A driving mechanism of a turbulent puff in pipe flow

A turbulent puff is numerically realized in a circular pipe flow driven by a constant uniform external force. The periodic boundary condition is imposed in the axial direction with a period of 16 pi pipe radius. The Reynolds number based on the pipe radius, the centerline velocity of the Hagen-Poiseuille flow corresponding to the external force, is 3000. Starting with the Hagen-Poiseuille flow superposed by a disturbance of finite amplitude, an equilibrium puff of about 11 pi pipe radius in length emerges and advects with nearly the mean flow velocity. Turbulence in the puff generates a number of low-speed streaks accompanied by streamwise vortices along the pipe wall. These low-speed streaks move upstream relative to the puff, across the trailing edge and create strong thin vortex layers, arched above the streaks, together with the laminar flow coming from upstream. The vortex layers, whose thickness is typically a few times smaller than the width, are unstable to roll up, through the Kelvin-Helmholtz instability, and induce velocity fluctuations that propagate downstream faster than the puff itself and enhance the turbulent activity in it. This self-sustenance cycle of an equilibrium puff is numerically verified.