Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions
arXiv:1709.06782 · doi:10.1017/jfm.2017.697
Abstract
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 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 ( 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.