- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Open Access
  • Access by Xinjiang University

Reynolds number scaling of velocity increments in isotropic turbulence

Kartik P. Iyer*

Katepalli R. Sreenivasan

P. K. Yeung

  • Department of Physics and INFN, University of Rome Tor Vergata, Rome 00133, Italy and Department of Mechanical Engineering, New York University, New York 11201, USA

  • Departments of Physics and Mechanical Engineering and the Courant Institute of Mathematical Sciences, New York University, New York 11201, USA

  • Schools of Aerospace Engineering and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

  • *kki2@nyu.edu
PDF

Phys. Rev. E 95, 021101(R) – Published 10 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.021101

Abstract

Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 81923 periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 299 (1941a).
  2. A. N. Kolmogorov, Dokl. Akad. Nauk. SSSR 434, 16 (1941b).
  3. K. R. Sreenivasan and R. A. Antonia, Annu. Rev. Fluid Mech. 29, 435 (1997).
  4. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2.
  5. U. Frisch, Turbulence (Cambridge University Press, Cambridge, UK, 1995).
  6. R. Camussi and R. Benzi, Phys. Fluids 9, 257 (1997).
  7. B. Dhruva, Y. Tsuji, and K. R. Sreenivasan, Phys. Rev. E 56, R4928 (1997).
  8. S. Chen, K. R. Sreenivasan, M. Nelkin, and N. Cao, Phys. Rev. Lett. 79, 2253 (1997).
  9. S. Grossmann, D. Lohse, and A. Reeh, Phys. Fluids 9, 3817 (1997).
  10. R. Benzi, L. Biferale, R. Fisher, D. Q. Lamb, and F. Toschi, J. Fluid Mech. 653, 221 (2010).
  11. G. Gotoh, D. Fukayama, and T. Nakano, Phys. Fluids 14, 1065 (2002).
  12. T. Ishihara, T. Gotoh, and Y. Kaneda, Annu. Rev. Fluid Mech. 41, 165 (2009).
  13. R. Grauer, H. Homann, and J. F. Pinton, New J. Phys. 14, 063016 (2012).
  14. A. Noullez, G. Wallace, W. Lempert, R. B. Miles, and U. Frisch, J. Fluid Mech. 339, 287 (1997).
  15. D. A. Donzis, P. K. Yeung, and K. R. Sreenivasan, Phys. Fluids 20, 045108 (2008).
  16. V. L'vov and I. Procaccia, Phys. Fluids 8, 2565 (1996).
  17. M. Nelkin, Phys. Fluids 11, 2202 (1999).
  18. L. Biferale and I. Procaccia, Phys. Rep. 414, 43 (2005).
  19. P. K. Yeung, X. M. Zhai, and K. R. Sreenivasan, Proc. Natl. Acad. Sci. USA 112, 12633 (2015).
  20. A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962).
  21. D. A. Donzis and P. K. Yeung, Physica D 239, 1278 (2010).
  22. K. P. Iyer, K. R. Sreenivasan, and P. K. Yeung, Phys. Rev. E 92, 063024 (2015).
  23. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Phys. Rev. E 48, R29(R) (1993).
  24. A. M. Oboukhov, J. Fluid Mech. 13, 77 (1962).
  25. S. T. Thoroddsen and C. W. Van Atta, Phys. Fluids A: Fluid Dyn. 4, 2592 (1992).
  26. A. A. Praskovsky, Phys. Fluids A: Fluid Dyn. 4, 2589 (1992).
  27. I. Hosokawa, C. W. Van Atta, and S. T. Thoroddsen, Fluid. Dyn. Res. 13, 329 (1994).
  28. G. Stolovitzky and K. R. Sreenivasan, Rev. Mod. Phys. 66, 229 (1994).
  29. G. Stolovitzky, P. Kailasnath, and K. R. Sreenivasan, Phys. Rev. Lett. 69, 1178 (1992).
  30. L. P. Wang, S. Chen, J. G. Brasseur, and J. C. Wyngaard, J. Fluid Mech. 309, 113 (1996).

Outline

Information

Phys. Rev. E 95, 021101(R)– Published 10 February, 2017
  • Received 30 October 2016
  • Revised 17 January 2017
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation