Lévy walks for turbulence: A numerical study

G. Zumofen*, A. Blumen, J. Klafter, M. F. Shlesinger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


We present a numerical study of enhanced diffusion, for which the mean-squared displacement follows asymptotically 〈r2(t)〉 ∼tγ, γ > 1. We simulate continuous time random walks with waiting-time distributions which couple the spatial and temporal parameters; this gives rise to Lévy-walks. Our results confirm the theoretically predicted long-time behavior and demonstrate its temporal regime of validity. Furthermore, the simulations document the appearance of (parameter-dependent) transitions between regular and enhanced diffusion regimes.

Original languageEnglish
Pages (from-to)1519-1528
Number of pages10
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Mar 1989


  • Kolmogorov spectrum
  • Lévy flights
  • Random walks
  • turbulence


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