Large is different: non-monotonic behaviour of elastic range scaling in polymeric turbulence at large Reynolds and Deborah numbers

We use direct numerical simulations to study homogeneous, and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wavenumbers $k$, the kinetic energy spectrum shows Kolmogorov--like behavior which crosses over at a larger $k$ to a novel, elastic scaling regime, $E(k) \sim k^{-\xi}$, with $\xi \approx 2.3$. We study the contribution of the polymers to the flux of kinetic energy through scales, and find that it can be decomposed into two parts: one increase in effective viscous dissipation, and a purely elastic contribution that dominates over the nonlinear flux in the range of $k$ over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wavenumber which depends non-monotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.