Nonlinear Dynamical Systems Methods for Turbulence

Brown University, Providence RI

Investigators

Abstract

NSF Award Abstract - DMS-0102940 Mathematical Sciences: Nonlinear Dynamical Systems Methods for Turbulence Abstract DMS-0102940 Haller The mathematics of turbulence, the "last unsolved problem of classical physics," has traditionally been statistical in nature. This approach leads to long-term predictions of the bulk properties of generic fluid flows. In contrast, many technological and geophysical mixing problems, such as mixing of fuel and air in a combustor, or the spread of an oil spill in the Gulf of Mexico, call for detailed finite-time predictions on turbulent mixing. This project is concerned with further development and novel applications of the recent theory of finite-time mixing. This new nonlinear theory enables one to analyze concrete numerical or experimental velocity fields and isolate global structures in the flow that is responsible for mixing or lack thereof. The project will involve applications of these new techniques and their extensions to global circulation models, vortex breakdown and merger, ocean drifter data analysis, mixing enhancement in combustors, and continuous steel casting.