Stable and unstable flow regimes for active fluids in the periodic setting

TL;DR

This paper provides a rigorous analytical framework for understanding stability and instability in active fluids within periodic environments, highlighting the onset of turbulence due to self-propulsion effects.

Contribution

It offers a novel mathematical justification for the stability and instability regimes in active fluids, especially the instability of ordered polar states caused by self-propulsion.

Findings

Proof of instability for ordered polar states due to self-propulsion

Analytical criteria for stability and instability in active fluids

Connection to active turbulence phenomena

Abstract

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular, occuring instability for the manifold of ordered polar states caused by self-propulsion is proved. This represents the prerequisite for active turbulence patterns as observed in a number of applications. The approach is carried out in the periodic setting and is based on the generalized principle of linearized (in)-stability related to normally stable and normally hyperbolic equilibria.