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

The higher-order correlation functions for the concentrationfluctuations arising from a two-point-source configuration have beencalculated analytically within the context of the phenomenology of afluctuating plume model (viz., a meandering plume model that explicitlyincorporates internal fluctuations). Explicit expressions for thesecond-, third-, and fourth-order correlationfunctions between the concentrationfluctuations produced by two point sources are given in terms of the sourceseparation d and the five physically based parameters that define thegeneralized fluctuating plume model: namely, the absolute plume dispersion,_a, which determines the outer plume length scale; the relative plume dispersion, _r, 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 fluctuationsof the two plumes in relative coordinates, which determines the degree ofinternal mixing of the two scalars. Furthermore, the form of the totalconcentration probability density function arising from the interferenceproduced by two point sources is presented. Predictions for the second-ordercorrelation function, , and for the total concentration probabilitydensity function have been compared with some new experimental data fora two-point-source configuration in grid turbulence generated in awater-channel simulation. These results are in good agreement with the dataand suggest that the analytical model for the second-order correlationfunction and the total concentration probability density function canreproduce many qualitative trends in the interaction of plumes from twosources.