Irreversiblity in Bacterial Turbulence: Insights from the Mean-Bacterial-Velocity Model

TL;DR

This study uses the mean-bacterial-velocity model to explore irreversibility in 2D bacterial turbulence, revealing that particles can gain energy faster than they lose it, contrasting with fluid turbulence.

Contribution

It provides the first detailed comparison of irreversibility between bacterial and fluid turbulence using direct numerical simulations.

Findings

Irreversibility manifests as positive skewness in energy increment distributions.

Particles in bacterial turbulence can gain energy faster than they lose it.

The skewness depends on the friction and activity parameters.

Abstract

We use the mean-bacterial-velocity model to investigate the \textit{irreversibility} of two-dimensional (2D) \textit{bacterial turbulence} and to compare it with its 2D fluid-turbulence counterpart. We carry out extensive direct numerical simulations of Lagrangian tracer particles that are advected by the velocity field in this model. Our work uncovers an important, qualitative way in which irreversibility in bacterial turbulence is different from its fluid-turbulence counterpart: For large positive (or large but negative) values of the \textit{friction} (or \textit{activity}) parameter, the probability distribution functions of energy increments, along tracer trajectories, or the power are \textit{positively} skewed; so irreversibility in bacterial turbulence can lead, on average, to \textit{particles gaining energy faster than they lose it}, which is the exact opposite of what is observed for tracers in 2D fluid turbulence.