Turbulence tracks recurrent solutions.

Abstract

Despite a long and rich history of scientific investigation, fluid turbulence remains one of the most challenging problems in science and engineering. One of the key outstanding questions concerns the role of coherent structures that describe frequently observed patterns embedded in turbulence. It has been suggested, but not proved, that coherent structures correspond to unstable, recurrent solutions of the governing equation of fluid dynamics. Here, we present experimental and numerical evidence that three-dimensional turbulent flow tracks, episodically but repeatedly, the spatial and temporal structure of multiple such solutions. Our results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.