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

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首席研究员贝克将使用三种不同的方法--涡旋法、谱方法和有限差分方法研究不可压缩流体中高雷诺数剪切层的极限。经典的极限是涡旋层，但最近的研究表明，涡旋层在有限时间内发展出曲率奇异性，并且在奇异性形成时，涡旋层从欧拉方程的弱解转变为测量值解。此外，不同的正则化可能导致不同的结果，使得消失粘度极限的性质成为人们关注的中心问题。考虑了不同的数值方法，以便直接检查结果的准确性，直接比较这些方法在剪切流方面的性能，并找出每种方法需要改进的地方。数值计算的结果将被用来研究粘性效应如何改变涡片发展曲率奇异性的趋势。数值结果也将被用来帮助回答一个公开的数学问题：当正则化消失时，欧拉方程的不同正则化是否收敛到不同的极限？