On the final stages of transition to turbulence in wall bounded flows*

Using immersed boundary DNS, we first examine all phases of the process of transition to turbulence caused by a discrete roughness element. We demonstrate that after the initial receptivity, spatial amplification of the steady distortion, and the subsequent modal instability of the lifted up structure, transition proceeds via a mutual, local, amplification of the fluctuating streamwise and spanwise vorticity. We observe that the near-wall spanwise vorticity is stretched by dw/dz induced by a  streamwise vortex tube present above it. This results in a local flow acceleration,  and the du/dx leads to the stretching of streamwise vorticity.   Thus this process is responsible for the amplification of streamwise vorticity near the wall, leading to the formation of familiar hairpin vortices.  The relation of this process to the subsequent breakdown to chaos and counter gradient transport of mean vorticity to the wall is discussed.  We study whether these observations are applicable to other routes to transition, such as free stream driven Klebanoff-mode bypass transition.