Long-Time Behavior in Free-Surface Problems in Fluid Dynamics

流体动力学中自由表面问题的长期行为

• 批准号: 0707807
• 负责人: David Ambrose
• 金额: $ 12万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2009-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0707807&HistoricalAwards=false
• 关键词: Long; Time; Behavior; Free; Surface

The motion of fluids with free surfaces occurs in many problems in engineering and science; the mathematical theory of such flows is only partially developed, however. While smooth flows for short times have recently become fairly well understood, there is little theory developed for other situations. This project explores models for interfacial Navier-Stokes flows after the onset of topological transitions, global existence of small solutions for vortex sheets, and the mathematical theory of non-Newtonian Hele-Shaw flow, among other problems.There are many possible applications of the theory of free-surface flows in fluid dynamics in science and engineering, such as the drilling and cementing of oil wells, understanding blood flow, or understanding the mixing of fluids in the atmosphere and ocean, as well as problems in microfluidics. In general terms, the proposed research will improve the understanding of wave breaking, fluid mixing, turbulence, and stability of such flows. The investigator will utilize techniques of both mathematical analysis and scientific computing, using insight gained from each approach to more efficiently and more effectively use the other.

自由表面的流体运动发生在工程和科学中的许多问题中。但是，这种流的数学理论仅部分发展。 尽管短时间平稳的流量最近已经众所周知，但在其他情况下几乎没有理论。 该项目探讨了拓扑过渡开始后的界面纳维尔流动的模型，全球涡流解决方案的全球存在以及非牛顿海尔 - 肖鹰流量的数学理论以及其他问题的数学理论，还有许多可能的应用。大气和海洋中的液体以及微流体的问题。 一般而言，拟议的研究将提高对这种流动的波浪破裂，流体混合，湍流和稳定性的理解。 研究人员将利用从每种方法中获得的洞察力来更有效，更有效地使用对方，利用数学分析和科学计算的技术。