# Universal scaling of active nematic turbulence

## TL;DR

This paper demonstrates that active nematic turbulence exhibits a universal kinetic energy spectrum scaling of q^{-1} at long wavelengths, revealing a distinct universality class at low Reynolds number.

## Contribution

The study introduces a minimal defect-free hydrodynamic model and shows universal scaling laws in active nematic turbulence through simulations and analytical insights.

## Key findings

- Kinetic energy spectrum scales as q^{-1} at long wavelengths.
- Energy injection peaks at a characteristic length scale.
- No energy cascade occurs, with energy dissipated at injection scale.

## Abstract

A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov's $E(q)\sim q^{-5/3}$ scaling of the kinetic energy spectrum of inertial turbulence with the wave vector $q$. In recent years, active fluids have been shown to exhibit turbulent-like flows at low Reynolds number. However, the existence of universal scaling properties in these flows has remained unclear. To address this issue, here we propose a minimal defect-free hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number. By means of large-scale simulations and analytical arguments, we show that the kinetic energy spectrum exhibits a universal scaling $E(q)\sim q^{-1}$ at long wavelengths. We find that the energy injection due to activity has a peak at a characteristic length scale, which is selected by a nonlinear mechanism. In contrast to inertial turbulence, energy is entirely dissipated at the scale where it is injected, thus precluding energy cascades. Nevertheless, the non-local character of the Stokes flow establishes long-ranged velocity correlations, which lead to the scaling behavior. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number.