Mathematical Sciences: Stability and Bifurcation in Two-Layer Flows

数学科学：两层流的稳定性和分岔

• 批准号: 8902166
• 负责人: Yuriko Renardy
• 金额: $ 3.5万
• 依托单位: Virginia Polytechnic Institute and 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: 1989-08-01 至 1992-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902166&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stability; Bifurcation; Two

8902166 Renardy This proposal will study the stability and bifurcation in two-layer flows involving two immiscible fluids. Such flows have many applications in industry, such as the formation of bicomponent fibers, the transport of oil in pipelines, ink-jet printing and lubrication. It is well known that such flows can also exhibit phenomena which are totally unexpected based on our knowledge of one-fluid flows. Theoretically, many possibilities exist for the shape of the boundary separating the two fluids. Yet experiments show that some shapes are preferred over others, although the underlying selection mechanisms are not well understood. A chief objective of this proposal is to study, analytically and computationally, the stability of the various steady arrangements of two-layer flows, and the evolution of new arrangements from unstable ones.

8902166本方案将研究包含两种不相容流体的两层流动的稳定性和分叉。这种流动在工业上有许多应用，如双组分纤维的形成、石油在管道中的输送、喷墨打印和润滑。众所周知，根据我们对单流体流动的了解，这种流动也可能表现出完全意想不到的现象。从理论上讲，分隔这两种流体的边界形状有很多种可能性。然而，实验表明，一些形状比其他形状更受欢迎，尽管潜在的选择机制还没有被很好地理解。这一建议的一个主要目的是用解析和计算的方法研究两层流动的各种定常排列的稳定性，以及从不稳定排列到新排列的演变。