Wavenumber

Physics

K-epsilon turbulence model

Turbulence kinetic energy

Reynolds number

Universality (dynamical systems)

K-omega turbulence model

Mathematics

Mechanics

Statistical physics

Length scale

Liquid crystal

Kinetic energy

Turbulence

Geometry

Condensed matter physics

Quantum mechanics

Reynolds decomposition

Classical mechanics

Scaling

Nature Physics

A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov’s E(q) ~ q−5∕3 scaling of the kinetic energy spectrum of inertial turbulence with the wavevector 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) ~ 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-range velocity correlations, which lead to the scaling behaviour. We conclude that active nematic fluids define a distinct universality class of turbulence at low Reynolds number. Determining the properties that emerge from the equations that govern turbulent flow is a fundamental challenge in non-equilibrium physics. A hydrodynamic theory for two-dimensional active nematic fluids at vanishing Reynolds number is now put forward, revealing a universal scaling behaviour for this class of systems.

Universal scaling of active nematic turbulence