Reduced Dimension Models for Hydrodynamical Systems: Experiment, Computation and Theory

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This project is designed to develop reduced dimension models for hydrodynamical systems and to foster undergraduate participation in mathematical research. While the fundamental equations describing fluid motion, the Navier-Stokes equations, are well-known, it is generally computationally expensive and analytically infeasible to solve the full equations exactly. To better understand these systems, it is necessary to turn to simplified or reduced models resulting from systematic approximations of the full equations. The semi-discrete approximation techniques which are utilized in this project focus primarily on reducing the dimension of the full fluid equations by exploiting symmetries or widely disparate lengthscales in specific systems. The resulting predictions from the reduced models will be compared qualitatively and quantitatively with experimental data.Fluid dynamics arises in a multitude of biological, environmental and industrial applications. This project is designed to develop models that describe basic hydrodynamical phenomena such as hydraulic jumps that can arise in jet impingement cooling systems and hydrodynamical systems with flexible boundaries. The latter include spinning magnetic media such as disk drives, and biological problems such as insect flight, blood flow in arteries and dynamics of the syrinx in song birds. Undergraduate participation is an integral part of both the experimental and mathematical aspects of the program. Mathematical models will be tested in the new Fluid Dynamics Laboratory which will provide a hands-on environment in which students learn to integrate mathematics with physical phenomena. This unique approach encourages students to apply their mathematical skills in consort with their physical intuition within the framework of contemporary research.