Elastic turbulence in two-dimensional Taylor-Couette flows

TL;DR

This paper demonstrates the emergence of elastic turbulence in a two-dimensional Taylor-Couette flow through numerical simulations of the Oldroyd-B model, revealing a supercritical transition at a critical Weissenberg number and analyzing the flow's spectral properties.

Contribution

It provides the first numerical evidence of elastic turbulence in 2D Taylor-Couette flows and characterizes the transition and flow fluctuations.

Findings

Elastic turbulence occurs beyond Wi_c=10.

Order parameter scales as (Wi - Wi_c)^0.45.

Velocity fluctuation spectra follow a power-law decay.

Abstract

We report the onset of elastic turbulence in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model, also performed at high Weissenberg numbers with the program OpenFOAM. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law $\Phi \propto (\mathrm{Wi} -\mathrm{Wi}_c)^{\gamma}$ with $\mathrm{Wi}_c=10$ and $\gamma = 0.45$. The power spectrum of the velocity fluctuations shows a power-law decay with a characteristic exponent, which strongly depends on the radial position. It is greater than two, which we relate to the dimension of the geometry.