Polymer additives in fluid turbulence and distributed chaos

TL;DR

This paper investigates how polymer additives alter fluid turbulence by breaking relabeling symmetry, leading to distributed chaos characterized by stretched exponential spectra, with effects confirmed through simulations and experiments.

Contribution

It reveals the spontaneous breaking of relabeling symmetry due to polymers and its impact on turbulence spectra, extending understanding of turbulence modification by additives.

Findings

Distributed chaos exhibits stretched exponential spectra with β=2/5.

Polymer additives suppress small-scale turbulence and enhance large-scale mixing.

Results are validated by DNS and experimental data across different turbulent flows.

Abstract

The fluids and polymers have different fundamental symmetries. Namely, the Lagrangian relabeling symmetry of fluids is absent for polymers (while the translational and rotational symmetries are still present). This fact results in spontaneous breaking of the relabeling symmetry in fluid turbulence even at a tiny polymer addition. Since helicity conservation in inviscid fluid motions is a consequence of the relabeling symmetry (due to the Noether's theorem) violation of this conservation by the polymer additives results in the strong effects in the distributed chaos. The distributed chaos in turbulence with the spontaneously broken relabeling symmetry is characterized by stretched exponential spectra $\propto \exp(-k/k_{\beta})^{\beta}$ with $\beta =2/5$. The spectral range of this distributed chaos is extended in direction of the small wavenumbers and $k_{\beta}$ becomes much larger in comparison with the pure fluid (Newtonian) case. This results in substantial suppression of small-scale turbulence and large-scale mixing enhancement. Good agreement with results of direct numerical simulations (DNS) and experimental data has been established for a channel flow (DNS), for Rayleigh-Taylor turbulent convection (DNS) and for Rayleigh-Benard turbulent convection (experiment).