Forecasting Turbulence Using Special Solutions of the Navier-Stokes Equations

Jeffrey Tithof

Hopeman 224

Fluid turbulence is a ubiquitous phenomenon present over a vast range of scales, but is notoriously difficult to forecast. Recently, increases in computational power and advancements in dynamical systems theory have suggested that many important aspects of turbulent dynamics can be understood using special unstable solutions of the Navier-Stokes equations, often called "exact coherent structures" (ECS). We study weak turbulence generated in a quasi-two-dimensional flow driven by electromagnetic forces and provide evidence for the existence and dynamical relevance of ECS.  We then provide the first experimental demonstration of how ECS can be used to forecast turbulence. We emphasize that this methodology is quite general and can be applied to gain new insights into a variety of systems which exhibit spatiotemporally complex dynamics.