A minute amount of long-chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and, in turn, alter the turbulence energy transfer. Here, we show how turbulent kinetic energy is transferred through different scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a previously unidentified scaling range, referred to as the elastic range, where increasing amount of energy is transferred by the elasticity of the polymers. In addition, the existence of the elastic range prescribes the scaling of high-order velocity statistics. Our findings have important implications to many turbulence systems, such as turbulence in plasmas or superfluids where interaction between turbulent eddies and other nonlinear physical mechanisms are often involved.

We present an experimental study on the effects of polymer additives on the entrainment of a circular water jet and their dependence on the polymer concentration $\phi$ (in the range of $0 - 40$ ppm) and Weissenberg number $Wi$ (in the range of 2.0-85.6), at the Reynolds number $Re = 7075$. Extensive particle image velocimetry (PIV) measurements were performed between 0 and 74$D$ ($D$ is the inner diameter of the pipe) downstream of the nozzle. Our results clearly show that the polymer-laden jet exhibits two regimes along the flow direction compared to the pure water case. In the first regime, close to the jet exit, the jet spreading rate is smaller (entrainment is suppressed) and the centerline mean velocity decays more slowly. However, as the polymer-laden jet evolves further downstream, the entrainment rate is enhanced by up to $33\%$ compared to that of the water jet. In this entrainment enhancement regime, the polymer-laden jet evolves into a new self-similar state. The turbulent intensities and Reynolds shear stress of different $\phi$ and $Wi$ collapse onto each other, and they are also much stronger compared to that of the water jet. We have also extended the integral entrainment analysis to the polymer-laden jet by adding a polymer stress term to the momentum equation. Our results show that the enhancement of the entrainment is originated from the stronger production of the Reynolds shear stress in the polymer-laden jets, implying that the entrainment rate is intimately related to the energy-containing vortices in the polymer-laden jets.

We present an experimental study of the effects of polymer additives on energy cascade in the bulk of turbulent von Karman swirling flow and its dependences on polymer concentration (Phi) and Weissenberg number (Wi). The turbulent flow is viscous driven by the rotation of a pair of smooth disks. The velocity measurements show that the flow is more coherent in the presence of the polymers. It is found that there is a critical concentration, below which the energy injection, transfer, and dissipation rates are rapidly suppressed to about 20% of the Newtonian case (referred to as rapid suppression regime), and above which the suppression is saturated at that level (referred to as saturated suppression regime). We found that the Wi dependence of the energy cascade resembles that of concentration dependence with one additional regime referred to as no suppression regime when Wi is very small. The sharp transition from the no suppression regime to the rapid suppression regime implies the occurrence of the coil-stretch transition of the polymers. Although the energy dissipation rate is greatly suppressed in the presence of polymers, the functional form of its probability density function is the same as that of the Newtonian case, suggesting that the mechanism governing the energy dissipation is universal for both the Newtonian and dilute polymeric turbulence. Our experiments show for the first time the similarity between the effects of Wi and Phi in dilute polymeric turbulence.