Application of Rice’s theory to recurrence statistics of concentration fluctuations in dispersing plumes

Abstract

Rice’s theory for the statistical properties of random noise currents has been employed in the context of concentration fluctuations in dispersing plumes. Within this context, the theory has been extended to calculate the distribution of excursion times above a small threshold for arbitrary spacings between an up-crossing and the successive down-crossing. This approach has then been applied to a second-order stochastic model for the evolution of odour concentrations and their time derivative (simple model), and to the superstatistics extension of this model [Reynolds (2007) Phys. Fluids]. In agreement with the measurements of Yee and coworkers [Yee et al. (1993) Boundary-Layer Meteorol. 65, Yee et al. (1994) J. Appl. Meteorol. 33 ], both formulations predict a distribution of excursion times that can be well approximated by a power-law profile with exponent close to −3/2. For the superstatistical model the power-law profile extends over approximately three or more decades, for the simple model this range is smaller. Compared to the simple model, predictions for the superstatistical model are in a better agreement with the measurements.