Asymptotic results for backwards two-particle dispersion in a turbulent flow

Damien Benveniste, Theodore D. Drivas

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for short times and arrive at approximate expressions for the mean-squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically compute an exact t3 contribution to the squared separation of stochastic paths. We argue that this contribution appears also for deterministic paths at long times and present direct numerical simulation results for incompressible Navier-Stokes flows to support this claim. We also numerically compute the probability distribution of particle separations for the deterministic paths and the stochastic paths and show their strong self-similar nature.

Original languageEnglish (US)
Article number041003
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume89
Issue number4
DOIs
StatePublished - Apr 17 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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