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We use direct numerical simulations to study homogeneous, and isotropicturbulent flows of dilute polymer solutions at high Reynolds and Deborahnumbers. We find that for small wavenumbers $k$, the kinetic energy spectrumshows 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 studythe 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 effectiveviscous dissipation, and a purely elastic contribution that dominates over thenonlinear flux in the range of $k$ over which the elastic scaling is observed.The multiscale balance between the two fluxes determines the crossoverwavenumber which depends non-monotically on the Deborah number. Consistently,structure functions also show two scaling ranges, with intermittency present inboth of them in equal measure.

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