Exact coherent structures in purely elastic turbulence

Newtonian fluids are known to exhibit hydrodynamic instabilities and/or transition to turbulence at sufficiently enough Reynolds numbers. Recently it has been discovered that in simple shear flows (like pressure-driven flows in a pipe or between two plates) there exist unstable coherent structures that organise the turbulent dynamics close to the laminar-turbulent transition. The corresponding dynamics are low-dimensional and can be described by a relatively small number of well-chosen degrees of freedom. Complex fluids, in general, and polymer solutions, in particular, do not flow like Newtonian fluids. Their flows exhibit instabilities at very low Reynolds numbers that are driven not by inertia, but rather by anisotropic elastic stresses. Further increase of the flow rate results in a chaotic flow, the so-called purely elastic turbulence. The mechanism of this new type of chaotic motion is poorly understood. In this talk I will discuss our recent attempts to generalise the Newtonian theory of the transition to turbulence to the purely elastic case. We identify the relevant coherent structures and construct a viscoelastic self-sustaining process that can organise flow dynamics close to the transition.