Mathematical Sciences: Singularities in Vortical Flows and Dispersive Systems

数学科学：涡流和色散系统中的奇点

• 批准号: 9623087
• 负责人: Russel Caflisch
• 金额: $ 13.8万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623087&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singularities; Vortical; Flows

9623087 Caflisch This proposal is for development of analytical and computational methods for describing singularities in the solutions of partial differential equations (PDEs), and for application of those methods to problems of fluid mechanics and other physical systems. The key step in the analysis is transformation of the variables of the PDE to obtain an "unfolded" system, the solutions of which are non-singular. This will be used for vortex sheets, swirling flow, magnetohydrodynamics and crystal patterns. For these problems we will attempt to find singular solutions and to classify their generic type. This proposal is for research on "singularities" in physics and engineering problems. Singularities are points at which the measurable quantities in the system change abruptly or become very large. An important example, which is a main focus of this project is the development of very large rotational velocity in a fluid such as air or liquid. These singularities are believed to be a primary cause of turbulence, an important but poorly understood phenomena in many applications. The goals of this research project are to find these singularities, classify their possible behavior and use them to gain understanding of turbulence and other problems.

9623087本建议是为了发展描述偏微分方程组(PDE)解的奇异性的分析和计算方法，并将这些方法应用于流体力学和其他物理系统的问题。分析的关键步骤是对偏微分方程组的变量进行变换，得到一个解为非奇异的“展开”系统。这将被用于涡旋片、旋流、磁流体动力学和晶体图案。对于这些问题，我们将尝试寻找奇异解，并对其泛型进行分类。这项建议是为了研究物理和工程问题中的“奇点”。奇点是系统中可测量的量突然变化或变得非常大的点。一个重要的例子，也是这个项目的主要焦点，是在空气或液体等液体中开发非常大的旋转速度。这些奇点被认为是湍流的主要原因，在许多应用中，湍流是一种重要但鲜为人知的现象。这个研究项目的目标是找到这些奇点，对它们可能的行为进行分类，并利用它们来了解湍流和其他问题。