Multistability of elasto-inertial two-dimensional channel flow

TL;DR

This study explores the multistability in elasto-inertial two-dimensional channel flows, revealing multiple co-existing states including laminar, steady arrowhead, and chaotic flow regimes, and clarifying their dynamical relationships.

Contribution

It identifies four co-existing attractors in elasto-inertial flow and clarifies that the arrowhead structure is not central to turbulence sustenance.

Findings

Four co-existing attractors identified: laminar, steady arrowhead, EIT, chaotic arrowhead.

Steady arrowhead is stable across all parameters studied.

Chaotic regimes share similar energy transfer mechanisms, with weak arrowhead structures not influencing turbulence.

Abstract

Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. It has been hypothesised that the dynamical origins of EIT are linked to a center-mode instability, whose nonlinear evolution leads to a travelling wave with an 'arrowhead' structure in the polymer conformation, a structure also observed instantaneously in simulations of EIT. In this work we conduct a suite of two-dimensional direct numerical simulations spanning a wide range of polymeric flow parameters to examine the possible dynamical connection between the arrowhead and EIT. Our calculations reveal (up to) four co-existent attractors: the laminar state and a steady arrowhead, along with EIT and a 'chaotic arrowhead'. The steady arrowhead is stable for all parameters considered here, while the final pair of (chaotic) flow states are visually very similar and can be distinguished only by the presence of a weak polymer arrowhead structure in the 'chaotic arrowhead' regime. Analysis of energy transfers between the flow and the polymer indicates that both chaotic regimes are maintained by an identical near-wall mechanism and that the weak arrowhead does not play a role. Our results suggest that the arrowhead is a benign flow structure that is disconnected from the self-sustaining mechanics of EIT.