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.

液压冲击和滚动波会严重影响倾斜的浅水流，这对于运河和大坝溢洪道的设计尤为重要。 主要研究者（PI）将使用理论和计算方法研究旋转和多维对倾斜浅水流中流动模式的存在和稳定性的影响。 希望通过防止其外观或通过将补救结构构建到现有理论要求的大小和力量来防止异常大浪损害的液压工程师会感兴趣。 PI将研究有关倾斜浅水流的稳定性和行为的新问题。 该项目的目的是将先前未指定的多维和旋转（涡度）效应纳入在流体力学工程环境中的稳定性和行为和液压冲击的研究中，以获得所有参数的全面稳定图。该项目涉及适用的和非标准的数学问题，这些问题解决了物理应用程序中具有挑战性的问题。例如，多维冲击和滚动波的成功处理将推动一般理论，同时在浅水流/液压工程中为滚动波行为提供坚实的框架。 项目中将使用的研究方法包括数值，正式渐近和动力学系统/转折点工具的混合物，并带有来自爆炸理论和双曲线保护法的专业技术。 在浅水流中滚动波的简单稳定性标准的验证以及新的渐近和数值方法的引入在水力工程和双曲线休克和边界价值问题的理论中都广泛应用。同样，对常见流量的全参数稳定图的计算是基本的基础科学兴趣。该奖项反映了NSF的法定任务，并且使用基金会的知识分子和更广泛的影响审查标准，被认为值得通过评估来获得支持。