  We report evidence of irregular unsteady flow of two-dimensional polymer
solutions in the absence of inertia in cross-slot geometry using numerical
simulations of Oldroyd-B model. By exploring the transition to time-dependent
flow versus both the fluid elasticity and the polymer concentration, we find
periodic behaviour close to the instability threshold and more complex flows at
larger elasticity, in agreement with experimental findings. For high enough
elasticity we obtain dynamics pointing to elastic turbulence, with temporal
spectra of velocity fluctuations showing a power-law decay, of exponent in
between -3 and -2, and probability density functions of velocity fluctuations
that weakly deviate from Gaussianity while high non-Gaussian tails characterise
those of local accelerations.
