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二维和三维空间涡旋片的奇点形成和卷曲的研究。对于二维情况，他将构建涡片卷起的模型，而对于三维情况，他将研究具有旋涡的轴对称涡片。这种流动现象出现在许多物理环境中，例如流动和绕翼型的流动的混合，它们的阐明是流体动力学家和工程师最关心的问题。下次你在大雾天气飞行时，看看飞机在起飞和降落时的翼尖。你应该能够看到圆锥形的空气漩涡和薄雾从机翼的尖端和挡板上脱落。这些漩涡被称为“漩涡”，它们出现在机翼上是飞机设计者最关心的问题，因为它们会影响飞机的阻力和升力特性。在这项提议中，首席研究员将在二维和三维空间中研究这种涡旋结构的形成、演化和衰变。

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.