Advances in Turbulence XII pp 47-50 | Cite as

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

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## 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
where

*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*)$$\partial_{t}P = \partial_{r}[r^{d-1} K (r)\partial_{r} (P/r^{d - 1})]$$

*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.J.P.L.C. Salazar and L.R.Collins, Annu. Rev. Fluid Mech.
**41**405–32 (2009)CrossRefMathSciNetADSGoogle Scholar - 2.T.Ogasawara and S.Toh, J. Phys. Soc. Japan
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© Springer-Verlag Berlin Heidelberg 2009