The invariant rate of energy extraction by polymers in turbulence

Abstract

Polymeric turbulence, flows of fluids with dilute polymer additives at high Reynolds numbers, exhibits striking deviations from the Kolmogorovean behaviour of Newtonian turbulence. Recent experiments as well as simulations have uncovered a robust self-similar energy spectrum scaling as $k^{-2.3}$, in sharp contrast to the $k^{-5/3}$ scaling of Newtonian flows. The origin of this novel scaling, however, has remained unresolved. In this work, we uncover the underlying physical mechanism responsible for this emergent behaviour. Using fundamental governing equations aided by scaling arguments, we show that the fluid energy cascade is depleted by the polymers at a constant rate across a wide range of scales. This constant depletion rate acts as a second invariant, alongside the total energy flux, thereby setting the scaling properties of the spectrum. Our results reveal that polymeric turbulence is governed by two simultaneous invariants, unlike the single-invariant structure of Newtonian turbulence, and suggest new strategies for turbulence control through suitably engineered and targeted polymer design.