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Symmetry-breaking waves and space-time modulation mechanisms in two-dimensional plane Poiseuille flow

Roger Ayats and Alvaro Meseguer*

Fernando Mellibovsky

  • Department of Physics, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain

  • Department of Physics–Aerospace Engineering Division, Universitat Politècnica de Catalunya, 08034, Barcelona

  • *Corresponding author: alvaro.meseguer@upc.edu
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Phys. Rev. Fluids 5, 094401 – Published 18 September, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.094401

Abstract

We investigate two distinct scenarios of spatial modulation that are candidate mechanisms for streamwise localization of waves in two-dimensional plane Poiseuille flow. The first one stems from a symmetry-breaking bifurcation that disrupts the half-shift and reflect equivariance of Tollmien-Schlichting waves (TSW). A new state, an asymmetric TSW (ATSW), emerges from unstable lower-branch TSWs at subcritical Reynolds number and undergoes subharmonic Hopf bifurcations that lead to branches of asymmetric time-periodic space-modulated waves (MATSW). Streamwise modulation does not evolve into localization within the range of parameters explored. In breaking the last standing remnants of the reflectional symmetry about the channel midplane, ATSW and MATSW admit a bias toward either one of the channel walls, thus bearing a potential for explaining near-wall structures that are typical of developed turbulence. The second scenario follows the fate of a branch of time-periodic space-modulated TSWs (MTSW) initially discovered by Mellibovsky and Meseguer [J. Fluid Mech. 779, R1 (2015)]. We find that these waves can lead to localization but the mechanism is not new, as they do so through their connection, by means of a codimension-2 bifurcation point, with other known localizing MTSWs. The codimension-2 point is, however, responsible for the appearance of MTSWs that exclusively bridge upper-branch TSW-trains of different number of replicas. In this respect, these MTSWs possess all required properties that single them out as possible constituents of the strange saddle that governs domain-filling turbulent dynamics at high Reynolds numbers.

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Phys. Rev. Fluids 5, 094401– Published 18 September, 2020
  • Received 2 April 2020
  • Accepted 25 August 2020
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