Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow

倾斜浅水流的多维和涡度效应

• 批准号: 2206105
• 负责人: Kevin Zumbrun
• 金额: $ 23.57万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206105&HistoricalAwards=false
• 关键词: Multi; Dimensional; Vorticity; Effects; Inclined

Hydraulic shocks and roll waves can drastically affect inclined shallow-water flow, which is particularly important to canal and dam spillway design. The Principal Investigator (PI) will use theoretical and computational methods to study the effects of rotational and multi-dimensions on the existence and stability of flow patterns in inclined shallow water flow. The results are expected be of interest to hydraulic engineers seeking to prevent damage from anomalous large waves, either by preventing their appearance, or by building remediating structures to a size and strength called for by the existing and developing theory. The PI will study a selection of novel problems on stability and behavior of inclined shallow water flow. The objective of the project is the incorporation of previously unaccounted multi-dimensional and rotational (vorticity) effects in the study of stability and behavior of roll waves and hydraulic shocks in a hydrodynamic engineering setting, to obtain comprehensive stability diagrams across all parameters. The project involves applicable and nonstandard mathematical issues addressing challenging problems from physical applications. For example, successful treatment of multidimensional shock and roll waves would advance general theory, while providing a solid framework on roll wave behavior in shallow water flow/hydraulic engineering. The research methods that will be used in the project include a blend of numerical, formal asymptotic, and dynamical systems/turning point tools with specialized techniques coming from detonation theory and hyperbolic conservation laws. The validation of simple stability criteria for roll waves in shallow water flow and the introduction of new asymptotic and numerical methods are of wider application in both hydraulic engineering and the theory of hyperbolic shock and boundary value problems. Likewise, the computation of all-parameters stability diagrams for commonly occurring flows is of basic foundational scientific interest.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

水力冲击和滚波会极大地影响倾斜的浅水流，这对于运河和大坝溢洪道设计尤为重要。 首席研究员（PI）将利用理论和计算方法研究旋转和多维对倾斜浅水流流型的存在性和稳定性的影响。 预计这些结果会引起寻求防止异常大波浪造成损害的水利工程师的兴趣，他们可以通过防止异常大波浪的出现，或通过建造符合现有和发展理论所需的尺寸和强度的修复结构来防止异常大波浪造成的损害。项目负责人将研究一系列有关倾斜浅水流稳定性和行为的新问题。 该项目的目标是将以前未考虑的多维和旋转（涡旋）效应纳入水动力工程环境中滚波和液压冲击的稳定性和行为研究中，以获得所有参数的综合稳定性图。该项目涉及适用和非标准的数学问题，解决物理应用中的挑战性问题。例如，多维冲击波和滚波的成功处理将推进一般理论，同时为浅水流/水力工程中的滚波行为提供坚实的框架。 该项目将使用的研究方法包括数值、形式渐近和动力系统/转折点工具与来自爆轰理论和双曲守恒定律的专门技术的结合。 浅水流中滚波的简单稳定性准则的验证以及新的渐近和数值方法的引入在水利工程以及双曲线冲击和边值问题理论中都有更广泛的应用。同样，计算常见流动的全参数稳定性图具有基本的基础科学意义。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。