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

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.