On the influence of the Eulerian velocity PDF closure on the eddy diffusion coefficient

The flux-gradient model, often used to describe turbulent dispersion, implicitly defines an eddy diffusion coefficient K that is known to be related to the Eulerian probability density function (pdf) of the turbulent velocity field. In the strict limit of applicability of Fick's law, the relationship between K and the pdf is used to investigate the influence of non-Gaussianity on dispersion in homogeneous turbulence. A bi-Gaussian pdf is used as a closure model that allows for separate studies of skewness and kurtosis variations. The choice of model parameters can have a significant influence on K, especially when the pdf is bimodal. Both arbitrariness of the closure and bimodality are then reduced using the maximum entropy criterion for the selection of the free parameter of the closure scheme, together with the assumption that the model is valid only for those values of the parameters for which a unimodal pdf is possible. The variations of K are found to be sensitive to both skewness and kurtosis showing a more complex behaviour than that found in literature.