Elastic turbulence in two-dimensional cross-slot viscoelastic flows

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.