The objective of this research program is to develop and to test experimentally a revolutionary new approach to modeling and predicting two-dimensional turbulent flows. A set of weakly unstable invariant Navier-Stokes solutions will be identified and transitions between invariant solutions will be characterized to provide a coarse global description of the nonlinear dynamics of turbulent flow. Quasi-2D flow in a shallow electrolyte layer continually driven by Lorentz forces provides the setting for theoretical, analytic and experimental development of this approach. Novel and proven techniques, such as periodic orbit theory, group representation theory, Krylov-subspace numerical methods, Newton and variational solvers will be used to develop this viewpoint, which will be tested in experiments where the flow can be measured with full spatial and temporal resolution throughout the entire flow domain.
If successful, the results of this research will impact several areas of science, engineering, and medicine. Although the focus of this investigation is on fluid turbulence in two dimensions, the proposed approach has the potential to provide new ways to model, and ultimately control, a wide range of spatiotemporally chaotic systems, such as magnetic confinement fusion reactors and abnormal cardiac dynamics (from mild arrhythmias to potentially lethal fibrillation). The most immediate practical application, however, is the reduction of turbulent drag responsible for a significant part of the fuel consumed in the automotive, aviation, and shipping industries. Even an incremental reduction of drag by the proposed flow control methodology would have a tremendous economic impact. All software and data produced by the research program will be made publicly available with a central aim of lowering the barrier of entry to dynamical systems research by providing well-documented, easy-to-use interfaces to state-of-the-art numerical algorithms.
