Two-dimensional elastic turbulence

TL;DR

This paper demonstrates through simulations that polymer additives induce elastic turbulence in a 2D flow at low Reynolds numbers, characterized by increased turbulence metrics and a power-law energy spectrum.

Contribution

It provides the first numerical evidence of elastic turbulence in a 2D Kolmogorov flow using the Oldroyd-B model, aligning with experimental and theoretical findings.

Findings

Elastic turbulence occurs above a threshold in polymer concentration.

Turbulent drag and Lyapunov exponent increase with Weissenberg number.

Energy spectrum exhibits a power-law scaling consistent with experiments.

Abstract

We investigate the effect of polymer additives on a two-dimensional Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of the Oldroyd-B viscoelastic model. We find that above the elastic instability threshold the flow develops the elastic turbulence regime recently observed in experiments. We observe that both the turbulent drag and the Lyapunov exponent increase with Weissenberg, indicating the presence of a disordered, turbulent-like mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.