Polymer additives in fluid turbulence and distributed chaos

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).