditions are zero gradient conditions, that is,
=
=
, ,0
, ,1
for
1
h
h
j k
j k
i
C
C
(9.28)
+
=
=
, ,
1
, ,
for
h
h
j k Nz
j k Nz
z
i N
C
C
(9.29)
9.3.6 DISPERSION EXPERIMENTS
In order to point out the differences in dispersion patterns between buoyancy- and
shear-driven PBLs, we generated different types of PBLs with the LES model by
varying the geostrophic wind speed (U g , V g ) and the surface heat fl ux Q * . Moeng and
Sullivan (1994) did a sensitivity analysis over such forcing parameters that generate
different turbulent regimes. Following these arguments, we reproduced two types of
PBLs: a buoyancy-dominated PBL, hereafter simulation B, and a neutral (pure shear)
PBL, hereafter simulation S.
Simulation B is buoyancy-dominated fl ow with little shear effect confi ned close
to the ground, while simulation S is a shear-dominated fl ow with no heat fl ux.
Calculations were performed in a rectangular domain arranged in such a way that
it could comprise several updrafts at a given time. For simulation B, the dimensions
of the box are 10 × 10 km in the horizontal directions and 2 km in the vertical direction, with a resolution of 128 grid points in the x- and y-directions and 96 grid points
in the z-direction. For simulation S, the dimensions of the box are 3 × 3 km in the
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
9.3.4 BOUNDARY CONDITIONS FOR THE ADVECTIVE TERMS
We assume, for every time step, zero gradient boundary conditions and zero outfl ow
boundary conditions, that is,
⎧ =
⎪
=
⎨
⎪
=
⎩
0
0, ,
0
for
1
0
h
h
k i
P
j
C
(9.24)
1, ,
0
for
0
h
Nx
x
h
Nx k i
P
j N
C +
⎧
=
⎪
=
⎨
⎪
=
⎩
(9.25)
Analogous conditions are applied in the y and z-directions.
9.3.5 BOUNDARY CONDITIONS FOR THE DIFFUSION TERMS
We assume, for every time step, zero outfl ow boundary conditions, that is,
+
+
=
=
=
1
1
2
0, ,
0, ,
for
1
0
h
h
k i
k i
j
C
C
(9.26)
+
+
+
+
=
=
=
1
1
2
1, ,
1, ,
for
0
h
h
Nx k i
x
Nx k i
j N C
C
(9.27)
Analogous conditions are applied in the y-direction. For diffusion in the z-direction,
the boundary conditions are zero gradient conditions, that is,
=
=
, ,0
, ,1
for
1
h
h
j k
j k
i
C
C
(9.28)
+
=
=
, ,
1
, ,
for
h
h
j k Nz
j k Nz
z
i N
C
C
(9.29)
9.3.6 DISPERSION EXPERIMENTS
In order to point out the differences in dispersion patterns between buoyancy- and
shear-driven PBLs, we generated different types of PBLs with the LES model by
varying the geostrophic wind speed (U g , V g ) and the surface heat fl ux Q * . Moeng and
Sullivan (1994) did a sensitivity analysis over such forcing parameters that generate
different turbulent regimes. Following these arguments, we reproduced two types of
PBLs: a buoyancy-dominated PBL, hereafter simulation B, and a neutral (pure shear)
PBL, hereafter simulation S.
Simulation B is buoyancy-dominated fl ow with little shear effect confi ned close
to the ground, while simulation S is a shear-dominated fl ow with no heat fl ux.
Calculations were performed in a rectangular domain arranged in such a way that
it could comprise several updrafts at a given time. For simulation B, the dimensions
of the box are 10 × 10 km in the horizontal directions and 2 km in the vertical direction, with a resolution of 128 grid points in the x- and y-directions and 96 grid points
in the z-direction. For simulation S, the dimensions of the box are 3 × 3 km in the
© 2010 by Taylor and Francis Group, LLC