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

在这个项目中，首席研究员将继续 他对涡的奇点形成和卷起的研究 二维和三维空间中的表。 对于两个- 三维情况下，他将建立模型的涡片卷， 对于三维的情况，他将研究轴， 有旋涡的对称涡面。 这种流动现象出现在 许多物理环境，如混合流， 绕翼型的流动，它们的说明是主要关心的问题 流体动力学家和工程师。 下一次你在雾天飞行的时候， 飞机在起飞和降落时。 你应该能够 看到空气和薄雾从翼尖流出的锥形漩涡 机翼上有挡板 这些漩涡被称为“漩涡”， 它们在机翼上的存在是飞机最关心的问题 设计师，因为他们影响阻力和升力特性的 飞机。 在本提案中，主要研究者将 研究这种涡旋的形成、演化和衰减， 二维和三维空间结构。

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.