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 internal plume time scale related to the break-up time for eddies (blobs of vorticity) with size comparable to the instantaneous plume width (whose scale is determined by relative or two-particle dispersion).  This physically-based model explicitly relates t_d to the inner time scale associated with the in-plume fluctuations, rather than the outer time scale associated with the entire portion of the concentration fluctuations spectrum (which must necessarily include the irregular, but non-dissipative, meandering of the instantaneous plume). The two lowest-order moments of concentration (viz., mean concentration and concentration variance) are used to determine the parameters of a pre-chosen functional form for the concentration probability density function (clipped-gamma distribution).

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.