Controlled route to active turbulence: filling an activity spot with topological defects

We present a controlled route to active turbulence in an active paranematic fluid, i.e., a suspension of rods that exhibit nematic order only under extensile activity. To this end, we introduce a spot of radius r with non-zero activity, embedded in an otherwise passive fluid. Due to the open boundary, defects can enter and leave the spot. As r increases starting from the nematic coherence length, we first observe paranematic order with a uniform director field, then transient +½ topological defects, followed by spiral or swirling pairs of +½ defects. Additional defects progressively enter until bulk active turbulence occurs. While positive and negative defect charges grow with the square of the spot radius r, the total charge only increases linearly in r. This hints to a length along the rim of the spot, comparable to the active length, so that activity can induce the director distortions needed for a defect to enter. In addition, the extensional active flow realizes active anchoring at the rim, which establishes a baseline charge of +1. Two dynamic regimes mark the progression toward bulk turbulence. The enstrophy rises sharply when the spot allows the stable circling motion of the two +½ defects, and the finite-time Lyapunov exponent, characterizing the chaotic flow pattern, jumps to a non-zero value, when a third +½ defect enters the spot noticeably. For large radii, both measures approach their bulk-turbulence values.