Beyond eddy diffusivity: an alternative model for turbulent dispersion

Turbulent dispersion proceeds not only much faster but also in a qualitatively different manner than molecular diffusion. Yet, the majority of hydraulic, oceanic and atmospheric models rely on the concept of an eddy diffusivity. It is shown here that an alternative model can be developed to exhibit observed behavior. The new term in the diffusion equation, which is non-local, may be interpreted in terms of the probability density function (pdf) of the turbulent velocity. Different assumptions about this distribution lead to a family of models, one of which is the model proposed here and another, the classical Fickian model of diffusion. A connection is also made with models using fractional calculus.