DOI: 10.1615/TSFP9
MINIMAL DYNAMICS OF SELF-SUSTAINING ATTACHED EDDIES IN A TURBULENT CHANNEL
SINOPSIS
Very recently, we have performed a numerical experiment designed to simulate only the energy-containing motions at a prescribed spanwise length scale using their selfsustaining nature (Hwang, 2015). The computed statistical structure of each of the energy containing-motions have been found to be self-similar with respect to the spanwise length scale, proportional to the distance from the wall. More importantly, the statistical structure was found to be remarkably similar to that given in the original theory of Townsend, demonstrating the existence of the attached eddies as energy-containing motions contributing to the logarithmic layer. In this work, we extend the previous work to explore the dynamical self-similarity of each of the attached eddies. It is shown that each of the attached eddies exhibit the so-called 'self-sustaining process' composed of 1) streak amplification via the lift-up effect, 2) streak breakdown via the secondary instability, 3) nonlinear regeneration of streamwise vortical structure. This process occurs self-similarly with respect to the spanwise length scale of each of the attached eddies and results in the time scale given by Tuτ /Lz ~ 2 ~ 3.