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University of Michigan |
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Abstract: Vortex sheets are commonly used in fluid dynamics to represent thin shear layers in slightly viscous flow, a concept going back to Prandtl. The initial value problem for vortex sheet motion is ill-posed in the sense of Hadamard, due to Kelvin-Helmholtz instability, and Moore showed that a curvature singularity forms in the shape of an evolving vortex sheet. It is believed that the singularity causes the sheet to roll up into a spiral and that these spiral vortex sheets are related to the large-scale coherent vortices observed in real fluid flows. This talk will review the topic of vortex sheet motion, with emphasis on computational methods used to study the problem. In particular, we consider Rosenhead's point vortex approximation and Chorin's vortex blob method, as well as more recent developments concerning the onset of chaos in vortex sheet flow and treecode algorithms for vortex sheet motion in three space dimensions. |
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