Linear stability analysis of purely elastic travelling wave solutions in pressure driven channel flows

TL;DR

This paper investigates the stability of purely elastic travelling wave solutions in pressure-driven channel flows, revealing their instability in three-dimensional settings and emphasizing the need for 3D simulations to understand elastic turbulence.

Contribution

It demonstrates that 2D travelling-wave solutions are unstable in 3D domains, highlighting the importance of three-dimensional analysis for elastic and elasto-inertial turbulence studies.

Findings

2D travelling-wave solutions are unstable in 3D domains.

Purely elastic and elasto-inertial turbulence require 3D simulations.

2D studies alone are insufficient for reliable conclusions.

Abstract

Recent studies of pressure-driven flows of dilute polymer solutions in straight channels demonstrated the existence of two-dimensional coherent structures that are disconnected from the laminar state and appear through a sub-critical bifurcation from infinity. These travelling-wave solutions were suggested to organise the phase-space dynamics of purely elastic and elasto-inertial chaotic channel flows. Here, we consider a wide range of parameters, covering the purely-elastic and elasto-inertial cases, and demonstrate that the two-dimensional travelling-wave solutions are unstable when embedded in sufficiently wide three-dimensional domains. Our work demonstrates that studies of purely elastic and elasto-inertial turbulence in straight channels require three-dimensional simulations, and no reliable conclusions can be drawn from studying strictly two-dimensional channel flows.