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Statistical properties of shear and nonshear velocity components in isotropic turbulence and turbulent jets

Ryo Enoki

Tomoaki Watanabe*

Koji Nagata

  • Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan

  • Education and Research Center for Flight Engineering, Nagoya University, Nagoya 464-8603, Japan

  • Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8530, Japan

  • *Author to whom correspondence should be addressed: watanabe.tomoaki@c.nagoya-u.jp
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Phys. Rev. Fluids 8, 104602 – Published 9 October, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.104602

Abstract

The triple decomposition of a velocity gradient tensor, which extracts local fluid motions of shear, rigid-body rotation, and irrotational strain, is extended to the decomposition of velocity vectors into shear and nonshear components. The present approach adapts the Biot-Savart law to reconstruct shear and nonshear velocities from the vorticity vectors of shear and rigid-body rotation, respectively. These velocities are related to the flows induced by small-scale shear layers or vortex tubes. The decomposed velocities are investigated with direct numerical simulations of isotropic turbulence and temporally evolving planar jets. The r.m.s. values of shear and nonshear velocities are about 70% and 30% of the r.m.s. value of total velocity fluctuations, and shear layers have a greater contribution to velocity fluctuations than vortex tubes. The shear and nonshear velocities are positively correlated at large scales, and the momentum transfer due to their interaction actively occurs at scales greater than 20 times the Kolmogorov scale. The contributions of shear and nonshear velocities to the Reynolds stress hardly depend on flows. The energy spectra of these velocities collapse well at small scales under Kolmogorov normalization. The present analysis of the turbulent jet confirms that shearing motion has dominant contributions to the production and diffusion of turbulent kinetic energy and the turbulent transport of a passive scalar. In addition, the energy transfer across scales is shown to be dominated by the large-scale velocity gradients arising from shearing motion and the small-scale stresses due to the shear velocity and its interaction with the nonshear component.

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References (79)

  1. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).
  2. K. R. Sreenivasan and R. A. Antonia, The phenomenology of small-scale turbulence, Annu. Rev. Fluid Mech. 29, 435 (1997).
  3. P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers (Oxford University Press, New York, 2004).
  4. 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).
  5. A. Vincent and M. Meneguzzi, The dynamics of vorticity tubes in homogeneous turbulence, J. Fluid Mech. 258, 245 (1994).
  6. M. Hayashi, T. Watanabe, and K. Nagata, The relation between shearing motions and the turbulent/non-turbulent interface in a turbulent planar jet, Phys. Fluids 33, 055126 (2021).
  7. V. Kolář, Vortex identification: New requirements and limitations, Int. J. Heat Fluid Flow 28, 638 (2007).
  8. C. Liu, Y. Gao, S. Tian, and X. Dong, Rortex-A new vortex vector definition and vorticity tensor and vector decompositions, Phys. Fluids 30, 035103 (2018).
  9. Y. Maciel, M. Robitaille, and S. Rahgozar, A method for characterizing cross-sections of vortices in turbulent flows, Int. J. Heat Fluid Flow 37, 177 (2012).
  10. J. Eisma, J. Westerweel, G. Ooms, and G. E. Elsinga, Interfaces and internal layers in a turbulent boundary layer, Phys. Fluids 27, 055103 (2015).
  11. R. Nagata, T. Watanabe, K. Nagata, and C. B. da Silva, Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence, Comput. Fluids 198, 104389 (2020).
  12. T. Watanabe, K. Tanaka, and K. Nagata, Characteristics of shearing motions in incompressible isotropic turbulence, Phys. Rev. Fluids 5, 072601(R) (2020).
  13. D. Fiscaletti, O. R. H. Buxton, and A. Attili, Internal layers in turbulent free-shear flows, Phys. Rev. Fluids 6, 034612 (2021).
  14. M. Breda and O. R. H. Buxton, Effects of multiscale geometry on the large-scale coherent structures of an axisymmetric turbulent jet, J. Vis. 21, 525 (2018).
  15. A. Attili, J. C. Cristancho, and F. Bisetti, Statistics of the turbulent/non-turbulent interface in a spatially developing mixing layer, J. Turbul. 15, 555 (2014).
  16. G. E. Elsinga and I. Marusic, Universal aspects of small-scale motions in turbulence, J. Fluid Mech. 662, 514 (2010).
  17. G. E. Elsinga, T. Ishihara, M. V. Goudar, C. B. da Silva, and J. C. R. Hunt, The scaling of straining motions in homogeneous isotropic turbulence, J. Fluid Mech. 829, 31 (2017).
  18. Y. Sakurai and T. Ishihara, Relationships between small-scale fluid motions and inertial particle clustering in turbulence, J. Phys. Soc. Jpn. 87, 093401 (2018).
  19. G. E. Elsinga and I. Marusic, The anisotropic structure of turbulence and its energy spectrum, Phys. Fluids 28, 011701 (2016).
  20. M. V. Goudar and G. E. Elsinga, Tracer particle dispersion around elementary flow patterns, J. Fluid Mech. 843, 872 (2018).
  21. T. Watanabe and K. Nagata, The response of small-scale shear layers to perturbations in turbulence, J. Fluid Mech. 963, A31 (2023).
  22. J. C. Vassilicos, Dissipation in turbulent flows, Annu. Rev. Fluid Mech. 47, 95 (2015).
  23. 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).
  24. M. Takahashi, K. Iwano, Y. Sakai, and Y. Ito, Three-dimensional visualization of destruction events of turbulent momentum transfer in a plane jet, Phys. Fluids 31, 105114 (2019).
  25. T. Akao, T. Watanabe, and K. Nagata, Vertical confinement effects on a fully developed turbulent shear layer, Phys. Fluids 34, 055129 (2022).
  26. M. Farge, K. Schneider, and N. Kevlahan, Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis, Phys. Fluids 11, 2187 (1999).
  27. M. Farge, G. Pellegrino, and K. Schneider, Coherent Vortex Extraction in 3D Turbulent Flows Using Orthogonal Wavelets, Phys. Rev. Lett. 87, 054501 (2001).
  28. N. Okamoto, K. Yoshimatsu, K. Schneider, M. Farge, and Y. Kaneda, Coherent vortices in high resolution direct numerical simulation of homogeneous isotropic turbulence: A wavelet viewpoint, Phys. Fluids 19, 115109 (2007).
  29. C. Beta, K. Schneider, M. Farge, and H. Bockhorn, Numerical study of mixing of passive and reactive scalars in two-dimensional turbulent flows using orthogonal wavelet filtering, Chem. Eng. Sci. 58, 1463 (2003).
  30. T. Watanabe, Y. Sakai, K. Nagata, Y. Ito, and T. Hayase, Wavelet analysis of coherent vorticity near the turbulent/non-turbulent interface in a turbulent planar jet, Phys. Fluids 26, 095105 (2014).
  31. L. Biferale, G. Boffetta, A. Celani, A. Lanotte, and F. Toschi, Particle trapping in three-dimensional fully developed turbulence, Phys. Fluids 17, 021701 (2005).
  32. T. Watanabe, R. Jaulino, R. R. Taveira, C. B. da Silva, K. Nagata, and Y. Sakai, Role of an isolated eddy near the turbulent/non-turbulent interface layer, Phys. Rev. Fluids 2, 094607 (2017).
  33. M. M. Neamtu-Halic, J.-P. Mollicone, M. Van Reeuwijk, and M. Holzner, Role of vortical structures for enstrophy and scalar transport in flows with and without stable stratification, J. Turbul. 22, 393 (2021).
  34. J. Kronborg and J. Hoffman, The triple decomposition of the velocity gradient tensor as a standardized real Schur form, Phys. Fluids 35, 031703 (2023).
  35. S. Pirozzoli, M. Bernardini, and F. Grasso, On the dynamical relevance of coherent vortical structures in turbulent boundary layers, J. Fluid Mech. 648, 325 (2010).
  36. T. Watanabe and K. Nagata, Energetics and vortex structures near small-scale shear layers in turbulence, Phys. Fluids 34, 095114 (2022).
  37. Y. Morinishi, T. S. Lund, O. V. Vasilyev, and P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143, 90 (1998).
  38. T. Watanabe and K. Nagata, Integral invariants and decay of temporally developing grid turbulence, Phys. Fluids 30, 105111 (2018).
  39. T. Watanabe, X. Zhang, and K. Nagata, Direct numerical simulation of incompressible turbulent boundary layers and planar jets at high Reynolds numbers initialized with implicit large eddy simulation, Comput. Fluids 194, 104314 (2019).
  40. K. Yamamoto, T. Ishida, T. Watanabe, and K. Nagata, Experimental and numerical investigation of compressibility effects on velocity derivative flatness in turbulence, Phys. Fluids 34, 055101 (2022).
  41. P. L. Carroll and G. Blanquart, A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence, Phys. Fluids 25, 105114 (2013).
  42. M. Hayashi, T. Watanabe, and K. Nagata, Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet, J. Fluid Mech. 920, A38 (2021).
  43. C. B. da Silva and J. C. F. Pereira, Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets, Phys. Fluids 20, 055101 (2008).
  44. M. van Reeuwijk and M. Holzner, The turbulence boundary of a temporal jet, J. Fluid Mech. 739, 254 (2014).
  45. A. Cimarelli, A. Fregni, J.-P. Mollicone, M. Van Reeuwijk, and E. De Angelis, Structure of turbulence in temporal planar jets, Phys. Fluids 34, 045109 (2022).
  46. M. Takahashi, R. Fukui, K. Tsujimoto, T. Ando, and T. Shakouchi, Helical structures in a temporally developing round jet in the developed state, Flow, Turbul. Combust. 111, 59 (2023).
  47. P. J. Diamessis, G. R. Spedding, and J. A. Domaradzki, Similarity scaling and vorticity structure in high-Reynolds-number stably stratified turbulent wakes, J. Fluid Mech. 671, 52 (2011).
  48. R. Jahanbakhshi, N. S. Vaghefi, and C. K. Madnia, Baroclinic vorticity generation near the turbulent/non-turbulent interface in a compressible shear layer, Phys. Fluids 27, 105105 (2015).
  49. M. Kozul, D. Chung, and J. P. Monty, Direct numerical simulation of the incompressible temporally developing turbulent boundary layer, J. Fluid Mech. 796, 437 (2016).
  50. T. Watanabe, X. Zhang, and K. Nagata, Turbulent/non-turbulent interfaces detected in DNS of incompressible turbulent boundary layers, Phys. Fluids 30, 035102 (2018).
  51. T. Watanabe, Y. Zheng, and K. Nagata, The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime, J. Fluid Mech. 946, A29 (2022).
  52. T. Watanabe and K. Nagata, Large-scale characteristics of a stably stratified turbulent shear layer, J. Fluid Mech. 927, A27 (2021).
  53. I. Namer and M. V. Ötügen, Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers, Exp. Fluids 6, 387 (1988).
  54. M. Klein, A. Sadiki, and J. Janicka, Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation, Int. J. Heat Fluid Flow 24, 785 (2003).
  55. 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).
  56. S. Pirozzoli, M. Bernardini, and F. Grasso, Characterization of coherent vortical structures in a supersonic turbulent boundary layer, J. Fluid Mech. 613, 205 (2008).
  57. O. Terashima, Y. Sakai, and K. Nagata, Simultaneous measurement of velocity and pressure in a plane jet, Exp. Fluids 53, 1149 (2012).
  58. T. Watanabe, Y. Sakai, K. Nagata, Y. Ito, and T. Hayase, Enstrophy and passive scalar transport near the turbulent/non-turbulent interface in a turbulent planar jet flow, Phys. Fluids 26, 105103 (2014).
  59. T. Watanabe, T. Naito, Y. Sakai, K. Nagata, and Y. Ito, Mixing and chemical reaction at high Schmidt number near turbulent/nonturbulent interface in planar liquid jet, Phys. Fluids 27, 035114 (2015).
  60. S. Veeravalli and Z. Warhaft, The shearless turbulence mixing layer, J. Fluid Mech. 207, 191 (1989).
  61. H. S. Kang and C. Meneveau, Experimental study of an active grid-generated shearless mixing layer and comparisons with large-eddy simulation, Phys. Fluids 20, 125102 (2008).
  62. R. C. Deo, G. J. Nathan, and J. Mi, Similarity analysis of the momentum field of a subsonic, plane air jet with varying jet-exit and local Reynolds numbers, Phys. Fluids 25, 015115 (2013).
  63. R. M. Kerr, Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence, J. Fluid Mech. 153, 31 (1985).
  64. J. Mi, M. Xu, and T. Zhou, Reynolds number influence on statistical behaviors of turbulence in a circular free jet, Phys. Fluids 25, 075101 (2013).
  65. R. A. Antonia and A. J. Chambers, On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer, Boundary Layer Meteorol. 18, 399 (1980).
  66. L. Mydlarski and Z. Warhaft, On the onset of high-Reynolds-number grid-generated wind tunnel turbulence, J. Fluid Mech. 320, 331 (1996).
  67. O. R. H. Buxton and B. Ganapathisubramani, Amplification of enstrophy in the far field of an axisymmetric turbulent jet, J. Fluid Mech. 651, 483 (2010).
  68. A. Y.-S. Kuo and S. Corrsin, Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid, J. Fluid Mech. 50, 285 (1971).
  69. C. W. Van Atta and R. A. Antonia, Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives, Phys. Fluids 23, 252 (1980).
  70. Y. Zheng, K. Nagata, and T. Watanabe, Energy dissipation and enstrophy production/destruction at very low Reynolds numbers in the final stage of the transition period of decay in grid turbulence, Phys. Fluids 33, 035147 (2021).
  71. S.-J. Kang, M. Tanahashi, and T. Miyauchi, Dynamics of fine scale eddy clusters in turbulent channel flows, J. Turbul. 8, N52 (2007).
  72. A. A. Ghira, G. E. Elsinga, and C. B. da Silva, Characteristics of the intense vorticity structures in isotropic turbulence at high Reynolds numbers, Phys. Rev. Fluids 7, 104605 (2022).
  73. F. T. Nieuwstadt, J. Westerweel, and B. Boersma, Introduction to Theory and Applications of Turbulent Flows (Springer, Cham, Switzerland, 2016).
  74. S. A. Stanley, S. Sarkar, and J. P. Mellado, A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation, J. Fluid Mech. 450, 377 (2002).
  75. T. Watanabe, Y. Sakai, K. Nagata, and Y. Ito, Large eddy simulation study of turbulent kinetic energy and scalar variance budgets and turbulent/non-turbulent interface in planar jets, Fluid Dyn. Res. 48, 021407 (2016).
  76. J. Wang, Y. Yang, Y. Shi, Z. Xiao, X. T. He, and S. Chen, Cascade of Kinetic Energy in Three-Dimensional Compressible Turbulence, Phys. Rev. Lett. 110, 214505 (2013).
  77. T. Watanabe, C. B. da Silva, and K. Nagata, Scale-by-scale kinetic energy budget near the turbulent/nonturbulent interface, Phys. Rev. Fluids 5, 124610 (2020).
  78. U. Piomelli, Y. Yu, and R. J. Adrian, Subgrid-scale energy transfer and near-wall turbulence structure, Phys. Fluids 8, 215 (1996).
  79. C. B. da Silva and O. Métais, On the influence of coherent structures upon interscale interactions in turbulent plane jets, J. Fluid Mech. 473, 103 (2002).

Outline

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Phys. Rev. Fluids 8, 104602– Published 9 October, 2023
  • Received 27 June 2023
  • Accepted 6 September 2023
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