Evidence for the dynamical relevance of relative periodic orbits in turbulence

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 proven, that coherent structures correspond to unstable, recurrent solutions of the governing equations of fluid dynamics. In this thesis, I present the first experimental evidence that three-dimensional turbulent flow mimics the spatial and temporal structure of multiple such solutions episodically but repeatedly. These results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.