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Self-sustaining process in Taylor-Couette flow

Tommy Dessup, Laurette S. Tuckerman, and José Eduardo Wesfreid

Dwight Barkley

Ashley P. Willis

  • Physique et Mécanique des Milieux Hétérogènes (PMMH), CNRS, ESPCI Paris, PSL Research University, Sorbonne Université, Univ. Paris Diderot 75005, France

  • Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

  • School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom

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Phys. Rev. Fluids 3, 123902 – Published 21 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.123902

Abstract

The transition from Tayor vortex flow to wavy-vortex flow is revisited. The self-sustaining process (SSP) of Waleffe [Phys. Fluids 9, 883 (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 (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.

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Phys. Rev. Fluids 3, 123902– Published 21 December, 2018
  • Received 22 August 2018
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