Scalar fluctuations in polymeric turbulence

Abstract

Turbulent polymeric flows show strong deviations from Kolomogorov-like behaviour resulting from more complex dynamics compared to Newtonian turbulence. We now study the nature of mixing in polymeric turbulence via Eulerian passive scalar fields of varying molecular diffusivities, given by the Schmidt number Sc. We show that polymeric turbulence is a less efficient mixer than the Newtonian one at small to moderate Sc numbers. Newtonian scalar turbulence (NST) forms large islands of fluctuations with extended, contiguous fronts. In contrast, polymeric scalar turbulence (PST) is marked by small, interspersed patches of strong but less intermittent fluctuations. These patches collectively comprise a larger volume fraction of strong fluctuations, indicating a less efficient mixing, alongwith smaller gradients and therefore smaller scalar flux across their boundaries. We also show that PST shows a novel, distinct self-similarity with the scalar fluctuation spectrum scaling as $k^{-4/3}$ as opposed to $k^{-5/3}$ in NST. Real space statistics also reveal that, while fluctuations are stronger in PST, they remain less intermittent.