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Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence

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Abstract

The Tsallis distribution and the stretched exponential distribution were successfully used to fit the experimental data of turbulence particle acceleration published in Nature (2001), which manifested a clear departure from the normal distribution. These studies, however, fall short of a clear physical mechanism behind the statistical phenomenological description. In this study, we propose a multiscale diffusion model which considers both normal diffusion in molecular-scale and anomalous diffusion in vortex-scale, and the latter is described by a novel fractal derivative modeling approach. This multi-scale model gives rise to a new probability density function which fits experimental data very well.

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References

  1. Wesseling P. Principles of Computational Fluid Dynamics. Berlin, Heidelberg: Springer-Verlag, 2001. 37–43

    Google Scholar 

  2. Shlesinger M F, West B J, Klafter J. Lévy dynamics of enhanced diffusion: Application to turbulence. Phys Rev Lett, 1987, 58(11): 1100–1103

    Article  MathSciNet  Google Scholar 

  3. Rani S L, Winkler C M, Vanka S P. Numerical simulations of turbulence modulation by dense particles in a fully developed pipe flow. Powder Technol, 2004, 141(1–2): 80–99

    Article  Google Scholar 

  4. La Porta A, Voth G A, Crawford A M, et al. Fluid particle accelerations in fully developed turbulence. Nature, 2001, 409(6823): 1017–1019

    Article  Google Scholar 

  5. Mordant N, Crawford A M, Bodenschatz E. Experimental Lagrangian acceleration probability density function measurement. Phys D, 2004, 193(1–4): 245–251

    Article  MATH  Google Scholar 

  6. Tsallis C. Nonextensive statistics: Theoretical, experimental and computational evidences and connections. Braz J Phys, 1999, 29(1): 1–35

    Article  Google Scholar 

  7. Beck C. On the small-scale statistics of Lagrangian turbulence. Phys Lett A, 2001, 287(3): 240–244

    Article  MATH  MathSciNet  Google Scholar 

  8. Daniels K E, Beck C, Bodenschatz E. Defect turbulence and generalized statistical mechanics. Phys D, 2004, 193(1–4): 208–217

    Article  MATH  MathSciNet  Google Scholar 

  9. Beck C. Superstatistics in hydrodynamic turbulence. Phys D, 2004, 193(1–4): 195–207

    Article  MATH  MathSciNet  Google Scholar 

  10. Reynolds A M. Superstatistical Lagrangian stochastic modeling. Phys A, 2004, 340(1–3): 298–308

    MathSciNet  Google Scholar 

  11. Arimitsu T, Arimitsu N. Multifractal analysis of fluid particle accelerations in turbulence. Phys D, 2004, 193(1–4): 218–230

    Article  MATH  MathSciNet  Google Scholar 

  12. Chen W. Time-space fabric underlying anomalous diffusion. Chaos, Solitons Fractals, 2006, 28(4): 923–929

    Article  MATH  Google Scholar 

  13. She Z S, Su W D. Hierarchical structures and scaling in turbulence (in Chinese). Adv Mech, 1999, 29(3): 289–303

    Google Scholar 

  14. Zeng Z X, Zhou L X, Zhang J. Two scales, second-order moment, two-phase turbulence model and its application (in Chinese). J Tsinghua University (Science Technics), 2005, 45(8): 1095–1098

    Google Scholar 

  15. Gao Z, Zhuang F G. Multi-scale equations for incompressible turbulent flows. J Shanghai University (English Edition), 2004, 8(2): 113–116

    Article  MATH  Google Scholar 

  16. Xu L R. On validation of turbulence multiscale statistical theory method (in Chinese). J Nanjing University (Natural Sciences), 1999, 35(6): 736–744

    Google Scholar 

  17. Bakunin O G, Schep T J. Multi-scale percolation and scaling laws for anisotropic turbulent diffusion. Phys Lett A, 2004, 322(1–2): 105–110

    Article  MATH  Google Scholar 

  18. Chen W. A speculative study of 2/3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures. Chaos, 2006, 16(2): 023126

    Google Scholar 

  19. Podlubny I. Fractional Differential Equations. San Diego: Academic Press, 1999. 55–57

    MATH  Google Scholar 

  20. Monin A S, Yaglom A M. Statistical Fluid Mechanics: Mechanics of Turbulence. Cambridge, Massachusetts, and London, England: The MIT Press, 1971, 1: 257–364

    Google Scholar 

  21. Tennekes H, Lumley J L. A First Course in Turbulence. Cambridge, Massachusetts, and London, England: The MIT Press, 1994. 52–58

    Google Scholar 

  22. Aringazin A K, Mazhitov M I. Gaussian factor in the distribution arising from the nonextensive statistics approach to fully developed turbulence. ArXiv: cond-mat/0301040 v3, 19 Nov 2003

  23. Huang Z L. Fractal character of turbulence (in Chinese). Adv Mech, 2000, 30(4): 581–596

    Google Scholar 

  24. Kanno R. Representation of random walk in fractal space-time. Phys A, 1998, 248(1): 165–175

    Article  Google Scholar 

  25. Aringazin A K, Mazhitov M I. One-dimensional Langevin models of fluid particle acceleration in developed turbulence. ArXiv: condmat/0305186v2 [cond-mat.stat-mech], 31 Oct 2003

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Authors and Affiliations

  1. Department of Engineering Mechanics, Hohai University, Nanjing, 210098, China

    HongGuang Sun & Wen Chen

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  1. HongGuang Sun
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  2. Wen Chen
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Correspondence to Wen Chen.

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Supported by the Program for New Century Excellent Talents in University China (Grant No. NCET-06-0480)

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Sun, H., Chen, W. Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence. Sci. China Ser. E-Technol. Sci. 52, 680–683 (2009). https://doi.org/10.1007/s11431-009-0050-3

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  • DOI: https://doi.org/10.1007/s11431-009-0050-3

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