Skin-friction generation by attached eddies in turbulent channel flow

Abstract

Despite a growing body of recent evidence on the hierarchical organization of the selfsimilar energy-containing motions in the form of Townsend’s attached eddies in wallbounded turbulent flows, their role in turbulent skin-friction generation is currently known very little. In this paper, the contribution of each of these self-similar energycontaining motions to turbulent skin friction is explored up to Reτ ≃ 4000. Three different approaches are employed to quantify the skin-friction generation by the motions, the spanwise length scale of which is smaller than a given cut-off wavelength: 1) FIK identity in combination with the spanwise wavenumber spectra of the Reynolds shear stress; 2) confinement of the spanwise computational domain; 3) artificial damping of the motions to be examined. The near-wall motions are found to continuously lose their role in skin-friction generation on increasing the Reynolds number, consistent with the previous finding at low Reynolds numbers. The largest structures given in the form of very-large-scale and large-scale motions are also found to be of limited importance: due to a non-trivial scale-interaction process, their complete removal yields only 5 ∼ 8% of skin-friction reduction at all the Reynolds numbers considered, although they are found to be responsible for 20 ∼ 30% of total skin friction at Reτ ≃ 2000. Application of all the three approaches consistently reveals that the largest amount of skin friction is generated by the self-similar motions populating the logarithmic region. It is further shown that the contribution of these motions to turbulent skin friction gradually increases with the Reynolds number, and that these coherent structures are eventually responsible for most of turbulent skin-friction generation at sufficiently high Reynolds numbers

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

“…friction generation). Smart enforcing of this transfer at large scale was demonstrated to reduce a substantial amount of drag by modifying the self-sustaining processes at other scales [36], and its artificial inhibition also yielded a significant amount of drag reduction at high Reynolds numbers [54,69,72], suggesting the practical importance of the self-sustaining processes in skin-friction control.…”

“…For instance, it has been recently experimentally shown [71] that proper orthogonal decomposition (POD) modes extracted in the logarithmic region from Princeton's superpipe data are self-similar with respect to the spanwise length scale and/or the distance from the wall. Furthermore, it has recently been found that most turbulent skin friction at sufficiently high Reynolds numbers (Re τ > 1000) is generated by the self-similar self-sustaining motions in the logarithmic region [69,72]. In particular, the coherent lift-up effect was found to play a crucial role in transferring the streamwise momentum to the near-wall region (i.e.…”

On the structure of streamwise wall-shear stress fluctuations in turbulent channel flows

“…τ x,rms /τ x = 0.298 + 0.018 ln(Re τ ), where Re τ = u τ δ/ν, u τ is the friction velocity, ν is the kinematic viscosity and δ is the boundary-layer thickness (or channel half-height). The Reynolds number dependence of τ x,rms suggests that large-scale energy-containing motions populating the logarithmic and outer regions in high-Reynolds-number wall turbulence have non-negligible influences on the near-wall dynamics and, hence, on the wall friction (Abe et al 2004;Örlü & Schlatter 2011;de Giovanetti, Hwang & Choi 2016;Renard & Deck 2016;Baidya et al 2019;Fan et al 2019a,b).…”

Exact coherent states of attached eddies in channel flow

“…Nevertheless, the question of what the main energy-containing eddies really are is very important, as these eddies would play the central role in momentum and mass transfer due to their energy-containing nature -indeed, it was recently shown that the energy-containing eddies which scale with the distance from the wall are the dominant source of turbulent skin-friction generation at high Reynolds numbers (de Giovanetti et al 2016). Recently, some important statistical and dynamical features of these main energy-containing eddies have also been reported.…”