Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation

TL;DR

This paper studies the phase ordering process in the 3D incompressible Toner-Tu equation, revealing how defect dynamics and turbulence influence the evolution at different Reynolds numbers, with turbulence dominating at high Re.

Contribution

It provides the first detailed analysis of phase ordering and defect dynamics in the 3D incompressible Toner-Tu equation, highlighting the role of turbulence at high Reynolds numbers.

Findings

Phase ordering occurs via defect merger events.

Low Re dynamics resemble Ginzburg-Landau behavior.

High Re dynamics are dominated by turbulence with energy cascade.

Abstract

We investigate phase ordering dynamics of the incompressible Toner-Tu equation in three dimensions. We show that the phase ordering proceeds via defect merger events and the dynamics is controlled by the Reynolds number Re. At low Re, the dynamics is similar to that of the Ginzburg-Landau equation. At high Re, turbulence controls phase ordering. In particular, we observe a forward energy cascade from the coarsening length scale to the dissipation scale.