Mathematical Sciences: Nonlinear Phenomena in Fluid Dynamicsand Related P.D.E.'s Theory, Asymptotics and Numerical Computation

数学科学：流体动力学中的非线性现象及相关的偏微分方程理论、渐近学和数值计算

• 批准号: 9001805
• 负责人: Andrew Majda
• 金额: $ 18万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001805&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Phenomena; Fluid

This is a proposal to study mathematical models of physical phenomena arising in the flow of compressible and turbulent gases. In particular, the principal investigator will use analytical and numerical tools to investigate the instability of solutions of nonlinear systems of hyperbolic equations in three dimensions, the evolution of vortex filaments, the derivation of macroscopic transport quantities from turbulent flows using techniques of homogenization theory, and the properties of weak solutions of systems of equations from fluid dynamics and plasma physics. Various types of physical phenomena involve flows containing vortices. Everyday examples of vortices are tornadoes or the bath water as it goes down the drain. Mathematicians study the properties of such vortex motions by constructing simplified sets of equations that have "vortex-like" solutions and then using analytical and numerical methods to predict how these solutions evolve in time. The principal investigator will examine models of vortex flows that arise in aerodynamics and plasma physics.

这是一个研究物理模型的建议， 在可压缩和湍流流动中出现的现象 气. 特别是，主要研究者将使用 分析和数值工具，以调查不稳定性， 三阶非线性双曲方程组的解 尺度，涡丝的演化， 湍流的宏观输运量， 均匀化理论的技术，以及弱 流体动力学和等离子体方程组的解 物理学 各种类型的物理现象都涉及包含 漩涡 每天都有龙卷风或 洗澡的水会流到下水道 数学家研究 通过构造简化的集合， 方程有“涡状”的解决方案，然后使用 分析和数值方法来预测这些解决方案 在时间中进化。 首席研究员将检查模型 在空气动力学和等离子体物理学中出现的涡流。