Coarsening in the 2D Incompressible Toner-Tu Equation: Signatures of Turbulence

We investigate coarsening dynamics in the two-dimensional (2D), incompressible Toner-Tu equation. We show that coarsening proceeds via vortex merger events, and the dynamics crucially depend on the Reynolds number ($\mathrm{Re}$). For low $\mathrm{Re}$, the coarsening process has similarities with Ginzburg-Landau dynamics. On the other hand, for high $\mathrm{Re}$, coarsening shows signatures of turbulence. In particular, we show the presence of an enstrophy cascade from the inter-vortex separation scale to the dissipation scale.