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Formation of power-law scalings of spectra and multiscale coherent structures in the near-field of grid-generated turbulence

Tatsuya Yasuda1,*, Susumu Goto2,†, and John Christos Vassilicos1,‡

  • 1Turbulence, Mixing and Flow Control Group, Department of Aeronautics, Imperial College London, United Kingdom
  • 2Graduate School of Engineering Science, Osaka University, Japan

  • *Current address: Department of Physical Science and Engineering, Nagoya Institute of Technology, Japan; yasuda.tatsuya@nitech.ac.jp
  • †goto@me.es.osaka-u.ac.jp
  • ‡Current address: Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, FRE 2017 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Feriet, F-59000 Lille, France; john-christos.vassilicos@centralelille.fr
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Phys. Rev. Fluids 5, 014601 – Published 13 January, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.014601

Abstract

We investigate the streamwise evolutions of energy and pressure spectra along the shear-layer region of very near-field grid-generated turbulence. The energy and pressure spectra evolve significantly in this near-field. The shear-layer and vortex-shedding frequencies appear immediately in different spectra but the shear-layer's spectral signature is very soon replaced by a broad power-law spectrum on both sides of that frequency. The spectra evolve further by filling the gap between the vortex shedding and the shear-layer frequencies eventually leading to near −5/3 power-law energy spectra at the point on the shear-layer region where the turbulence intensity reaches a maximum. The pressure spectrum reaches a −7/3 power-law shape significantly further downstream. These spectral scalings cover a range between the vortex-shedding frequency and frequencies larger than the shear-layer frequency. They are discussed in relation to turbulent coherent structures of various sizes, obtained by using Gaussian low-pass filtering of instantaneous turbulent flow fields. High enstrophy small-scale structures originate from the shear-layer instability whereas low enstrophy large-scale structures originate from the vortex shedding. The generation of near-field −5/3 energy and −7/3 pressure spectra involves cooperative interactions between these two different size structures.

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References (62)

  1. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941).
  2. W. K. George, P. D. Beuther, and R. E. A. Arndt, Pressure spectra in turbulent free shear flows, J. Fluid Mech. 148, 155 (1984).
  3. Y. Tsuji and T. Ishihara, Similarity scaling of pressure fluctuation in turbulence, Phys. Rev. E 68, 026309 (2003).
  4. O. Terashima, Y. Sakai, and K. Nagata, Simultaneous measurement of velocity and pressure in a plane jet, Exp. Fluids 53, 1149 (2012).
  5. T. Gotoh and D. Fukayama, Pressure Spectrum in Homogeneous Turbulence, Phys. Rev. Lett. 86, 3775 (2001).
  6. 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).
  7. S. Goto, Y. Saito, and G. Kawahara, Hierarchy of antiparallel vortex tubes in spatially periodic turbulence at high Reynolds numbers, Phys. Rev. Fluids 2, 064603 (2017).
  8. S. Laizet, J. C. Vassilicos, and C. Cambon, Interscale energy transfer in decaying turbulence and vorticity-strain-rate dynamics in grid-generated turbulence, Fluid Dyn. Res. 45, 061408 (2013).
  9. R. Gomes-Fernandes, B. Ganapathisubramani, and J. C. Vassilicos, The energy cascade in near-field non-homogeneous non-isotropic turbulence, J. Fluid Mech. 771, 676 (2015).
  10. I. Paul, G. Papadakis, and J. C. Vassilicos, Genesis and evolution of velocity gradients in near-field spatially developing turbulence, J. Fluid Mech. 815, 295 (2017).
  11. J. Nedić, J. C. Vassilicos, and B. Ganapathisubramani, Axisymmetric Turbulent Wakes with New Nonequilibrium Similarity Scalings, Phys. Rev. Lett. 111, 144503 (2013).
  12. F. Alves Portela, G. Papadakis, and J. C. Vassilicos, The turbulence cascade in the near wake of a square prism, J. Fluid Mech. 825, 315 (2017).
  13. Y. Zhou, K. Nagata, Y. Sakai, H. Suzuki, Y. Ito, O. Terashima, and T. Hayase, Development of turbulence behind the single square grid, Phys. Fluids 26, 045102 (2014).
  14. Y. Zhou, K. Nagata, Y. Sakai, H. Suzuki, Y. Ito, O. Terashima, and T. Hayase, Relevance of turbulence behind the single square grid to turbulence generated by regular- and multiscale-grids, Phys. Fluids 26, 075105 (2014).
  15. S. Laizet, J. Nedić, and J. C. Vassilicos, The spatial orgin of −5/3 spectra in grid-generated turbulence, Phys. Fluids 27, 065115 (2015).
  16. G. Melina, P. J. K. Bruce, and J. C. Vassilicos, Vortex shedding effects in grid-generated turbulence, Phys. Rev. Fluids 1, 044402 (2016).
  17. Y. Zhou, K. Nagata, Y. Sakai, Y. Ito, and T. Hayase, Spatial evolution of the helical behavior and the 2/3 power-law in single-square-grid-generated turbulence, Fluid Dyn. Res. 48, 021404 (2016).
  18. S. Goto, A physical mechanism of the energy cascade in homogeneous isotropic turbulence, J. Fluid Mech. 605, 355 (2008).
  19. T. Leung, N. Swaminathan, and P. A. Davidson, Geometry and interaction of structures in homogeneous isotropic turbulence, J. Fluid Mech. 710, 453 (2012).
  20. S. Goto, Coherent structures and energy cascade in homogeneous turbulence, Prog. Theor. Phys. Suppl. 195, 139 (2012).
  21. J. I. Cardesa, A. Vela-Martín, and J. Jiménez, The turbulent cascade in five dimensions, Science 357, 782 (2017).
  22. Y. Motoori and S. Goto, Generation mechanism of a hierarchy of vortices in a turbulent boundary layer, J. Fluid Mech. 865, 1085 (2019).
  23. A. Lozano-Durán, M. Holzner, and J. Jiménez, Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at a friction Reynolds number of 932, J. Fluid Mech. 803, 356 (2016).
  24. J. Lee, H. J. Sung, and T. A. Zaki, Signature of large-scale motions on turbulent/non-turbulent interface in boundary layers, J. Fluid Mech. 819, 165 (2017).
  25. S. Laizet and E. Lamballais, High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy, J. Comput. Phys. 228, 5989 (2009).
  26. S. Laizet and N. Li, Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) computational cores, Int. J. Numer. Meth. Fluids 67, 1735 (2011).
  27. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).
  28. P. Parnaudeau, J. Carlier, D. Heitz, and E. Lamballais, Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900, Phys. Fluids 20, 085101 (2008).
  29. S. Laizet, J. Nedić, and J. C. Vassilicos, Influence of the spatial resolution on fine-scale features in DNS of turbulence generated by a single square grid, Int. J. Comput. Fluid Dyn. 29, 286 (2015).
  30. M. S. Chong, A. E. Perry, and B. J. Cantwell, A general classification of three-dimensional flow fields, Phys. Fluids A 2, 765 (1990).
  31. N. Mazellier and J. C. Vassilicos, Turbulence without Richardson–Kolmogorov cascade, Phys. Fluids 22, 075101 (2010).
  32. R. Gomes-Fernandes, B. Ganapathisubramani, and J. C. Vassilicos, Particle image velocimetry study of fractal-generated turbulence, J. Fluid Mech. 711, 306 (2012).
  33. U. Fey, M. König, and H. Eckelmann, A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47<Re<2×105, Phys. Fluids 10, 1547 (1998).
  34. K. Yamamoto and I. Hosokawa, A decaying isotropic turbulence pursued by the spectral method, J. Phys. Soc. Jpn. 57, 1532 (1988).
  35. 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).
  36. J. Soria, R. Sondergaard, B. J. Cantwell, M. S. Chong, and A. E. Perry, A study of the fine-scale motions of incompressible time-developing mixing layers, Phys. Fluids 6, 871 (1994).
  37. H. M. Blackburn, N. N. Mansour, and B. J. Cantwell, Topology of fine-scale motions in turbulent channel flow, J. Fluid Mech. 310, 269 (1996).
  38. J. M. Chacín, B. J. Cantwell, and S. J. Kline, Study of turbulent boundary layer structure using the invariants of the velocity gradient tensor, Exp. Therm. Fluid Sci. 13, 308 (1996).
  39. A. Tsinober, An Informal Introduction to Turbulence (Springer, Netherlands, 2014).
  40. R. Gomes-Fernandes, B. Ganapathisubramani, and J. C. Vassilicos, Evolution of the velocity-gradient tensor in a spatially developing turbulent flow, J. Fluid Mech. 756, 252 (2014).
  41. O. R. H. Buxton, M. Breda, and X. Chen, Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow, J. Fluid Mech. 817, 1 (2017).
  42. F. H. Champagne, The fine-scale structure of the turbulent velocity field, J. Fluid Mech. 86, 67 (1978).
  43. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, UK, 1995).
  44. D. Hurst and J. C. Vassilicos, Scalings and decay of fractal-generated turbulence, Phys. Fluids 19, 035103 (2007).
  45. J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
  46. M. S. Bloor, The transition to turbulence in the wake of a circular cylinder, J. Fluid Mech. 19, 290 (1964).
  47. C. H. K. Williamson, Vortex dynamics in the cylinder wake, Annu. Rev. Fluid Mech. 28, 477 (1996).
  48. A. Prasad and C. H. K. Williamson, The instability of the shear layer separating from a bluff body, J. Fluid Mech. 333, 375 (1997).
  49. J. Jiménez, R. Martinez-Val, and M. Rebollo, On the origin and evolution of three dimensional effects in the mixing layer, USA-ERO Rep. 79-G-079, London.
  50. C.-M. Ho and P. Huerre, Perturbed free shear layers, Annu. Rev. Fluid Mech. 16, 365 (1984).
  51. T. Watanabe, J. J. Riley, K. Nagata, R. Onishi, and K. Matsuda, A localized turbulent mixing layer in a uniformly stratified environment, J. Fluid Mech. 849, 245 (2018).
  52. K. Takamure, Y. Ito, Y. Sakai, K. Iwano, and T. Hayase, Momentum transport process in the quasi self-similar region of free shear mixing layer, Phys. Fluids 30, 015109 (2018).
  53. S. Goto and J. C. Vassilicos, Unsteady turbulence cascades, Phys. Rev. E 94, 053108 (2016).
  54. P. C. Valente and J. C. Vassilicos, The energy cascade in grid-generated non-equilibrium decaying turbulence, Phys. Fluids 27, 045103 (2015).
  55. T. Yasuda and J. C. Vassilicos, Spatio-temporal intermittency of the turbulent energy cascade, J. Fluid Mech. 853, 235 (2018).
  56. T. Yasuda, G. Kawahara, L. van Veen, and S. Kida, A vortex interaction mechanism for generating energy and enstrophy fluctuations in high-symmetric turbulence, J. Fluid Mech. 874, 639 (2019).
  57. Q. Nie and S. Tanveer, A note on third-order structure functions in turbulence, Proc. R. Soc. London A 455, 1615 (1999).
  58. J. Duchon and R. Robert, Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations, Nonlinearity 13, 249 (2000).
  59. G. L. Eyink, Local 4/5-law and energy dissipation anomaly in turbulence, Nonlinearity 16, 137 (2003).
  60. R. J. Hill, Exact second-order structure-function relationships, J. Fluid Mech. 468, 317 (2002).
  61. L. Danaila, J. F. Krawczynski, F. Thiesset, and B. Renou, Yaglom-like equation in axisymmetric anisotropic turbulence, Physica D 241, 216 (2012).
  62. http://www.archer.ac.uk.

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Phys. Rev. Fluids 5, 014601– Published 13 January, 2020
  • Received 13 August 2019
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