On the mechanism of turbulence suppression and turbulent skin-friction drag reduction with hairy surfaces*

Both DNS studies (Akhavan & Lee 2023) and experiments (Takata et al. 1996) have shown that by implanting a uniform carpet of flexible filaments, of appropriate characteristics, on the inner walls of a pipe or a channel, one can suppress the production of turbulence and get skin-friction drag reduction. In DNS studies performed in turbulent channel flows at a bulk Reynolds number of Re_b=7200 (Re_τ0≈221) with filaments of height 4 ≤ h⁺⁰ ≤ 16 and diameter of d⁺⁰≈0.5 (in base flow wall units), filament height to spacing ratios of 1/4 ≤ h/s ≤ 2, canopy solidities of 0.01 ≤ λ= (hd/s²) ≤ 0.25, filament to fluid density ratios of 30 ≤ ρ_r= (ρ_s/ρ_fε) ≤ 1000, and Cauchy numbers of Ca= (ρ_f u_τ0² d h³ / K_b) ≈ 0, 10, 20, 40, 60, 80, it was found that the magnitude of drag reduction is determined primarily by the ratio of the characteristic timescale of the filaments, T_fil, to the eddy turnover time of the largest turbulent eddies, H/u_τ0. Highest drag reductions of DR ≈ 5.5% were observed at T_filu_τ0/H≈1.5 (for filaments with h⁺⁰≈8, d⁺⁰≈0.5, 1/2 ≤ h/s ≤ 1, ρ_r=700 and Ca≈20). It has been suggested that such filamentous structures suppress the turbulence through a spectral shortcut mechanism, in which the energy of the largest turbulent eddies is redirected to the motion of the filaments. However, we find no such spectral shortcut mechanism at play. Instead, the filaments suppress the turbulence by disrupting the pressure-strain correlations, which results in accumulation of the turbulence kinetic energy in the streamwise component of the velocity, and a concomitant reduction in the Reynolds shear stress, turbulence production and streamwise vorticity fluctuations. Examination of the pre-multiplied spectra reveals that these effects are most pronounced at the largest turbulent scales and extend to wall-normal distances far beyond the height of the filaments. Reexamination of the mechanism of DR with polymer additives and spanwise wall oscillations reveals that a similar disruption of the pressure-strain correlations is also present in DR with these agents. These results suggest that targeting the pressure-strain correlations may be the path to more effective passive DR technologies.