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

Abstract

We present a controlled route to active turbulence in an active paranematic fluid, <i>i.e.</i>, a suspension of rods that exhibit nematic order only under extensile activity. To this end, we introduce a spot of radius <i>r</i> with non-zero activity, embedded in an otherwise passive fluid. Due to the open boundary, defects can enter and leave the spot. As <i>r</i> 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 <i>r</i>, the total charge only increases linearly in <i>r</i>. 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.