Intermittency in the not-so-smooth elastic turbulence

Abstract

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($${{{{{{{\rm{Re}}}}}}}}$$ Re ) numbers. Our direct numerical simulations show that elastic turbulence, though a low $${{{{{{{\rm{Re}}}}}}}}$$ Re phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy E(k) ~ k−4 and polymeric energy Ep(k) ~ k−3/2, independent of the Deborah (De) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale r, δu ~ r but, crucially, with a non-trivial sub-leading contribution r3/2 which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order 6 show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius r, εr, from which we compute the multifractal spectrum.