Turbulence and turbulent pattern formation in a minimal model for active fluids

TL;DR

This paper develops a quantitative statistical framework for active turbulence in a minimal model, revealing turbulence-driven pattern formation including a dynamic vortex lattice state.

Contribution

It introduces a turbulence-based statistical approach to active matter and uncovers novel pattern formation phenomena beyond linear instability.

Findings

Quantitative correlation functions and spectra for active turbulence.

Identification of a turbulence-driven dynamic vortex lattice.

Discovery of pattern formation emerging from turbulent transients.

Abstract

Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the active turbulence phase calls for a statistical description. Borrowing techniques from turbulence theory, we here establish a quantitative description of correlation functions and spectra of a minimal continuum model for active turbulence. Further exploring the parameter space, we also report on a surprising type of turbulence-driven pattern formation far beyond linear onset: the emergence of a dynamic hexagonal vortex lattice state after an extended turbulent transient, which can only be explained taking into account turbulent energy transfer across scales.