We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers (Re), the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number (Wi), this lattice undergoes a series of nonequilibrium phase transitions, first to a distorted, steady crystals, then to a sequence of crystals that oscillate in time, periodically, at low Wi, and quasiperiodically, for slightly larger Wi. Finally, the system becomes disordered and displays spatiotepmoral chaos and turbulence. We obtain the nonequilibrium phase diagram for this system in the Wi − Re plane. We show that the Okubo-Weiss parameter Λ provides us with a natural measure for characterizing the phases and transitions in this diagram. Copyright © ETC 2013 - 14th European Turbulence Conference.All rights reserved.