Mathematical Sciences: Nonlinear Wave Phenomena in Hydrodynamics

数学科学：流体动力学中的非线性波现象

• 批准号: 8902473
• 金额: $ 17.99万
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-08-01 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902473&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Wave; Phenomena

This research effort is concerned with several topics of current interest in applied mathematics, especially those associated with nonlinear phenomena in continuum mechanics. Emphasis is placed on both the physical phenomena and the mathematical theories used to describe nonlinear wave and stability characteristics in hydrodynamics. Specifically, a systematic study will be made of a new theoretical approach to nonlinear stability. This development emphasizes the importance of mean flow/first harmonic interactions, rather than the more usual ones that involve the generation of higher harmonics, as the driving mechanism underlying the evolution of 3-D disturbances in shear flows. Some special cases have already been considered and it is believed that this approach could have important consequences to a broad range of instability problems. The PI intends to consider a number of further applications so that the range of its applicability can be fully assessed.

这项研究工作涉及几个主题， 当前对应用数学的兴趣，特别是那些 与连续介质力学中的非线性现象有关。 重点放在物理现象和 描述非线性波的数学理论， 流体动力学中的稳定性特征。 具体而言，将对一种新的 非线性稳定性的理论方法。 这一发展 强调平均流量/一次谐波的重要性 相互作用，而不是更常见的涉及 产生高次谐波，作为驱动机制 剪切流中三维扰动演化的基础。 一些特殊情况已经考虑过， 相信这种方法会产生重要的影响， 一系列的不稳定问题。 PI计划 考虑一些进一步的应用程序，使范围 可以充分评估其适用性。