250
Air Pollution and Turbulence: Modeling and Applications
contaminant is injected at every time step. In this way, our results can be interpreted
in terms of plume diffusion from a continuous point source. After the initial time,
we continued the integration of the large-eddy model, and the evolution of the given
source was calculated simultaneously by solving the conservation equation of the
scalar. The time step of our simulation is determined by the LES numerical stability
conditions (never greater than 2 s). As mentioned above, we imposed the zero-outfl ow boundary conditions in both horizontal directions, while at the top and bottom
of the simulation domain, we used zero-gradient boundary conditions.
9.3.6.1.1 Convective Dispersion
The main characteristics of passive plume dispersion from an elevated source in the
convective boundary layer (CBL) have been demonstrated through numerical predictions (Lamb, 1978, 1979, 1981), fi eld observations (Nieuwstadt, 1981; Moninger
et al., 1983), and in a more detailed way through laboratory experiments (Willis and
Deardorff, 1976, 1981). In this section, we study the plume dispersion from an elevated
continuous point source. Our main goal is to reproduce classical plume behavior in a
CBL taking as reference the pioneering works of Deardorff (1972), Lamb (1981), Weil
(1988), and Nieuwstadt and De Walk (1987). In the numerical scheme described above,
we kept the full set of (advective/diffusive) operators in order to properly describe all
of the physical processes involved in the contaminant transport and diffusion.
The contaminant was injected throughout the duration of the simulation (release
time = 2000 time steps). The travel time, which is a rough estimate of how long it
takes to cross the longitudinal domain (10 km), is about 200 time steps. To get proper
plume behavior, both the sampling and the release time must be greater than the
travel time. In order to satisfy this constraint, we chose a concentration averaging
time of 4000 time steps.
We introduce the crosswind integrated concentration by
1
( , , )
y
y
T L
C
Cxyz
T
Δ
=
∫ ∫
Δ
dy dt where ΔT is an arbitrary average interval. This concentration is made dimensionless by dividing by Q/Uh, where U is the mean longitudinal wind velocity, Q is
the source strength, and the nondimensional distance X * is defi ned by (x/U)/(h/w * ).
Figure 9.1 shows the evolution of the dispersion process. In Figure 9.1, each graph is
obtained by averaging the instantaneous concentration fi eld over 250 time steps. As
expected, the contaminant fi lls the box until it reaches a quasisteady situation (Figure
9.1d) due to the equilibrium between the outfl ow and infl ow of the pollutant mass.
Figure 9.2 shows the crosswind integrated concentration patterns, where U is the
mean longitudinal wind velocity. This fi gure illustrates the main aspect of passive
plume dispersion in a CBL.
We can see that the plume centerline from an elevated source descends until it
reaches the ground, causing a maximum concentration, remains there for some distance, and then rises. The descent of the plume centerline is due to the size, long life,
and organized nature of the downdrafts in a convective mixed layer. Because the
downdrafts cover a greater area than the updrafts, the probability of material being
released into them is higher.
These characteristics agree qualitatively very well with the laboratory results of
Willis and Deardorff (1976, 1981), at least in the range of nondimensional distance
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
contaminant is injected at every time step. In this way, our results can be interpreted
in terms of plume diffusion from a continuous point source. After the initial time,
we continued the integration of the large-eddy model, and the evolution of the given
source was calculated simultaneously by solving the conservation equation of the
scalar. The time step of our simulation is determined by the LES numerical stability
conditions (never greater than 2 s). As mentioned above, we imposed the zero-outfl ow boundary conditions in both horizontal directions, while at the top and bottom
of the simulation domain, we used zero-gradient boundary conditions.
9.3.6.1.1 Convective Dispersion
The main characteristics of passive plume dispersion from an elevated source in the
convective boundary layer (CBL) have been demonstrated through numerical predictions (Lamb, 1978, 1979, 1981), fi eld observations (Nieuwstadt, 1981; Moninger
et al., 1983), and in a more detailed way through laboratory experiments (Willis and
Deardorff, 1976, 1981). In this section, we study the plume dispersion from an elevated
continuous point source. Our main goal is to reproduce classical plume behavior in a
CBL taking as reference the pioneering works of Deardorff (1972), Lamb (1981), Weil
(1988), and Nieuwstadt and De Walk (1987). In the numerical scheme described above,
we kept the full set of (advective/diffusive) operators in order to properly describe all
of the physical processes involved in the contaminant transport and diffusion.
The contaminant was injected throughout the duration of the simulation (release
time = 2000 time steps). The travel time, which is a rough estimate of how long it
takes to cross the longitudinal domain (10 km), is about 200 time steps. To get proper
plume behavior, both the sampling and the release time must be greater than the
travel time. In order to satisfy this constraint, we chose a concentration averaging
time of 4000 time steps.
We introduce the crosswind integrated concentration by
1
( , , )
y
y
T L
C
Cxyz
T
Δ
=
∫ ∫
Δ
dy dt where ΔT is an arbitrary average interval. This concentration is made dimensionless by dividing by Q/Uh, where U is the mean longitudinal wind velocity, Q is
the source strength, and the nondimensional distance X * is defi ned by (x/U)/(h/w * ).
Figure 9.1 shows the evolution of the dispersion process. In Figure 9.1, each graph is
obtained by averaging the instantaneous concentration fi eld over 250 time steps. As
expected, the contaminant fi lls the box until it reaches a quasisteady situation (Figure
9.1d) due to the equilibrium between the outfl ow and infl ow of the pollutant mass.
Figure 9.2 shows the crosswind integrated concentration patterns, where U is the
mean longitudinal wind velocity. This fi gure illustrates the main aspect of passive
plume dispersion in a CBL.
We can see that the plume centerline from an elevated source descends until it
reaches the ground, causing a maximum concentration, remains there for some distance, and then rises. The descent of the plume centerline is due to the size, long life,
and organized nature of the downdrafts in a convective mixed layer. Because the
downdrafts cover a greater area than the updrafts, the probability of material being
released into them is higher.
These characteristics agree qualitatively very well with the laboratory results of
Willis and Deardorff (1976, 1981), at least in the range of nondimensional distance
© 2010 by Taylor and Francis Group, LLC