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Conditional Relative Acceleration Statistics and Relative Dispersion Modelling

Submitted for the Special Issue Dedicated to S. B. Pope

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Abstract

We have used direct numerical simulation results for the Eulerian velocity difference probability density function and the mean acceleration difference conditioned on the velocity difference, to explore some of the assumptions underlying the formulation of Lagrangian stochastic models for relative dispersion. We focussed on the ability of the models to quantitatively represent Richardson’s t 3-law and in particular the value of Richardson’s constant. As a result of intermittency, with decreasing spatial separation and with increasing Reynolds number these Eulerian quantities become more extreme and the model predictions for Richardson’s constant also become more extreme (larger). This is in contrast with recent numerical simulations showing that Richardson’s constant depends only weakly on Reynolds number. We conclude that, at least in the present Lagrangian stochastic modelling framework, in two-particle models (and presumably in multi-particle models) intermittency must be included explicitly in the dissipation rate as well as in the relative velocity statistics.

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References

  1. Taylor, G.I.: Diffusion by continuous movements. Proc. Lond. Math. Soc. 20, 196–212 (1921)

    Article  Google Scholar 

  2. Obukhov, A.M.: On the distribution of energy in the spectrum of turbulent flow. Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz. 5, 453–468 (1941)

    Google Scholar 

  3. Batchelor, G.K.: The application of the similarity theory of turbulence to atmospheric diffusion. Q. J. R. Meteorol. Soc. 76, 133–146 (1950)

    Article  Google Scholar 

  4. Richardson, L.F.: Atmospheric diffusion shown on a distance-neighbour graph. Proc. R. Soc. Lond., A 110, 709–737 (1926)

    Article  Google Scholar 

  5. Sawford, B.L.: Turbulent relative dispersion. Annu. Rev. Fluid Mech. 33, 289–317 (2001)

    Article  Google Scholar 

  6. Ott, S., Mann, J.: An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223 (2000)

    Article  MATH  Google Scholar 

  7. Ishihara, T., Kaneda, Y.: Relative diffusion of a pair of fluid particles in the inertial subrange of turbulence. Phys. Fluids 14, L69–L72 (2002)

    Article  Google Scholar 

  8. Biferale, L., Boffetta, G., Celani, A., Devenish, B.J., Lanotte, A., Toschi, F.: Lagrangian statistics of particle pairs in homogeneous isotropic turbulence. Phys. Fluids 17, 115101-1–9 (2005)

    MathSciNet  Google Scholar 

  9. Berg, J., Luthi, B., Mann, J., Ott, S.: Backwards and forwards relative dispersion in turbulent flow: an experimental investigation. Phys. Rev., E 74, 016304-1–016304-7 (2006)

    Article  Google Scholar 

  10. Sawford, B.L., Yeung, P.K., Hackl, J.F.: Reynolds number dependence of relative dispersion statistics in isotropic turbulence. Phys. Fluids 20, 065111-1–065111-13 (2008)

    Google Scholar 

  11. Wilson, J.D., Sawford, B.L.: Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere. Boundary - Layer Meteorol. 78, 191–210 (1996)

    Article  Google Scholar 

  12. Pope, S.B.: Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26, 23–63 (1994)

    Article  MathSciNet  Google Scholar 

  13. Thomson, D.J.: A stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence, and its application to the problem of concentration variance. J. Fluid Mech. 210, 113–153 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Borgas, M.S., Sawford, B.L.: A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence. J. Fluid Mech. 279, 69–99 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kurbanmuradov, O.A.: Stochastic Lagrangian models for two-particle relative dispersion in high-Reynolds number turbulence. Monte Carlo Methods Appl. 3, 37–52 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Borgas, M.S, Yeung, P.K.: Conditional fluid-particle accelerations in turbulence. Theor. Comput. Fluid Dyn. 11, 69–93 (1998)

    Article  MATH  Google Scholar 

  17. Sawford, B.L., Yeung, P.K., Borgas, M.S.: Comparison of backwards and forwards relative dispersion in turbulence. Phys. Fluids 17, 095109-1–095109-9 (2005)

    Article  Google Scholar 

  18. Pagnini, G.: Lagrangian stochastic models for turbulent relative dispersion based on particle pair rotation. J. Fluid Mech. 616, 357–395 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Donzis, D.A., Yeung, P.K., Sreenivasan K.R.: Dissipation and enstrophy in isotropic turbulence: resolution effects and scaling in direct numerical simulations. Phys. Fluids 20, 045108-1–045108-16 (2008)

    Article  Google Scholar 

  20. Yeung, P.K., Pope, S.B., Sawford, B.L.: Reynolds number dependence of Lagrangian statistics in large numerical simulations of turbulence. J. Turbul. 7(N58), 1–12 (2006)

    MathSciNet  Google Scholar 

  21. Gardiner, C.W.: Handbook of Stochastic Methods for Physics Chemistry and the Natural Sciences. Springer, Berlin (1983)

    MATH  Google Scholar 

  22. Pope, S.B.: Consistency conditions for random-walk models of turbulent dispersion. Phys. Fluids 30, 2374–2379 (1987)

    Article  MATH  Google Scholar 

  23. Thomson, D.J.: Criteria for the selection of stochastic models of particle trajectories in turbulent flows, J. Fluid Mech. 180, 529–556 (1987)

    Article  MATH  Google Scholar 

  24. Pope, S.B.: PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119–192 (1985)

    Article  MathSciNet  Google Scholar 

  25. Sreenivasan, K.R.: On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  26. Gotoh, T., Fukayama, D., Nakano, T.: Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys. Fluids 14, 1065–1081 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  27. Gotoh, T., Nakano, T.: Role of pressure in turbulence. J. Stat. Phys. 113, 855–874 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  28. Borgas, M.S., Yeung, P.K.: Relative dispersion in isotropic turbulence. Part 2. A new stochastic model with Reynolds-number dependence. J. Fluid Mech. 503, 125–160 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  29. Meneveau, C., Sreenivasan, K.R.: Simple cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1424–1427 (1987)

    Article  Google Scholar 

  30. Borgas, M.S.: The multifractal Lagrangian nature of turbulence. Philos. Trans. R. Soc. Lond., Ser. A 342, 379–411 (1993)

    Article  MATH  Google Scholar 

  31. Heppe, B.M.O.: Generalized Langevin equation for relative turbulent dispersion. J. Fluid Mech. 357, 167–198 (1998)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Monash University, Clayton Campus, Wellington Road, Clayton, VIC, 3800, Australia

    Brian L. Sawford

  2. School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    P. K. Yeung

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  1. Brian L. Sawford
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  2. P. K. Yeung
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Correspondence to Brian L. Sawford.

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Sawford, B.L., Yeung, P.K. Conditional Relative Acceleration Statistics and Relative Dispersion Modelling. Flow Turbulence Combust 85, 345–362 (2010). https://doi.org/10.1007/s10494-010-9255-6

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