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Transition route to elastic and elasto-inertial turbulence in polymer channel flows

M. Beneitez1,*, J. Page2,†, Y. Dubief3,‡, and R. R. Kerswell1,§

  • 1DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 2School of Mathematics, University of Edinburgh, EH9 3FD, United Kingdom
  • 3Department of Mechanical Engineering, University of Vermont, Burlington, Vermont, USA

  • *Contact author: mb2467@cam.ac.uk
  • †Contact author: jacob.page@ed.ac.uk
  • ‡Contact author: ydubief@uvm.edu
  • §Contact author: rrk26@cam.ac.uk
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Phys. Rev. Fluids 9, 123302 – Published 18 December, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.123302

Abstract

Viscoelastic shear flows support additional chaotic states beyond simple Newtonian turbulence. In vanishing Reynolds number flows, the nonlinearity in the polymer evolution equation alone can sustain inertialess “elastic” turbulence (ET) while “elasto-inertial” turbulence (EIT) appears to rely on an interplay between elasticity and finite-Re effects. Despite their distinct phenomenology and industrial significance, transition routes and possible connections between these states are unknown. We identify here a common Ruelle-Takens transition scenario for both of these chaotic regimes in two-dimensional direct numerical simulations of FENE-P fluids in a straight channel. The primary bifurcation is caused by a recently discovered “polymer diffusive instability” associated with small but nonvanishing polymer stress diffusion which generates a finite-amplitude, small-scale traveling wave localized at the wall. This is found to be unstable to a large-scale secondary instability which grows to modify the whole flow before itself breaking down in a third bifurcation to either ET or EIT. The secondary large-scale instability waves resemble “center” and “wall” modes, respectively—instabilities which have been conjectured to play a role in viscoelastic chaotic dynamics but were previously only thought to exist far from relevant areas of the parameter space.

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Phys. Rev. Fluids 9, 123302– Published 18 December, 2024
  • Received 13 May 2024
  • Revised 20 August 2024
  • Accepted 5 November 2024
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