Model for the Statistics of Concentration Fluctuations Arising from Dual Source Releases

摘要

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 phenomenology of a fluctuating plume model (viz., a meandering plume model which explicitly incorporates internal fluctuations). Explicit expressions for the second-, third-, and fourth-order correlation functions between the concentration fluctuations produced by two point sources are given in terms of the source separation d and the 5 physically based parameters that define the generalized fluctuating plume model: namely, the absolute plume dispersion, alpha(a), which determines the outer plume length scale; the relative plume dispersion, alpha(n), which determines the inner plume length scale; the fluctuation intensity, i(r), 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. Results for the profiles of the second-order correlation function, p, 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 suggests that the analytical model for p can reproduce many qualitative trends.