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Hessian-based Lagrangian closure theory for passive scalar turbulence

Taketo Ariki1,* and Kyo Yoshida2,†

  • 1Department of Aerospace Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aobaku, Sendai, Japan
  • 2Division of Physics, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba 305-8571, Japan

  • *taketo.ariki.c5@tohoku.ac.jp
  • †yoshida.kyo.fu@u.tsukuba.ac.jp
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Phys. Rev. Fluids 6, 104603 – Published 11 October, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.104603

Abstract

Self-consistent closure theory for passive scalar turbulence has been developed on the basis of the Hessian of the scalar field. As a primitive indicator of spatial structure of the scalar, we employ the Hessian into the core of the theory to properly characterize the time scale intrinsic to the scalar field itself. The resultant closure model is now endowed with several realistic features, i.e., the scale locality of the interscale interaction, the detailed conservation, and the memory-fading effect. Applying the current theory to the inertial-convective range eventually leads to self-consistent derivation of the Obukhov-Corrsin spectrum with its universal constant consistent with numerical and experimental data.

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References (27)

  1. Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech. 32, 203 (2000).
  2. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 299 (1941); A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, reprinted in Proc. R. Soc. London A 434, 9 (1991).
  3. A. M. Obukhov, Temperature field structure in a turbulent flow, Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz 13, 58 (1949).
  4. S. Corrsin, On the spectrum of isotropic temperature fluctuations in an isotropic turbulence, J. Appl. Phys. 22, 469 (1951).
  5. K. R. Sreenivasan, The passive scalar spectrum and the Obukhov-Corrsin constant, Phys. Fluids 8, 189 (1996).
  6. L. Mydlarski and Z. Warhaft, Passive scalar statistics in high-Péclet-number grid turbulence, J. Fluid Mech. 358 135 (1998).
  7. L. P. Wang, S. Chen, and J. G. Brasseur, Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field, J. Fluid Mech. 400, 163 (1999).
  8. P. K. Yeung, S. Xu, and K. R. Sreenivasan, Schmidt number effects on turbulent transport with uniform mean scalar gradient, Phys. Fluids 14, 4178 (2002).
  9. T. Watanabe and T. Gotoh, Statistics of a passive scalar in homogeneous turbulence, New J. Phys. 6, 40 (2004).
  10. T. Gotoh and T. Watanabe, Power and Nonpower Laws of Passive Scalar Moments Convected by Isotropic Turbulence, Phys. Rev. Lett. 115, 114502 (2015).
  11. Y. Zhou, Turbulence theories and statistical closure approaches, Phys. Rep. 935, 1 (2021).
  12. A. Briard, T. Gomez, and C. Cambon, Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence, J. Fluids Mech. 799, 159 (2016).
  13. S. Orszag, Analytical theories of turbulence, J. Fluids Mech. 41, 363 (1970).
  14. R. H. Kraichnan, Lagrangian-history closure approximation for turbulence, Phys. Fluids 8, 575 (1965).
  15. R. H. Kraichnan, Dispersion of particle pairs in homogeneous turbulence, Phys. Fluids 9, 1937 (1966).
  16. Y. Kaneda, Renormalized expansions in the theory of turbulence with the use of the Lagrangian position function, J. Fluid Mech. 107, 131 (1981).
  17. Y. Kaneda, Inertial range structure of turbulent velocity and scalar fields in Lagrangian renormalized approximation, Phys. Fluids 29, 701 (1986).
  18. S. Goto and S. Kida, Passive-scalar spectrum in isotropic turbulence: Prediction by the Lagrangian direct-interaction approximation, Phys. Fluids 11, 1936 (1999).
  19. R. H. Kraichnan, The structure of isotropic turbulence at very high Reynolds numbers, J. Fluid Mech. 5, 497 (1959).
  20. W. J. T. Bos and J.-P. Bertoglio, A single-time two-point closure based on fluid particle displacements, Phys. Fluids 18, 031706 (2006).
  21. Y. Kaneda, Lagrangian renormalized approximation of turbulence, Fluid Dyn. Res. 39, 526 (2007).
  22. T. Gotoh, J. Nagaki, and Y. Kaneda, Passive scalar spectrum in the viscous-convective range in two-dimensional steady turbulence, Phys. Fluids 12, 155 (2000).
  23. R. H. Kraichnan and R. H. Herring, A strain-based Lagrangian-history turbulence theory, J. Fluid Mech. 88, 355 (1978).
  24. T. Ariki, K. Yoshida, K. Matsuda, and K. Yoshimatsu, Scale-similar clustering of heavy particles in the inertial range of turbulence, Phys. Rev. E 97, 033109 (2018).
  25. R. H. Kraichnan, Isotropic turbulence and inertial-range structure, Phys. Fluids 9, 1728 (1966).
  26. T. Ishihara, K. Morishita, M. Yokokawa, A. Uno, and Y. Kaneda, Energy spectrum in high-resolution direct numerical simulations of turbulence, Phys. Rev. Fluids 1, 082403(R) (2016).
  27. R. H. Kraichnan, Eulerian and Lagrangian renormalization in turbulence theory, J. Fluid Mech. 83, 349 (1977).

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Phys. Rev. Fluids 6, 104603– Published 11 October, 2021
  • Received 1 October 2019
  • Accepted 3 September 2021
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