Period-doubling route to chaos in viscoelastic Kolmogorov flow

Newtonian turbulence has been the object of study for 150 years with mechanisms driving transitions to turbulence of paramount interest. Recently discovered elastic turbulence in polymeric fluids occurs even at Re=0, thus is driven by different mechanisms. Coherent structures such as traveling wave, oscillatory, and chaotic solutions have been observed, without an understanding of the transitions between states. Here we provide a characterization of transitions from coherent structures which oscillate undergoing period-doubling bifurcations to chaos. The system we study is sufficiently ``simple'' that further analysis will provide insight into mechanisms driving elastic turbulence.