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

TL;DR

This paper uncovers a common transition scenario for elastic and elasto-inertial turbulence in polymer flows, revealing how small-scale instabilities lead to different chaotic regimes through a series of bifurcations.

Contribution

It identifies a unified Ruelle-Takens transition pathway for both elastic and elasto-inertial turbulence in viscoelastic channel flows, linking their onset mechanisms.

Findings

A polymer diffusive instability triggers initial flow bifurcation.

Large-scale secondary instabilities develop, leading to turbulence.

Distinct wall and center modes are involved in the transition.

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 non-vanishing polymer stress diffusion which generates a finite-amplitude, small-scale travelling wave localised 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 'centre' 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.