Coherent structures in plane channel flow of dilute polymer solutions with vanishing inertia

TL;DR

This paper reveals that in dilute polymer solutions flowing through straight channels, elastic turbulence is organized by exact two-dimensional travelling wave structures, which are purely elastic and do not require linear instability for their existence.

Contribution

It identifies and characterizes exact coherent travelling wave solutions in elastic channel flows, highlighting their purely elastic origin and role in elastic turbulence transition.

Findings

Travelling wave solutions are purely elastic and do not need linear instability.

Polymer stress profiles form thin, filament-like structures.

Vortices sustain the polymer stretch in these solutions.

Abstract

When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids, and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organised by exact coherent structures that take the form of two-dimensional travelling waves. Our results demonstrate that no linear instability is required to sustain such travelling wave solutions, and that their origin is purely elastic in nature. We show that the associated stress profiles are characterised by thin, filament-like arrangements of polymer stretch, which is sustained by a solitary pair of vortices. We discuss the implications of the travelling wave solutions for the transition to elastic turbulence in straight channels, and propose ways for their detection in experiments.