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 generated with the program OpenFOAM®. Beyond a critical Weissenberg number, an elastic instability causes a supercritical transition from the laminar Taylor-Couette flow to a turbulent flow. The order parameter, the time average of secondary-flow strength, follows the scaling law with and . Additionally, the flow resistance increases beyond Wic. The temporal power spectra of the velocity fluctuations show a power-law decay with a characteristic exponent in the range , which strongly depends on the radial position. The characteristic exponent β for the spatial power spectra obeys the necessary condition , associated with elastic turbulence, for all .