Environmental Engineering Reference
In-Depth Information
Chapter 16
2D and 3D Transport Solutions
(Gaussian Puffs and Plumes)
16.1
Introduction
In the Chaps. 4-7 several solutions of the transport equation in a single space
dimension (1D) have been presented. Analytical solutions were presented including
various kinds of different processes. The models are valid under restricted
conditions. In this chapter we show that analytical solutions are also available for
higher dimensional problems.
The 1D formula can be applied to various situations in almost all environmental
compartments. Such models are especially popular in air pollution modeling, for
example in the modeling the local concentration distribution due to emissions from
stacks, but they can also be applied to problems of point pollution in rivers,
channels, lakes, reservoirs and the sea, in ground- and soil water.
Most solutions are derived from the 1D solution for a plume, which is given by
the
normal distribution
function
f
(
x
):
2
1
2
1
2
x
m
s
f ðxÞ¼
p
exp
(16.1)
p
s
The normal distribution has most applications in statistics.
m
is the mean value of
the distribution and
the standard deviation. As the normal distribution is also
referred to as Gaussian
1
distribution, these methods are also named
Gaussian
plumes
(in case of steady state) or
Gaussian puffs
(for the transient case). One
may find the term
Gaussian models
too.
The normal distribution
f
(
x
) with
s
p
2
Dt
m ¼
0 and
s ¼
is the solution of the
transport equation
@
c
@t
¼
@
@x
D
@
c
(16.2)
@x
1
Carl Friedrich Gauss (1777-1855), German mathematician.
