The interplay of inertia and elasticity in polymeric flows

Addition of polymers modifies a turbulent flow in a manner that depends non-trivially on the interplay of fluid inertia, quantified by the Reynolds number $\textit{Re}$ , and the elasticity of the dissolved polymers, given by the Deborah number $\textit{De}$ . We use direct numerical simulations to study polymeric flows at different $\textit{Re}$ and $\textit{De}$ numbers, and uncover various features of their dynamics. Polymeric flows exhibit a non-unique scaling of the energy spectrum that is a function of $\textit{Re}$ and $\textit{De}$ , owing to different dominant contributions to the total energy flux across scales, with the weakening of fluid nonlinearity with decreasing $\textit{Re}$ also leading to the reduction of the polymeric scaling range. This behaviour is also manifested in the real space scaling of structure functions. We also shed light on how the addition of polymers results in slowing down the fluid nonlinear cascade resulting in a depleted flux, as velocity fluctuations with less energy persist for longer times in polymeric flows, especially at intermediate $\textit{Re}$ numbers. These velocity fluctuations exhibit intermittent, large deviations similar to that in a Newtonian flow at large $\textit{Re}$ , but differ more and more as $\textit{Re}$ becomes smaller. This observation is further supported by the statistics of fluid energy dissipation in polymeric flows, whose distributions collapse on to the Newtonian at large $\textit{Re}$ , but increasingly differ from it as $\textit{Re}$ decreases. We also show that polymer dissipation is significantly less intermittent compared with fluid dissipation, and even less so when elasticity becomes large. Polymers, on an average, dissipate more energy when they are stretched more, which happens in extensional regions of the flow. However, owing to vortex stretching, regions with large rotation rates also correlate with large polymer extensions, albeit to a relatively less degree than extensional regions.