Turbulent pair dispersion as a continuous-time random walk

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.

10 pages, 5 figures

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• Turbulent pair dispersion as a ballistic cascade phenomenology
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• Explosive Particle Dispersion in Plasma Turbulence
• Intermittency in the relative separations of tracers and of heavy particles in turbulent flows
• Relative dispersion of particle pairs in turbulent channel flow
• Universal alignment in turbulent pair dispersion
• The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
• Non-local dispersion and the reassessment of Richardson's t3-scaling law
• Nonergodicity of $d$-dimensional generalized Lévy walks and their relation to other space-time coupled models
• Single-particle dispersion in stably stratified turbulence
• Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
• Two-time Lagrangian velocity correlation function for particle pairs in two-dimensional inverse energy-cascade turbulence
• Turbulent Mass Inhomogeneities induced by a point-source