A Period-Doubling Route to Chaos in Viscoelastic Kolmogorov Flow

TL;DR

This paper investigates how viscoelastic Kolmogorov flow transitions to chaos through a period-doubling route, revealing the role of traveling wave solutions and bifurcations in elastic turbulence.

Contribution

It demonstrates a novel period-doubling route to chaos in 2D viscoelastic flow, expanding understanding of elastic turbulence mechanisms.

Findings

Traveling wave solutions become oscillatory with increasing elasticity.

A sequence of period-doubling bifurcations leads to chaotic flow.

The study provides numerical evidence for a route to chaos in elastic fluids.

Abstract

Polymer solutions can develop chaotic flows, even at low inertia. This purely elastic turbulence is well studied, but little is known about the transition to chaos. In 2D channel flow and parallel shear flow, traveling wave solutions involving coherent structures are present for sufficiently large fluid elasticity. We numerically study 2D periodic parallel shear flow in viscoelastic fluids and show that these traveling waves become oscillatory and undergo a series of period-doubling bifurcations en-route to chaos.