Scaling regimes of active turbulence with external dissipation

TL;DR

This study investigates the energy spectrum of active nematic turbulence in contact with a passive oil layer, revealing universal scaling laws and the influence of external dissipation on turbulence behavior.

Contribution

It provides the first experimental measurement of the energy spectrum in active nematics with external dissipation and derives a comprehensive model connecting different scaling regimes.

Findings

Confirmed theoretical scaling laws at small and intermediate scales.

Discovered a new large-scale scaling regime due to 3d dissipation.

Controlled the crossover scale by tuning oil viscosity.

Abstract

Active fluids exhibit complex turbulent-like flows at low Reynolds number. Recent work predicted that 2d active nematic turbulence follows universal scaling laws. However, experimentally testing these predictions is conditioned by the coupling to the 3d environment. Here, we measure the spectrum of the kinetic energy, $E(q)$, in an active nematic film in contact with a passive oil layer. At small and intermediate scales, we find the scaling regimes $E(q)\sim q^{-4}$ and $E(q)\sim q^{-1}$, respectively, in agreement with the theoretical prediction for 2d active nematics. At large scales, however, we find a new scaling $E(q)\sim q$, which emerges when the dissipation is dominated by the 3d oil layer. In addition, we derive an explicit expression for the spectrum that spans all length scales, thus explaining and connecting the different scaling regimes. This allows us to fit the data and extract the length scale that controls the crossover to the new large-scale regime, which we tune by varying the oil viscosity. Overall, our work experimentally demonstrates the emergence of universal scaling laws in active turbulence, and it establishes how the spectrum is affected by external dissipation.