Conditional Relative Acceleration Statistics and Relative Dispersion Modelling

Abstract

We have used direct numerical simulation results for the Eulerian velocity difference probability density function and the mean acceleration difference conditioned on the velocity difference, to explore some of the assumptions underlying the formulation of Lagrangian stochastic models for relative dispersion. We focussed on the ability of the models to quantitatively represent Richardson’s t 3-law and in particular the value of Richardson’s constant. As a result of intermittency, with decreasing spatial separation and with increasing Reynolds number these Eulerian quantities become more extreme and the model predictions for Richardson’s constant also become more extreme (larger). This is in contrast with recent numerical simulations showing that Richardson’s constant depends only weakly on Reynolds number. We conclude that, at least in the present Lagrangian stochastic modelling framework, in two-particle models (and presumably in multi-particle models) intermittency must be included explicitly in the dissipation rate as well as in the relative velocity statistics.