Dynamical connections between Exact Coherent Structures in Kolmogorov flow

The geometry of state space for a turbulent flow can be shaped by non-chaotic Navier-Stokes solutions known as Exact Coherent Structures (ECS), which influence the evolution of flows in their neighborhood. We report on experimental and numerical work to identify and characterize heteroclinic connections between ECS that may serve to guide turbulent flows from the neighborhood of one ECS to that of another. Using symmetry considerations, we have discovered two such connections, calculated in a numerical model of a Kolmogorov flow. We describe efforts to test the dynamical relevance of these heteroclinic orbits in experiments on weakly turbulent quasi-two-dimensional Kolmogorov flows.