Elastic range scaling in polymeric turbulence at high and low Reynolds number

Turbulent flows containing modest amounts of long-chained polymers have remained an intriguing area of research since the discovery of turbulent drag reduction. Here, we perform direct numerical simulations of statistically stationary, homogeneous, and isotropic turbulent flows of dilute solutions of polymers at both high and low Reynolds numbers. We show that the interplay of fluid inertia, viscous dissipation and polymer elasticity results in multi-scaling statistics. We explain the mechanism of the multi-scaling behavior by studying the contribution of the polymers to the flux of kinetic energy through scales, and further show how energy dissipation rate shows strong departures from a log-normal behavior. Finally, we extend the results to canonical shear flows.