Comparisons with recent physical experiments are also remarkably consistent. The model is able to account for the spatial representation of straining regions as well as incompressibility of the flow, and is shown to reproduce strong non-Gaussianity and intermittency in the Lagrangian separation statistics observed in DNS. Up to fourth-order moments for these quantities are examined, as well as the separation-distance probability density function, which is discussed in the context of recent claims of Richardson scaling in the literature. Detailed comparisons are presented at several Reynolds numbers using the DNS database reported in a companion paper (Part 1). The model is quasi-one-dimensional in nature, and is focused on the statistics of particle-pair separation distance and its rate of change, referred to as the separation speed. However, this failure can now be recognized as inadequate detail in formulation, which is explained and rectified in this paper. Previous stochastic models of relative dispersion have produced unrealistic behaviour, particularly in the dissipation subrange where viscous effects are important, which have led to questions on the adequacy of stochastic modelling.
The model formulation emphasizes (i) non-Gaussian behaviour in Eulerian and Lagrangian statistics, (ii) the occurrence of large separation velocities, (iii) the role of straining and streaming flow structure as recognized in kinematic simulations of turbulence, and (iv) the role of conditionally averaged accelerations in stochastic modelling of turbulent relative dispersion. A new model for Lagrangian particle-pair separation in turbulent flows is developed and compared with data from direct numerical simulations (DNS) of isotropic turbulence.
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