Exact travelling wave solutions in viscoelastic channel flow

TL;DR

This paper identifies exact travelling wave solutions in viscoelastic channel flow, linking them to elasto-inertial turbulence and revealing their role as attractors in the complex dynamics of polymer solutions.

Contribution

It introduces the first known exact coherent structures in viscoelastic flows, connecting linear instabilities to turbulent states in polymer solutions.

Findings

Exact travelling waves are linked to elasto-inertial turbulence.

Travelling waves exhibit a distinctive 'arrowhead' structure.

These solutions act as attractors in EIT dynamics at high Weissenberg numbers.

Abstract

Elasto-inertial turbulence (EIT) is a new, two-dimensional chaotic flow state observed in polymer solutions with possible connections to inertialess elastic turbulence and drag-reduced Newtonian turbulence. In this Letter, we argue that the origins of EIT are fundamentally different from Newtonian turbulence by finding a dynamical connection between EIT and an elasto-inertial linear instability recently found at high Weissenberg numbers (Garg et al. Phys. Rev. Lett. 121, 024502, 2018). This link is established by isolating the first known exact coherent structures in viscoelastic parallel flows - nonlinear elasto-inertial travelling waves (TWs) - borne at the linear instability and tracking them down to substantially lower Weissenberg numbers where EIT exists. These TWs have a distinctive ``arrowhead'' structure in the polymer stretch field and can be clearly recognised, albeit transiently, in EIT, as well as being attractors for EIT dynamics if the Weissenberg number is sufficiently large. Our findings suggest that the dynamical systems picture in which Newtonian turbulence is built around the co-existence of many (unstable) simple invariant solutions populating phase space carries over to EIT, though these solutions rely on elasticity to exist.