Simple solutions for the concentration fluctuations of a passive scalar

The dispersion dynamics of a contaminant released in the atmosphere is crucial for risk assessments and environmental analyses. Yet, because of the unsolved problem of turbulence, analytical solutions physically-derived are currently limited to the Gaussian models for the mean concentration field. In this work, we have obtained simple solutions for the concentration statistics of a passive scalar released from a punctual source. The main result is a novel analytical solution for the passive scalar variance, which is obtained from the contaminant transport equation. We have verified this solution against wind-tunnel data, and further adopted it in a simple stochastic model to provide closed relationships for the temporal statistics of concentration (e.g., the mean duration and occurrence of the peak events). These results may serve as a rapid and practical way to estimate the intensity and duration of the concentration fluctuations of a pollutant released in the atmosphere.