Turbulent pair dispersion as a continuous-time random walk

TL;DR

This paper models turbulent pair dispersion as a continuous-time random walk, providing new predictions for separation probabilities that differ from traditional models, and validates these against high-resolution simulations.

Contribution

It introduces a novel heuristic model of turbulent dispersion as a CTRW, offering new insights and predictions beyond classical eddy-diffusivity frameworks.

Findings

Logarithm of tracer separation self-averages

Predictions differ from Richardson's eddy-diffusivity models

Model validated against high-resolution simulations

Abstract

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This approach suggests that the logarithm of the distance between tracers self-averages and performs a continuous-time random walk. This leads to specific predictions for the probability distribution of separations, that differ from those obtained using scale-dependent eddy-diffusivity models (e.g. in the framework of Richardson's approach). Such predictions are tested against high-resolution simulations and shed new lights on the explosive separation between tracers.