Exploring regular and turbulent flow states in active nematic channel flow via Exact Coherent Structures and their invariant manifolds

This work is a unified study of stable and unstable steady states of 2D active nematic channel flow using the framework of Exact Coherent Structures (ECSs). ECSs are station-ary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, organize the dynamics of nonlinear continuum systems. We extend our earlier work on ECSs in the preturbulent regime by performing a comprehensive study of stable and unstable ECSs for a wide range of activity values spanning the preturbulent and turbulent regimes. In the weakly turbulent regime, we com-pute more than 200 unstable ECSs that coexist at a single set of parameters, and uncover the role of symmetries in organizing the phase space geometry. We provide conclusive numerical evidence that in the preturbulent regime, generic trajectories shadow a series of unstable ECSs before settling onto an attractor. Finally, our studies hint at shadowing of quasiperiodic-type ECSs in the turbulent regime.