The Limit of High Reynolds Number for Shear Layers

剪切层高雷诺数的极限

• 批准号: 8903484
• 负责人: Gregory Baker
• 金额: --
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-15 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903484&HistoricalAwards=false
• 关键词: Limit; Reynolds; Number; Shear; Layers; Limit; Reynolds; Number; Shear; Layers

8903484 Baker The principal investigator will study the limit at high Reynolds number of shear layers in incompressible fluid using three different methods--vortex methods, spectral methods, and finite difference methods. Classically, the limit is thought to be a vortex sheet, but recent studies suggest that vortex sheets develop curvature singularities in finite time, and that at the time of singularity formation, the vortex sheet changes from a weak solution to a measure-valued solution of Euler equations. Moreover, different regularizations may lead to different results, making the nature of the limit of vanishing viscosity a central concern. The different numerical methods are considered in order to obtain a direct check on the accuracy of the results, to make a direct comparison of the performance of these methods on shear flows and to identify areas for improvement in each method. Results of the numerical calculations will be used to study how viscous effects modify the tendency for vortex sheets to develop curvature singularities. Numerical results will also be used to help answer the open mathematical question: do different regularizations of the Euler equations converge to different limits as the regularization vanishes?

8903484贝克首席研究员将使用三种不同的方法 - 涡流方法，光谱方法和有限差异方法研究不可压缩流体中剪切层的极限。从经典上讲，极限被认为是涡旋表，但最近的研究表明，涡流表在有限的时间内会发展出曲率奇异性，并且在奇异性形成时，涡流纸从弱解决方案变为Euler方程的测量溶液。此外，不同的正规化可能会导致不同的结果，这使消失粘度极限的性质成为核心问题。考虑了不同的数值方法，以直接检查结果的准确性，直接比较这些方法在剪切流中的性能，并确定每种方法改进的区域。数值计算的结果将用于研究粘性效应如何改变涡流表发展曲率奇点的趋势。数值结果还将用于帮助回答开放的数学问题：随着正则化的消失，Euler方程的不同正规化是否会收敛到不同的限制？