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Two-particle dispersion by correlated random velocity fields.

I M Sokolov1

  • 1Laboratoire des Milieux Désordonnées et Hétérogènes, Université Pierre et Marie Curie, 4, Place Jussieu, 75252 Paris, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study examines two-particle dispersion in velocity fields, revealing that diffusion approximation holds for specific scaling laws (alpha/2 + beta < 1). Experimental data suggests ballistic separation in turbulent flows, challenging standard diffusion models.

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Area of Science:

  • Fluid dynamics
  • Statistical physics
  • Turbulence theory

Background:

  • Understanding particle dispersion is crucial in fluid dynamics.
  • Previous models often rely on diffusion approximations, which may not universally apply.

Purpose of the Study:

  • To investigate the scaling laws governing two-particle dispersion in velocity fields.
  • To determine the conditions under which diffusion approximation is valid.
  • To explore regimes beyond the diffusion approximation, including turbulent flows.

Main Methods:

  • Analysis of two-particle velocity correlations v(2)(r) scaling as r(alpha).
  • Analysis of correlation time scales tau(r) scaling as r(beta).
  • Derivation of conditions for diffusion approximation validity (alpha/2 + beta < 1).

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Main Results:

  • The diffusion approximation is valid when alpha/2 + beta < 1.
  • Interparticle distance increase is governed by K(r) proportional r(alpha+beta) under diffusion approximation.
  • Kolmogorov scaling (alpha=beta=2/3) represents a borderline case.
  • Experimental data for Kolmogorov scaling suggests ballistic separation.

Conclusions:

  • The validity of diffusion approximation for two-particle dispersion is dependent on specific scaling parameters.
  • Ballistic separation may be prevalent in turbulent flows, necessitating alternative models.
  • Further research is needed to fully characterize non-diffusive dispersion regimes.