Taylor dispersion in two-dimensional bacterial turbulence

TL;DR

This study investigates bacterial turbulence by analyzing particle dispersion, revealing super-diffusive behavior with two distinct regimes and weak intermittency, which enhances bacteria's food acquisition efficiency.

Contribution

It provides the first detailed analysis of Lagrangian particle dispersion and super-diffusion behavior in bacterial turbulence, including high-order displacement functions and Hurst number measurements.

Findings

Identified two-regime power-law behavior in particle dispersion.

Measured high Hurst numbers indicating super-diffusion.

Detected very weak intermittency correction.

Abstract

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. Two-regime power-law behavior for short and long time evolutions were identified experimentally, which were separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be $0.94$ and $0.97$ for short and long times evolutions, respectively. For the case without the mean velocity effect, the values were $0.88$ and $0.58$. Moreover, very weak intermittency correction was detected. All measured Hurst number were above $1/2$, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food.