Route to turbulence via oscillatory states in polar active fluid under confinement

We report a novel route to active turbulence, observed in numerical simulations of a polar active fluid model under confinement. To deal with large-scale computations with arbitrary geometries, we developed a GPU-based scheme that can be used for any boundary shape in a unified manner. For the circular confinement, as the radius was increased, we found a series of transitions first from a single stationary vortex to an oscillating pair of vortices, then through reentrant transitions between oscillatory and chaotic dynamics before finally reaching the active turbulence. The first transition turned out to be hysteretic, with the emergence of the oscillatory state consistent with the subcritical Hopf bifurcation. In dumbbell-shaped boundaries composed of two overlapping circles, we observed a transition comparable to the ferromagnetic-antiferromagnetic vortex-order transition reported in previous experiments, but the transition point turned out to show a qualitatively different geometry dependence.