It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an 'amplified' streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to Re τ ≃ 2000 where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51-73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of λ x /h ≃ 1−5 (h is the half-height of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuous-mode instability of the streak, a sub-process of the self-sustaining mechanism of the large-scale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the large-scale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of very-large-scale motion.

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

The regeneration cycle of streaks and streamwise vortices plays a central role in the sustainment of near-wall turbulence. In particular, the streak breakdown phase in the regeneration cycle is the core process in the formation of the streamwise vortices, but its current understanding is limited particularly in a real turbulent environment. This study is aimed at gaining fundamental insight into the underlying physical mechanism of the streak breakdown in the presence of background turbulent fluctuation. We perform a numerical experiment based on direct numerical simulation, in which streaks are artificially generated by a body forcing computed from previous linear theory. Upon increasing the forcing amplitude, the artificially driven streaks are found to generate an intense fluctuation of the wall-normal and spanwise velocities in a fairly large range of amplitudes. This cross-streamwise velocity fluctuation shows its maximum at λ + x ≈ 200 − 300 (λ + x is the inner-scaled streamwise wavelength), but it only appears for λ + x 3000 − 4000. Further examination with dynamic mode decomposition reveals that the related flow field is composed of sinuous meandering motion of the driven streaks and alternating cross-streamwise velocity structures, clearly reminiscent of sinuousmode streak instability found in previous studies. Finally, it is shown that these structures are reasonably well aligned along the critical layer of the secondary instability, indicating that the surrounding turbulence does not significantly modify the inviscid inflectional mechanism of the streak breakdown via streak instability and/or streak transient growth.

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