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

The flux-gradient model, often used to describe turbulent dispersion, impli citly defines an eddy diffusion coefficient K that is known to be related t o the Eulerian probability density function (pdf) of the turbulent velocity field. In the strict limit of applicability of Fick's law, the relationshi p between K and the pdf is used to investigate the influence of non-Gaussia nity on dispersion in homogeneous turbulence. A bi-Gaussian pdf is used as a closure model that allows for separate studies of skewness and kurtosis v ariations. 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 th e 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 s ensitive to both skewness and kurtosis showing a more complex behaviour tha n that found in literature.