  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.
