Exact coherent structures (ECS) and transition to turbulence in a confined active nematic

Active matter describes a class of systems that are maintained far from equilibrium by driving forces acting on the constituent particles. This internal driving allows for rich flow behavior even in the absence of external boundary driving. Confined active matter in particular exhibits rich phenomenology. Upon increasing activity from zero, such systems pass from 1) quiescent states to 2) complex, but spatiotemporally ordered states, and finally to 3) spatiotemporal chaos, i.e., 'active/mesoscale turbulence'. There is immense potential, both fundamental and practical, in developing control capabilities for steering active systems towards or away from given flow states. Here, we address this challenge for the specific case of active nematic channel flow. We take a deterministic dynamical systems approach, beginning with the corresponding set of nematohydrodynamic PDEs. The infinite-dimensional phase space of all possible flow configurations is populated by Exact Coherent Structures (ECS), which are exact solutions of the physical dynamics with distinct and regular spatiotemporal structure; examples include unstable equilibria, periodic orbits, and traveling waves. The ECSs are connected by dynamical pathways called invariant manifolds. Our main hypothesis is that active/mesoscale turbulence corresponds to a trajectory meandering in this phase space, transitioning between neighborhoods of the ECSs by traveling on the invariant manifolds. Similar approaches have been successful in characterizing high Reynolds number turbulence of passive fluids. Here, we perform the first systematic study of active nematic ECS and their invariant manifolds, and discuss their role in characterizing the phenomenon of active turbulence.