The Self-Sustaining Process in Taylor-Couette Flow

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.

References in corpus (3)

• Universal continuous transition to turbulence in a planar shear flow
• Reduced description of exact coherent states in parallel shear flows
• Experiments on transient growth of turbulent spots

Cited by in corpus (10)

• Vortex merging and splitting events in viscoelastic Taylor Couette flow
• Dynamics and evolution of Turbulent Taylor rolls
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Spirals and ribbons in counter-rotating Taylor-Couette flow: frequencies from mean flows and heteroclinic orbits
• Amplitude equations for wave bifurcations in reaction-diffusion systems
• On high Taylor number Taylor vortices
• Three-dimensional coherent structures in a curved pipe flow
• Lift-up and streak waviness drive the self-sustained process in wall-bounded transition to turbulence
• Large-scale structures in high Reynolds number rotating Waleffe flow
• Closing the loop: nonlinear Taylor vortex flow through the lens of resolvent analysis