The Interference of Higher-Order Statistics of the Concentration Field Produced by Two Point Sources According to a Generalized Fluctuating Plume Model

Abstract

The higher-order correlation functions for the concentration fluctuations arising from a two-point-source configuration have been calculated analytically within the context of the phenomen- ology of a fluctuating plume model (viz., a meandering plume model that explicitly incorporates internal fluctuations). Explicit expressions for the second-, third-, and fourth-order correlation func- tions between the concentration fluctuations produced by two point sources are given in terms of the source separation d and the five physically based parameters that define the generalized fluctu- ating plume model: namely, the absolute plume dispersion, σa, which determines the outer plume length scale; the relative plume dispersion, σr , which determines the inner plume length scale; the fluctuation intensity, ir , in relative coordinates, which determines the internal concentration fluctuation level; the correlation coefficient, r, between the positions of the centroids of the two interfering plumes; and, the correlation coefficient, r ∗ , between the concentration fluctuations of the two plumes in relative coordinates, which determines the degree of internal mixing of the two scalars. Furthermore, the form of the total concentration probability density function arising from the interference produced by two point sources is presented. Predictions for the second-order correlation function, ρ, and for the total concentration probability density function have been compared with some new experimental data for a two-point-source configuration in grid turbulence generated in a water-channel simulation. These results are in good agreement with the data and suggest that the analytical model for the second-order correlation function and the total concentration probability density function can reproduce many qualitative trends in the interaction of plumes from two sources.