Exploring regular, exotic and turbulent flow states in active fluids via the framework of Exact Coherent Structures

Active fluids in biological and artificial systems are governed by fully nonequilibrium dynamics, and their emergent spatiotemporal structures span multiple scales. The dominant flow patterns of such systems can be understood in a systematic manner in terms of Exact Coherent Structures (ECS) and the dynamical pathways connecting them. An ECS is a (stable or unstable) equilibrium, time-periodic, relative time-periodic, quasi-periodic or traveling wave solution of the governing equations, while their invariant manifolds form the connecting pathways between different ECS. The ECS framework enables a fully nonlinear but highly reduced-order description in terms of a directed graph. We provide a unified study of stable and unstable coherent states of 2D active nematic channel flow using the framework of ECS. We compute more than 150 unstable ECS that co-exist at a single set of parameters in the weakly `active turbulent' regime. Using the reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. By comparing with simulations in the active turbulence regime, we also provide numerical evidence of a chaotic trajectory shadowing various ECSs.