Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.