Turbulence of polymer solutions.

We investigate high-Reynolds-number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number, which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible, so they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.