Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion

Abstract

An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. The solution approach is to identify a representation of the Dirac delta function for large times in the same integral occurring in both variances. This particular function acts as an effective filter and provides a way to obtain an analytical solution. Considering these asymptotic dispersion parameters in a Gaussian diffusion model, analysis of the simulated concentration results shows that the model reproduces well the experimental ground-level concentration data. The variance between the temporal and ensemble averages is evaluated using turbulent observational data collected in a convective boundary layer. The results show that the difference between the temporal and ensemble means is of the order of 5% for an average time window of 1800 s. The present development can be used in a variety of situations involving different types of turbulence.