Intermittency in the not-so-smooth elastic turbulence

TL;DR

This paper demonstrates that elastic turbulence, despite occurring at low Reynolds numbers, exhibits spectral and intermittency features similar to classical turbulence, revealing new insights into its underlying dynamics.

Contribution

The study provides the first detailed numerical analysis showing power-law spectra and multifractal intermittency in elastic turbulence, linking it more closely to classical turbulence.

Findings

Power-law spectra for kinetic and polymeric energy independent of Deborah number

Velocity field is smooth with non-trivial sub-leading contributions

Evidence of intermittency and multifractality in 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 ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic turbulence, though a low $\mbox{Re}$ phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy $E(k) \sim k^{-4}$ and polymeric energy $E_{\rm p}(k) \sim k^{-3/2}$, independent of the Deborah ($\mbox{De}$) 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 $r$, $\delta u \sim r$ but, crucially, with a non-trivial sub-leading contribution $r^{3/2}$ 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 $r$, $\varepsilon_{r}$, from which we compute the multifractal spectrum.