Reynolds number invariance in the coherent structures of wall-bounded turbulence

Estimation of instantaneous and statistical properties of wall-bounded turbulence across different Reynolds numbers has significant applications in scientific research and engineering, where the key challenge is to identify the Reynolds number invariance underlying the varying flow properties as Reynolds number changes. In this study, we develop a refined inner–outer interaction model (IOIM) that isolates the footprints of large-scale structures populating within a prescribed wall-normal range $y_{R}^+ \in [ y_{R1}^+ , y_{R2}^+ )$ . When the reference layers are located within $ 80 \leqslant y_{R1}^+ \lt y_{R2}^+ \leqslant 0.3\textit{Re}_\tau$ , the energy spectral densities of the isolated large-scale structures, including the wall-attached and wall-detached eddies, are found to be independent of Reynolds numbers with direct numerical simulations spanning $ \textit{Re}_\tau \sim O(10^2)$ – $O(10^3)$ . The spectral energy densities of the near-wall small-scale motions also show little Reynolds number dependence. The increase in near-wall turbulent kinetic energy with Reynolds number is explained from the identified Reynolds number invariance of coherent structures. Meanwhile, certain amplitude and scale modulation effects caused by large-scale structures are found to make the distribution patterns of fluctuation amplitudes and scales of near-wall structures more susceptible to Reynolds number influence. The findings of this study provide insights for the developments of predictive models for wall-bounded turbulence across different Reynolds numbers.