Level-crossing statistics of a passive scalar dispersed in a neutral boundary layer

The concentration of a passive scalar dispersed in a turbulent flow exhibits a complex stochastic dynamics. In this paper, we present a minimalist stochastic model that resembles the concentration statistics of a passive scalar emitted from a localized source in a neutral boundary layer. The model provides closed forms for the crossing rates and times — the mean frequency of exceeding a certain concentration level and the mean time above it. Three concentration statistics are needed as model inputs: the mean, the standard deviation, and the integral scale. By giving analytical relationships also for these statistics, we provide a completely closed methodology that may serve as a rapid and practical tool to estimate the dynamics of a pollutant dispersed in the atmosphere. Results are validated against wind-tunnel measurements.