Correlation lengths in hydrodynamic models of active nematics

TL;DR

This study investigates how active nematic liquid crystals exhibit a single dominant length scale in their chaotic turbulence, regardless of the specific hydrodynamic model or active stress type, unifying previous findings.

Contribution

It demonstrates that a single active length scale governs the turbulence in active nematics across different models and stress types, clarifying prior discrepancies.

Findings

Chaotic dynamics are controlled by a single active scale.

Scaling of kinetic energy and enstrophy aligns with dimensional analysis.

Results are consistent across models and stress types.

Abstract

We examine the scaling with activity of the emergent length scales that control the nonequilibrium dynamics of an active nematic liquid crystal, using two popular hydrodynamic models that have been employed in previous studies. In both models we find that the chaotic spatio-temporal dynamics in the regime of fully developed active turbulence is controlled by a single active scale determined by the balance of active and elastic stresses, regardless of whether the active stress is extensile or contractile in nature. The observed scaling of the kinetic energy and enstropy with activity is consistent with our single-length scale argument and simple dimensional analysis. Our results provide a unified understanding of apparent discrepancies in the previous literature and demonstrate that the essential physics is robust to the choice of model.