- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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
  • Letter
  • Open Access

Asymmetry of velocity increments in turbulence

Katepalli R. Sreenivasan1,2,*, Kartik P. Iyer3,4,†, and Ashvin Vinodh4

  • 1Department of Mechanical and Aerospace Engineering, New York University, New York, New York 11201, USA
  • 2Department of Physics and the Courant Institute of Mathematical Sciences, New York University, New York, New York 11201, USA
  • 3Department of Physics, Michigan Technological University, Houghton, Michigan 49931, USA
  • 4Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, Michigan 49931, USA

  • *krs3@nyu.edu
  • †kiyer@mtu.edu
PDF

Phys. Rev. Research 4, L042002 – Published 4 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042002

Abstract

We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence—the asymmetry of velocity increments—with likely implications on important dynamics. This property, ignored by existing small-scale phenomenological models, manifests most prominently in the nonmonotonic trend of velocity increment moments (or structure functions) with the moment order, and in differences between ordinary and absolute structure functions for a given separation distance. We show that high-order structure functions arise nearly entirely from the negative side of the probability density of velocity increments, essentially removing the ambiguity between ordinary and absolute moments, and provide a plausible dynamical interpretation of this result.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (34)

  1. A. N. Kolmogorov, Dissipation of energy in locally isotropic turbulence, Dokl. Akad. Nauk. SSSR 32, 16 (1941).
  2. A. N. Kolmogorov, The local structure of turbulence in an incompressible fluid for very large Reynolds number, Dokl. Akad. Nauk. SSSR 30 (1941).
  3. A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13, 82 (1962).
  4. R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, On the multifractal nature of fully developed turbulence and chaotic systems, J. Phys. A: Math. Gen. 17, 3521 (1984).
  5. C. Meneveau and K. R. Sreenivasan, Simple Multifractal Cascade Model for Fully Developed Turbulence, Phys. Rev. Lett. 59, 1424 (1987).
  6. Z. S. She and E. Leveque, Universal Scaling Laws in Fully Developed Turbulence, Phys. Rev. Lett. 72, 336 (1994).
  7. V. Yakhot, Mean-field approximation and a small parameter in turbulence theory, Phys. Rev. E 63, 026307 (2001).
  8. D. P. Ruelle, Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics, Proc. Natl. Acad. Sci. USA 109, 20344 (2012).
  9. C. Eling and Y. Oz, The anomalous scaling exponents of turbulence in general dimension from random geometry, J. High Energy Phys. 2015, 150 (2015).
  10. L. Biferale, F. Bonaccorso, M. Buzzicotti, and K. P. Iyer, Self-Similar Subgrid-Scale Models for Inertial Range Turbulence and Accurate Measurements of Intermittency, Phys. Rev. Lett. 123, 014503 (2019).
  11. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29(R) (1993).
  12. K. R. Sreenivasan and B. R. Dhruva, Is there scaling in high-Reynolds-number turbulence? Prog. Theor. Phys. Suppl. 130, 103 (1998).
  13. B. R. Dhruva, An experimental study of high Reynolds number turbulence in the atmosphere. Ph.D. thesis, Yale University, New Haven, 2000.
  14. T. Gotoh, D. Fukayama, and T. Nakano, Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation, Phys. Fluids 14, 1065 (2002).
  15. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, MA, 1975), Vol. 2.
  16. D. A. Donzis and P. K. Yeung, Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence, Physica D 239, 1278 (2010).
  17. K. R. Sreenivasan, A. Prabhu, and R. Narasimha, Zero-crossings in turbulent signals, J. Fluid Mech. 137, 251 (1983).
  18. K. P. Iyer, K. R. Sreenivasan, and P. K. Yeung, Scaling exponents saturate in three-dimensional isotropic turbulence, Phys. Rev. Fluids 5, 054605 (2020).
  19. S. I. Vainshtein and K. R. Sreenivasan, Kolmogorov's 45th Law and Intermittency in Turbulence, Phys. Rev. Lett. 73, 3085 (1994).
  20. K. R. Sreenivasan, S. I. Vainshtein, R. Bhiladvala, I. San Gil, S. Chen, and N. Cao, Asymmetry of Velocity Increments in Fully Developed Turbulence and the Scaling of Low-Order Moments, Phys. Rev. Lett. 77, 1488 (1996).
  21. U. Frisch, Turbulence – The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, UK, 1995).
  22. K. R. Sreenivasan, B. R. Dhruva, and I. San Gil, The effects of large scales on the inertial range in high-Reynolds-number turbulence, arXiv:chao-dyn/9906041.
  23. S. Khurshid, D. A. Donzis, and K. R. Sreenivasan, Slow spectral transfer and energy cascades in isotropic turbulence, J. Fluid Mech. 908, A21 (2021).
  24. J. Herweijer and W. van de Water, Universal Shape of Scaling Functions in Turbulence, Phys. Rev. Lett. 74, 4651 (1995).
  25. S. I. Soluyan and R. V. Khokhlov, Propagation of acoustic waves of finite amplitude in a dissipative medium. Vestnik Moscow State Univ., Phys. Astron. 3, 52 (1961).
  26. J. Bec and K. Khanin, Burgers turbulence, Phys. Rep. 447, 1 (2007).
  27. A. Celani, A. Lanotte, A. Mazzino, and M. Vergassola, Universality and Saturation of Intermittency in Passive Scalar Turbulence, Phys. Rev. Lett. 84, 2385 (2000).
  28. K. P. Iyer, J. Schumacher, K. R. Sreenivasan, and P. K. Yeung, Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence, Phys. Rev. Lett. 121, 264501 (2018).
  29. A. Staicu and W. van de Water, Small Scale Velocity Jumps in Shear Turbulence, Phys. Rev. Lett. 90, 094501 (2003).
  30. K. R. Sreenivasan and V. Yakhot, Dynamics of three-dimensional turbulence from Navier-Stokes equations, Phys. Rev. Fluids 6, 104604 (2021).
  31. T. D. Drivas, Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment, Philos. Trans. R. Soc. A 380, 20210033 (2022).
  32. T. Ishihara, T. Gotoh and Y. Kaneda, Study of high-Reynolds-number isotropic turbulence by direct numerical simulations, Annu. Rev. Fluid Mech. 41, 165 (2009).
  33. B. Dhruva, Y. Tsuji and K. R. Sreenivasan, Transverse structure functions in high-Reynolds-number turbulence, Phys. Rev. E 56, R4928(R) (1997).
  34. S. Chen, K. R. Sreenivasan, M. Nelkin, and N. Cao, A Refined Similarity Hypothesis for Transverse Structure Functions, Phys. Rev. Lett. 79, 2253 (1997).

Outline

Information

Phys. Rev. Research 4, L042002– Published 4 October, 2022
  • Received 7 August 2022
  • Accepted 19 September 2022
Crossmark - Check for updates button
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