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Two-particle dispersion in 2D inverse cascade turbulence and its telegraph equation model

  • Atsushi MIZUTAEmail author
  • Sadayoshi TOH
  • Takeshi MATSUMOTO
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 132)

Abstract

How the distance between two fluid particles advected by a turbulent flow evolves in time is one of the fundamental questions in turbulence research. The final goal of this two-particle dispersion problem is to describe the probability density function (PDF) of the dispersion P(r, t), which gives probability to have a pair of particles whose relative distance is r at time t. L.F. Richardson made the first attempt to phenomenologically derive an equation of P(r, t)
$$\partial_{t}P = \partial_{r}[r^{d-1} K (r)\partial_{r} (P/r^{d - 1})]$$
where d is the spatial dimension and the diffusion coefficient is given by the inertial range scaling as \(K(r) \propto \epsilon^{1/3}r^{4/3}\) with the energy dissipation rate \(\epsilon\).

Keywords

Probability Density Function Probability Density Function Direct Numerical Simulation Exit Time Energy Dissipation Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    J.P.L.C. Salazar and L.R.Collins, Annu. Rev. Fluid Mech. 41 405–32 (2009)CrossRefMathSciNetADSGoogle Scholar
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    T.Ogasawara and S.Toh, J. Phys. Soc. Japan 75 083401 (2006); J. Phys. Soc. Japan 75 104402 (2006).CrossRefADSGoogle Scholar
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    S.Goto and J.C.Vassilicos, New J. Phys. 6 65 (2004)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Atsushi MIZUTA
    • 1
    Email author
  • Sadayoshi TOH
    • 1
  • Takeshi MATSUMOTO
    • 1
  1. 1.Division of Physics and AstronomyGraduate School of Science, Kyoto University Kitashirakawa Oiwakecho Sakyo-kuKyotoJapan

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