2D and 3D Transport Solutions (Gaussian Puffs and Plumes) - Environmental Modeling - page 299

concentration

0.1

0.05

0

-0.05

0.1

- 0.1

0

y

0.85

0.9

0.95

1

-0.1

1.05

1.1

1.15

x

Fig. 16.5 Concentration distribution from a 3D Gaussian puff

Gaussian puff solution with no advection in order to evaluate pollen disposal from
genetically modified crops in agricultural ecosystems. The method can be chosen as
an option in the 'GaussianPuff.m ' file.

@ c

@t ¼ @ @x D x @c @x þ @ @y D y @ c @y þ @ @z D z @ c @z v @ c @x lc

(16.16)

A 3D Gaussian puff is visualized in Fig. 16.5 . The result was obtained using the
'GaussianPuff.m' file with input data:

For applications in the atmosphere, the formula is extended to take the ground
surface into account. The ground surface is located at z ¼ 0, while the release of the

pollutant appears at height H . In applications H can correspond with the stack or
chimney height, but often an increased value has to be adopted in order to account
for the initial rise of an emission plume with an increased temperature compared to
the ambient environment. H is also referred to as effective stack height .
At the ground surface, it is common to require a no-flow boundary condition. As
demonstrated in Chap. 15 the no-flow condition can be fulfilled by adding another
source in mirror position on the other side of the boundary, i.e. for the situation here
at location ( x,y,z )

H ). For a linear transport equation the solution can be
constructed by using the principle of superposition (see Chaps. 13 and 14):

¼ (0,0,