Symmetry, Invariant Manifolds and Flow Reversals in Active Nematic Channel Flow

Exact coherent structures (ECSs) offer a powerful framework for understanding the rich spatiotemporal dynamics of active fluids. We perform equivariant bifurcation analyses in a minimal flow unit (MFU) of 2D active nematic periodic channel flow to uncover the origin of key ECSs and establish a symmetry-based classification scheme. Building on this foundation, we focus on a significant dynamical phenomenon that has been reported in experiments: spontaneous reversals between the left and right flowing nearly uniaxial states. We identify the primary mechanisms driving this process as heteroclinic connections between certain ECSs, forming structured pathways in the preturbulent regime. Furthermore, we demonstrate that similar connections persist into the turbulent regime, where typical trajectories shadow ECSs and their invariant manifolds. In doing so, we provide numerical evidence of ECS shadowing in active turbulence.