J18.1

**Quantitative probabilistic model for urban dispersion**

**Eugene Yee**, Defence R&D Canada - Suffield, Medicine Hat, AB, Canada; and B. C. Wang

The assessment of actual or potential hazards
(toxicity, flammability, malodor), resulting from the dispersion of a pollutant
plume of noxious material in a built-up (urban) area, requires a probabilistic
model for the prediction of the statistical characteristics of the fluctuating concentration.
Towards this objective, a simple and practical probabilistic model for
concentration fluctuations in plumes dispersing in an urban environment is
formulated. This formulation uses Reynolds-averaged Navier-Stokes (RANS), with
a two-equation *k*-*ε* turbulence closure model, to predict the complex
and highly disturbed wind flows in an urban area. This mean flow and turbulence
model provides the spatially-varying velocity statistics of the urban flow
required by the turbulent-transport model for the concentration fluctuations, the
latter of which involves the solution of the transport equations for the mean
concentration and concentration variance (both of which are formulated in the
Eulerian framework). The critical term in the closure of the concentration
variance transport equation is the scalar dissipation rate, which is modeled
here with reference to a dissipation time scale *t _{d}* that
corresponds to an

A detailed comparison between the measurements obtained from a comprehensive water-channel experiment (involving flow through a large group of obstacles and dispersion from a localized source) and the predictions obtained from the proposed probabilistic model of concentration fluctuations is provided. These results include quantitative comparisons of the mean velocity, turbulence kinetic energy, mean concentration, concentration variance, and concentration probability density function. The model predictions are in overall good quantitative agreement with the measurements. The downwind evolution of the magnitudes and shapes of the mean concentration and concentration variance are predicted remarkably well by the model. The clipped-gamma model for the concentration probability density function, whose parameters are determined using the predicted values for the mean concentration and concentration variance, is in very good conformance with the measurements.

Joint Session 18, Urban Transport and Dispersion Modeling—Part I (Joint with the Meteorological Aspects of Air Pollution Committee)

**Wednesday, 14 January 2009, 1:30 PM-2:30 PM**, Room 124B** Next paper
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