Characterisation and modelling of interscale energy transfers in high Reynolds number boundary layers

High Reynolds number effects of wall-bounded flows, involving interscale energy transfers between small and large scales of turbulence within and between the inner and outer regions, challenge the classical description of the structure of these flows and the ensuing turbulence models. The two-scale Reynolds stress model recently proposed by Chedevergne et al. (2024, J. Fluid Mech . vol. 1000), was able to reproduce the small- and large-scale contributions in turbulent channel flows that follow the scale separation performed by Lee & Moser (2019, J. Fluid Mech . vol. 860, pp. 886–938), by partitioning energy spectra at a given wavelength. However, the interscale interactions within the inner region were modelled in an ad hoc manner, but without physical relevance, making the two-scale Reynolds stress model less and less accurate for boundary layer applications as the Reynolds number was increased. In this study, by re-analysing direct numerical simulations data from Lee & Moser (2019), with the objective of modelling these scale interactions, crucial observations on energy transfers between large and small scales could be made. In particular, the analysis reveals the important role played by the spanwise component of the Reynolds stress in the logarithmic region. From the analysis undertaken, a revisited version of the two-scale model was thus proposed, focusing efforts on interscale transfer modelling. The resulting model is then successfully tested on high Reynolds number boundary layer configurations without pressure gradient, up to $\textit{Re}_{\tau }=20\,000$ . The excellent agreement reflects the good prediction capabilities of the proposed model, and above all, the relevance of the modelling of the energy transfers within and between the inner and outer regions of wall-bounded flows.