Exact Coherent Structures and the Nature Shear Turbulence

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

Over the past 40 years, substantial experimental and computational efforts have revealed the existence and importance of complex coherent structures in shear turbulence. The nature and role of the coherent structures have remained subjects of debate at a qualitative level due to a lack of theoretical understanding and foundation for these structures. However, the gap between theory and experiments is closing thanks to recent discoveries of three-dimensional traveling wave solutions of the Navier-Stokes equations that are best described as exact coherent structures. This research will continue the study and characterization of these rich solutions in plane shear flows and seek to elucidate the connections between their instabilities and the disorder that is characteristic of turbulence. The approach is that of bifurcation and dynamical systems theory applied to the nonlinear partial differential equations of hydrodynamics. Extensions of these traveling wave solutions to pipe flow and mixing layers will be considered. Shear turbulence is an ubiquitous phenomenon that occurs in the flow of simple fluids, such as air and water, and the more complex fluids that arise in biological and industrial processes. Turbulence has an enormous impact on the properties of fluid flows, such as the transport of momentum and energy and the mixing of chemicals in combustion, manufacturing and the environment. However, the complexity of turbulent flows severely limits our ability to predict the properties of fluid flows. This research promises to provide a fundamental understanding of the nature of shear turbulence thanks in large part to high-performance scientific computing. A database of the exact coherent structures mentioned above will be developed and posted on the Internet.