Mathematical Sciences: Dynamics of Vortex Sheets in Two and Three Dimensions

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In this project the principal investigator will continue his studies of singularity formation and roll-up for vortex sheets in two and three space dimensions. For the two- dimensional case he will construct models of vortex-sheet roll- up, while for the three-dimensional case he will investigate axi- symmetric vortex sheets with swirl. Such flow phenomena arise in a number of physical contexts such as the mixing of flows and flows around airfoils, and their elucidation is of prime concern to fluid dynamicists and engineers. The next time you fly on a foggy day look at the wingtips of the plane during take-offs and landings. You should be able to see conical swirls of air and mist shedding from the wing-tips and baffles on the wing. These swirls are called "vortices" and their presence on the wings is of prime concern to aircraft designers since they affect the drag and lift characteristics of the airplane. In this proposal the principal investigator will study the formation, evolution and decay of such vortical structures in two and three space dimensions.