Turbulent transport for wall-shear-stress fluctuations

Statistical structure and the underlying energy budget of wall-shear-stress fluctuations are studied in both Poiseuille and Couette flows with emphasis on its streamwise component. Using a dimensional analysis and direct numerical simulation data, it is shown that the spectra of streamwise wall dissipation for λ 1000 δ _ν are asymptotically invariant with the Reynolds number ( Re ), whereas those for λ δ decay with Re (here, λ is a nominal wall-parallel wavelength, and δ _ν and δ are the viscous inner and outer length scales, respectively). The wall dissipation increases with Re due to the increasing contribution of the spectra at 1000 δ _ν λ δ . The subsequent analysis of the energy budget shows that the near-wall motions associated with these wall-dissipation spectra are driven mainly by turbulent transport and are ‘inactive’ in the sense that they contain very little Reynolds shear stress (or turbulence production). As such, turbulent-transport spectra near the wall are also found to share the same Re -scaling behaviour with wall dissipation, and this is observed in the spectra of both the wall-normal and inter-scale turbulent transports. The turbulent transport underpinning the increase of wall dissipation with Re is characterised by energy fluxes towards the wall, together with inverse energy transfer from small to large length scales along the wall-parallel directions.