Meso-scale turbulence in living fluids

TL;DR

This study investigates meso-scale turbulence in living bacterial suspensions, combining experiments, simulations, and theory to understand universal features and develop a minimal continuum model for active fluids.

Contribution

It provides the first comprehensive analysis of bacterial turbulence across dimensions and introduces a minimal continuum model that captures key experimental observations.

Findings

Energy spectra and structure functions match predictions from a minimal model.

Bacterial collective motion is dominated by short-range interactions at high concentrations.

The continuum model reproduces many features of active turbulence observed experimentally.

Abstract

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest forms of life, and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which generalizations of the Navier-Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.