Exact Coherent Structures in a Quasi-Two-Dimensional Kolmogorov-like Flow

Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this talk, we present a combined experimental and numerical study of a weakly turbulent quasi-two-dimensional flow in an electromagnetically driven shallow fluid layer.
Identifying instants when turbulent evolution slows down, we compute 31 dynamically relevant unstable equilibria of a realistic 2D model for the flow in experiment.
Using two illustrative examples, we quantitatively validate that turbulent trajectories departing from the neighborhoods of unstable equilibria shadow their unstable manifolds over large distances in state space. Lastly, exploring dynamics along trajectories that lie in the unstable manifold of an equilibrium, we identify heteroclinic connections that terminate at another equilibrium/limit-cycle far away.