Pair reversal in homogeneous isotropic turbulence

Abstract

We show that the separation of particle pairs in the inertial subrange of homogeneous isotropic turbulence is strongly influenced by the pairs that separate quasi-diffusively. We quantify the influence of the diffusive separators by considering the probability that a pair will 'reverse' direction across a given separation i.e. its separation will decrease (before eventually increasing) and derive an analytical expression for the expected number of reversals across this separation for a quasi-one-dimensional model of relative dispersion in the inertial subrange with Gaussian turbulence. We compare this theoretical result with three different Lagrangian stochastic models in which the influence of the diffusive and ballistic separators (the latter dominated by velocity memory) can be varied by means of the value of C0, the constant of proportionality in the Lagrangian velocity structure function, which appears explicitly in Lagrangian stochastic models. We also compare these results with data from a direct numerical simulation of turbulence. The results indicate the importance of the transverse relative velocity component (i.e. the ability of pairs to rotate), which is absent in Q1D models, in determining the correct quantitative relative dispersion statistics.