Host: Prof. Mike Schatz

Title: The Self-Sustaining-Process in Taylor-Couette Flow

Abstract:
The self-sustaining process (SSP) of Waleffe (1997) proposes that a key ingredient in transition to turbulence in wall-bounded shear flows is a three-step process involving rolls advecting streamwise velocity, leading to streaks which become unstable to a wavy perturbation whose nonlinear interaction with itself feeds the rolls. Waleffe obtains this process in the linearly stable plane Couette and Poiseuille flow by including a forcing term, but it occurs naturally in Taylor-Couette flow via the esthetic and much-reproduced transition from laminar to Taylor-vortex and wavy-Taylor-vortex flows. More specifically, the instability of Taylor-vortex flow to wavy-vortex flow, a process which is the inspiration for the second phase of the SSP, is shown to be caused by the streaks, with the rolls playing a negligible role. In the third phase of the SSP, the nonlinear interaction of the waves with themselves reinforces the rolls. We show this both quantitatively and qualitatively, identifying physical regions in which this reinforcement is strongest, and also demonstrate that this nonlinear interaction depletes the streaks.