Instabilities and turbulence in extensile swimmer suspensions

TL;DR

This paper investigates the mechanisms behind turbulence in suspensions of extensile, self-propelled swimmers at low Reynolds number, revealing how instabilities lead to various turbulent states through theoretical and numerical analysis.

Contribution

It introduces a minimal 1D model for splay instability transition and uses 2D simulations to explore turbulence regimes in extensile swimmer suspensions.

Findings

Suspension is always unstable to bend perturbations.

Splay instability transition occurs via a supercritical Hopf bifurcation.

Turbulence varies from defect turbulence to concentration-wave turbulence depending on a key parameter.

Abstract

We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend perturbations. Using a minimal 1D model, we show that the splay-stable to splay-unstable transition occurs via a supercritical Hopf bifurcation. We perform high-resolution numerical simulations in 2D to study the varieties of turbulence present in this system transitioning from defect turbulence to concentration-wave turbulence depending on a single non-dimensional number, denoting the ratio of the splay-concentration wavespeed to the swimmer motility.