Elastic turbulence in two-dimensional Taylor-Couette flows

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.