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

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.

5 pages, 6 figures

References in corpus (5)

• Meso-scale turbulence in living fluids
• The Role of Projection in the Control of Bird Flocks
• A trilinear method for finding null points in a 3D vector space
• Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
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Cited by in corpus (5)

• Metastability of Constant-Density Flocks
• Flocking turbulence of microswimmers in confined domains
• An analytical and computational study of the incompressible Toner-Tu Equations
• Incompressible polar active fluids with quenched disorder in dimensions $d>2$
• Coarsening of topological defects in 2D polar active matter