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  • Letter
  • Open Access

Deep-learning-based assessment of skin friction in wall-bounded turbulence

Sergio Hoyas* and Nils Benedikt†

Andres Cremades and Ricardo Vinuesa‡

  • *Contact author: serhocal@mot.upv.es
  • †Present address: Technical University of Darmstadt, Chair of Fluid Dynamics, Otto-Bernd-Straße 2, 64287 Darmstadt, Germany.
  • ‡Contact author: rvinuesa@mech.kth.se

Phys. Rev. Fluids 10, L062601 – Published 25 June, 2025

DOI: https://doi.org/10.1103/b36b-m5hd

Abstract

This work investigates the influence of classically coherent structures on wall-shear stress and energy dissipation in turbulent channel flow, utilizing direct numerical simulations (DNS) data and explainable deep learning (XDL). Sweeps, defined as regions of low streamwise velocity moving toward the wall, are found to be the most influential structures for both energy dissipation and drag. Moreover, the volume of these key structures falls within a narrow range, making it easier to identify the most significant ones. Consequently, this work paves the way for the development of novel, highly efficient turbulence-control strategies for the reduction of drag.

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References (36)

  1. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, England, 2000).
  2. O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels, Phil. Trans. R. Soc. 174, 935 (1883).
  3. A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Proc.: Math. Phys. Sci. 434, 9 (1991).
  4. A. Townsend, The Structure of Turbulent Shear Flows, 2nd ed. (Cambridge University Press, New York, 1976).
  5. M. Raffel, C. E. Willert, F. Scarano, C. J. Kähler, S. T. Wereley, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide (Springer, New York, 2018).
  6. J. Kim, P. Moin, and R. Moser, Turbulence statistics in fully developed channels flows at low Reynolds numbers, J. Fluid Mech. 177, 133 (1987).
  7. 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).
  8. A. Cremades, S. Hoyas, and R. Vinuesa, Additive-feature-attribution methods: A review on explainable artificial intelligence for fluid dynamics and heat transfer, Int. J. Heat Fluid Flow 112, 109662 (2025).
  9. J. Jiménez, Coherent structures in wall-bounded turbulence, J. Fluid Mech. 842, P1 (2018).
  10. L. F. Moody, Friction factors for pipe flow, Trans. ASME 66, 671 (2022).
  11. J. P. Slotnick, K. Abdollah, J. Alonso, D. Darmofal, W. Gropp, E. Lurie, and D. J. Mavriplis, CFD vision 2030 study: a path to revolutionary computational aerosciences, No. NF1676L-18332 (2014).
  12. L. Guastoni, A. Güemes, A. Ianiro, S. Discetti, P. Schlatter, H. Azizpour, and R. Vinuesa, Convolutional-network models to predict wall-bounded turbulence from wall quantities, J. Fluid Mech. 928, A27 (2021).
  13. L. Guastoni, J. Rabault, P. Schlatter, H. Azizpour, and R. Vinuesa, Deep reinforcement learning for turbulent drag reduction in channel flows, The European Physical Journal E 46, 27 (2023).
  14. A. Cremades, S. Hoyas, R. Deshpande, P. Quintero, M. Lellep, W. J. Lee, J. P. Monty, N. Hutchins, M. Linkmann, I. Marusic, and R. Vinuesa, Identifying regions of importance in wall-bounded turbulence through explainable deep learning, Nat. Commun. 15, 3864 (2024).
  15. C. Canuto, M. Y. Hussaini, A. M. Quarteroni, A. Thomas, Jr. et al., Spectral Methods in Fluid Dynamics (Springer Science & Business Media, New York, 2012).
  16. J. Jiménez and S. Hoyas, Turbulent fluctuations above the buffer layer of wall-bounded flows, J. Fluid Mech. 611, 215 (2008).
  17. S. Hoyas and J. Jiménez, Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003, Phys. Fluids 18, 011702 (2006).
  18. F. Lluesma-Rodríguez, F. Álcantara Ávila, M. J. Pérez-Quiles, and S. Hoyas, A code for simulating heat transfer in turbulent channel flow, Mathematics 9, 756 (2021).
  19. M. Z. Yousif, L. Yu, S. Hoyas, R. Vinuesa, and H. Lim, A deep-learning approach for reconstructing 3D turbulent flows from 2D observation data, Sci. Rep. 13, 2529 (2023).
  20. 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).
  21. A. Cremades, S. Hoyas, and R. Vinuesa, Classically studied coherent structures only paint a partial picture of wall-bounded turbulence, arXiv:2410.23189.
  22. S. J. Kline, W. C. Reynolds, F. A. Schraub, and P. W. Runstadler, The structure of turbulent boundary layers, J. Fluid Mech. 30, 741 (1967).
  23. S. S. Lu and W. W. Willmarth, Measurements of the structure of the Reynolds stress in a turbulent boundary layer, J. Fluid Mech. 60, 481 (1973).
  24. A. Lozano-Durán and J. Jiménez, Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades, J. Fluid Mech. 759, 432 (2014).
  25. M. Chong, A. Perry, and B. Cantwell, A general classification of three-dimensional flow fields, J. Phys. A 2, 765 (1990).
  26. U. Frisch and A. N. Kolmogorov, Turbulence: The legacy of AN Kolmogorov (Cambridge University Press, Cambridge, England, 1995).
  27. O. Ronneberger, P. Fischer, and T. Brox, U-net: Convolutional networks for biomedical image segmentation, in MICCAI 2015, Proceedings, Part III 18 (Springer, New York, 2015), pp. 234–241.
  28. S. M. Lundberg and S.-I. Lee, A unified approach to interpreting model predictions, in Advances in Neural Information Processing Systems, edited by I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, Vol. 30 (Curran Associates, Inc., 2017).
  29. M. T. Ribeiro, S. Singh, and C. Guestrin, “Why should I trust you?” Explaining the predictions of any classifier, in Proceedings of the 22nd ACM SIGKDD (ACM, New York, 2016), pp. 1135–1144.
  30. S. Lipovetsky and M. Conklin, Analysis of regression in game theory approach, Applied Stochastic Models Business Industry 17, 319 (2001).
  31. A. Lozano-Duran and G. Borrell, Algorithm 964: an efficient algorithm to compute the genus of discrete surfaces and applications to turbulent flows, ACM Trans. Math. Softw. 42, 1 (2016).
  32. K. Osawa and J. Jiménez, Causal features in turbulent channel flow, J. Fluid Mech. 1000, A4 (2024).
  33. Á. Martínez-Sánchez, G. Arranz, and A. Lozano-Durán, Decomposing causality into its synergistic, unique, and redundant components, Nat. Commun. 15, 9296 (2024).
  34. G. Arranz and A. Lozano-Durán, Informative and non-informative decomposition of turbulent flow fields, J. Fluid Mech. 1000, A95 (2024).
  35. J. Jiménez, S. Hoyas, M. P. Simens, and Y. Mizuno, Turbulent boundary layers and channels at moderate reynolds numbers, J. Fluid Mech. 657, 335 (2010).
  36. M. Beneitez, A. Cremades, L. Guastoni, and R. Vinuesa, Improving turbulence control through explainable deep learning, arXiv:2504.02354.

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