Civil Engineering Reference
In-Depth Information
Turbulence
Turbulence
Wind
Wind
Gaussian
distribution of
concentration
Gaussian
distribution of
concentration
Fig. 20.3
Schematic representation of a Gaussian plume model
spatial 3D grid of time-dependent meteorological data (wind vectors, turbulence).
All puffs will be superimposed, thus forming an aggregate plume.
In a Gaussian puff model, the horizontal and vertical concentration profiles of
the puffs are modeled by Gaussian distributions. As in the Gaussian plume model,
the widths of these distributions are described by distance and turbulence dependent
diffusion parameters, cf. Fig.
20.4
.
For both Gaussian plume and Gaussian puff models, the thermal rise of a plume
or puff, respectively, in releases with thermal energy can be modeled by plume rise
formulae, see [
12
].
In case of rather complex meteorological conditions, such as wind directions
highly variable in space, spatially extended puffs can no longer be considered
because they will lose spatial resolution. Here, so-called particle models offer a
solution: They describe the releases of gases and aerosols by a “mathematical”
particle cloud. Each particle is propagated in time steps in accordance with the local
wind vector. Additionally a stochastic motion component is added that corresponds
to the turbulence (random walk model), cf. Fig.
20.5
. In principle, a particle model
can deliver highly detailed simulations of dispersion processes in the atmosphere.
However, high resolutions in space and time will be achieved only when the
calculations are carried out with large numbers of particles and small time steps.
This, in turn, requires long computation times. In addition, the quality of the
dispersion calculation cannot be any better than that of the input data required,
here, the computed three-dimensional time-dependent wind vector and the turbu-
lence and precipitation fields from meteorological prediction models.
The German Weather Service for example operates a Lagrange particle disper-
sion model, LPDM [
13
], for dispersion calculations of radioactive substances over
long distances.
A fundamentally different approach to calculating atmospheric transport and
dispersion is used in Eulerian grid models. They are based on a general equation for
the transport of matter in turbulent fluids, the advection—diffusion differential
equation. The wind vector fields contained in meteorological data correspond to
advection while the turbulence fields correspond to diffusion. Solutions of these
