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Fluid particle accelerations in fully developed turbulence

Nature volume 409, pages 1017–1019 (2001)Cite this article

Abstract

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport1,2, processes in stirred chemical reactors and combustion systems3, and in the industrial production of nanoparticles4. The concept of particle trajectories has been used successfully to describe mixing and transport in turbulence3,5, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg–Yaglom prediction of fluid particle accelerations6,7, based on the 1941 scaling theory of Kolmogorov8,9. Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that, within experimental errors, Kolmogorov scaling of the acceleration variance is attained at high Reynolds numbers. Our data indicate that the acceleration is an extremely intermittent variable—particles are observed with accelerations of up to 1,500 times the acceleration of gravity (equivalent to 40 times the root mean square acceleration). We find that the acceleration data reflect the anisotropy of the large-scale flow at all Reynolds numbers studied.

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Figure 1: Measured particle trajectory.
Figure 2: Apparatus.
Figure 3: Acceleration distribution.
Figure 4: Acceleration a0 as a function of Rλ.

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References

  1. Vaillancourt, P. A. & Yau, M. K. Review of particle-turbulence interactions and consequences for cloud physics. Bull. Am. Meteorol. Soc. 81, 285–298 (2000).

    Article  ADS  Google Scholar 

  2. Weil, J. C., Sykes, R. I. & Venkatram, A. Evaluating air-quality models: Review and outlook. J. Appl. Meteorol. 31, 1121–1145 (1992).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  4. Pratsinis, S. E. & Srinivas, V. Particle formation in gases, a review. Powder Technol. 88, 267–273 (1996).

    Article  CAS  Google Scholar 

  5. Shraiman, B. I. & Siggia, E. D. Scalar turbulence. Nature 405, 639–646 (2000).

    Article  ADS  CAS  Google Scholar 

  6. Heisenberg, W. Zur statistichen theorie der turbulenz. Z. Phys. 124, 628–657 (1948).

    Article  ADS  CAS  Google Scholar 

  7. Yaglom, A. M. On the acceleration field in a turbulent flow. C.R. Acad. URSS 67, 795–798 (1949).

    MathSciNet  MATH  Google Scholar 

  8. Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305 (1941).

    ADS  MathSciNet  Google Scholar 

  9. Kolmogorov, A. N. Dissipation of energy in the locally isotropic turbulence. Dok. Akad. Nauk SSSR 31, 538–540 (1941).

    MATH  Google Scholar 

  10. Virant, M. & Dracos, T. 3D PTV and its application on Lagrangian motion. Meas. Sci. Technol. 8, 1539–1552 (1997).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  12. Skubic, P. et al. The CLEO III silicon tracker. Nucl. Instrum. Meth. A 418, 40–51 (1998).

    Article  ADS  CAS  Google Scholar 

  13. Batchelor, G. K. Pressure fluctuations in isotropic turbulence. Proc. Camb. Phil. Soc. 47, 359–374 (1951).

    Article  ADS  Google Scholar 

  14. Vedula, P. & Yeung, P. K. Similarly scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11, 1208–1220 (1999).

    Article  ADS  CAS  Google Scholar 

  15. Obukhov, A. M. & Yaglom, A. M. The microstructure of turbulent flow. Prikl. Mat. Mekh. 15, (1951); translation TM 1350 (National Advisory Committee for Aeronautics (NACA), Washington DC, 1953).

  16. Gotoh, T. & Fukayama, D. Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. (submitted).

  17. Gotoh, T. & Rogallo, R. S. Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285 (1999).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  18. Borgas, M. S. The multifractal Lagrangian nature of turbulence. Phil. Trans. R. Soc. Lond. A 342, 379–411 (1993).

    Article  ADS  Google Scholar 

  19. Kurien, S. & Sreenivasan, K. R. Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence. Phys. Rev. E 62, 2206–2212 (2000).

    Article  ADS  CAS  Google Scholar 

  20. Shen, X. & Warhaft, Z. The anisotropy of the smale scale structure in high Reynolds number (Rλ ∼ 1000) turbulent shear flow. Phys. Fluids 12, 2976–2989 (2000).

    Article  ADS  CAS  Google Scholar 

  21. Reynolds, A. M. A second-order Lagrangian stochastic model for particle trajectories in inhomogeneous turbulence. Q. J. R. Meteorol. Soc. 125, 1735–1746 (1999).

    Article  ADS  Google Scholar 

  22. Sawford, B. L. & Yeung, P. K. Eulerian acceleration statistics as a discriminator between Lagrangian stochastic models in uniform shear flow. Phys. Fluids 12, 2033–2045 (2000).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Bidlingmayer, W. L., Day, J. F. & Evans, D. G. Effect of wind velocity on suction trap catches of some Florida mosquitos. J. Am. Mosquito Contr. 11, 295–301 (1995).

    CAS  Google Scholar 

  24. Voth, G. A., Satyanarayan, K. & Bodenschatz, E. Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10, 2268–2280 (1998).

    Article  ADS  CAS  Google Scholar 

  25. La Porta, A., Voth, G. A., Moisy, F. & Bodenschatz, E. Using cavitation to measure statistics of low-pressure events in large-Reynolds-number turbulence. Phys. Fluids 12, 1485–1496 (2000).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This research is supported by the Physics Division of the National Science Foundation. We thank R. Hill, M. Nelkin, S. B. Pope, E. Siggia, and Z. Warhaft for stimulating discussions and suggestions throughout the project. We also thank C. Ward, who assisted in the initial development of the strip detector. E.B. and A.L.P. are grateful for support from the Institute of Theoretical Physics at the University of California, Santa Barbara.

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  1. Laboratory of Atomic and Solid State Physics, Laboratory of Nuclear Studies, Cornell University, Ithaca, New York, 14853-2501, USA

    A. La Porta, Greg A. Voth, Alice M. Crawford, Jim Alexander & Eberhard Bodenschatz

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  1. A. La Porta
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Correspondence to A. La Porta.

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La Porta, A., Voth, G., Crawford, A. et al. Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019 (2001). https://doi.org/10.1038/35059027

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