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Reynolds number effect on dynamical state in a fully developed turbulent channel flow

Yusuke Nabae*

Hiroya Mamori

Hiroshi Gotoda

  • *Contact author: yusuke.nabae@rs.tus.ac.jp
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Phys. Rev. Research 8, 023205 – Published 26 May, 2026

DOI: https://doi.org/10.1103/rn7z-msq2

Abstract

We investigate the Reynolds number effect on the dynamical state of a turbulent channel flow by means of orbital-instability-based forecasting method (OIFM) and ordinal partition transition network (OPTN). In the near-wall region, i.e., viscous sublayer and buffer layer, the coexistence of streaky structures with a spanwise spacing of about 100 wall units and large-scale structures with a spanwise spacing on the order of channel half-width decreases the predictive accuracy of streamwise velocity and increases the randomness of streamwise velocity. The low-dimensional chaotic state of streamwise velocity persists in the near-wall region regardless of the friction Reynolds number. In the far-wall region, the high-dimensional chaotic state of streamwise velocity emerges at low friction Reynolds numbers owing to the obvious low-Reynolds-number effect, whereas the low-dimensional chaotic state of streamwise velocity emerges at high friction Reynolds numbers owing to the formation of streamwise and spanwise large-scale structures, i.e., the large-scale motions. The chaotic state of the streamwise velocity at high friction Reynolds numbers is strongly associated with hierarchical structures. The formation of hierarchical structures can be clearly identified at high friction Reynolds numbers through the analyses of the premultiplied streamwise Reynolds stress spectrum and the instantaneous streamwise velocity fluctuations in the z–y plane, whereas it is hardly observed at low friction Reynolds numbers. The results of this study demonstrate that the OIFM and OPTN have high capabilities of elucidating the dynamics in turbulent flows and predicting their behavior.

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Phys. Rev. Research 8, 023205– Published 26 May, 2026
  • Received 22 November 2025
  • Accepted 9 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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