The Self-Sustaining Process in Taylor-Couette Flow

TL;DR

This paper investigates the Self-Sustaining Process in Taylor-Couette flow, confirming the roles of streaks and waves in transition to turbulence, and clarifying the negligible role of rolls in the instability process.

Contribution

It demonstrates that streaks, rather than rolls, cause the instability of Taylor-vortex flow to wavy-vortex flow, and shows how nonlinear wave interactions reinforce rolls and deplete streaks.

Findings

Streaks cause the instability of Taylor-vortex flow to wavy-vortex flow.

Nonlinear wave interactions reinforce rolls and deplete streaks.

The process aligns with the SSP framework in wall-bounded shear flows.

Abstract

The transition from Tayor vortex flow to wavy-vortex flow is revisited. The Self-Sustaining Process (SSP) of Waleffe [Phys. Fluids 9, 883-900 (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. We investigate this process in Taylor-Couette flow. 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, as predicted by Jones [J. Fluid Mech. 157, 135-162 (1985)] and demonstrated by Martinand et al. [Phys. Fluids 26, 094102 (2014)]. 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.