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)


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 \(\epsilon\).


Probability Density Function Probability Density Function Direct Numerical Simulation Exit Time Energy Dissipation Rate 
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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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