Local Properties of Turbulent Flows

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This project concerns local properties of solutions of the Navier-Stokes system and other equations arising in fluid dynamics. It addresses determination of solutions of partial differential equations by observables, description and interplay of different length scales arising in turbulent flows, and existence and properties of invariant manifolds. Special emphasis is given to qualitative description of solutions, such as the study of spatial and temporal complexity of solutions, degree of vanishing, and properties of fluid vortices.Questions in fluid dynamics arise in many scientific fields, including atmospheric science, oceanography, and aerodynamics. The Navier-Stokes system, one of the most widely studied systems of partial differential equations, is one of the principal models of fluid motion. This project addresses qualitative properties of solutions of the Navier-Stokes system and related models. Potential applications include better understanding of fine structures of turbulent flows (vortices and oscillations), reconstruction of dynamics from measurements, and rigorous interpretation of numerical simulations of fluid motion.