Velocity probability density functions in Lagrangian dispersion models for inhomogeneous turbulence

The correct representation of the probability density function of Eulerian turbulent velocity is a key problem in modelling pollutant dispersion using Lagrangian stochastic models. Analysis of measurements in various kinds of turbulent flows shows that the value of the fourth moment μ4 of the distribution spans a wide range of values that are considerably larger than the Gaussian value even if the skewness is negligible. A review of different approaches used in building non-Gaussian pdfs clearly reveals that in most cases, the fourth moment is either not considered (i.e. a relationship between μ3 and μ4 is chosen in order to close the problem) or covers a small range of values. A new approach using a bi-Gaussian distribution is developed that is able to handle every value for μ4 while satisfying the necessary continuity requirements in accord with Thomson’s (1997) model, excluding the half line μ3=0, μ4 6μ22. Results of a simulation for a test case in non-Gaussian inhomogeneous turbulence satisfactorily reproduces the well-mixed condition.