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We investigate the dynamics of the two-dimensional periodic Kolmogorov flowof a viscoelastic fluid, described by the Oldroyd-B model, by means of directnumerical simulations. Above a critical Weissenberg number the flow displays atransition from stationary to randomly fluctuating states, via periodic ones.The increasing complexity of the flow in both time and space at progressivelyhigher values of elasticity accompanies the establishment of mixing features.The peculiar dynamical behavior observed in the simulations is found to berelated to the appearance of filamental propagating patterns, which developeven in the limit of very small inertial non-linearities, thanks to thefeedback of elastic forces on the flow.

Elastic waves and transition to elastic turbulence in a two-dimensional viscoelastic Kolmogorov flow