Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow

水力冲击和横摇波对倾斜浅水水流的影响很大，这在渠坝泄洪道设计中尤为重要。项目负责人将运用理论和计算方法研究旋转和多维度对倾斜浅水流流型存在和稳定性的影响。研究结果有望引起水利工程师的兴趣，他们试图通过防止异常大浪的出现，或通过建造修复结构以满足现有和发展中的理论所要求的尺寸和强度。PI将研究一系列关于倾斜浅水流动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（涡度）效应纳入水动力工程环境中横摇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。该项目涉及应用和非标准数学问题，解决物理应用中的挑战性问题。例如，成功处理多维激波和横摇波将推进一般理论，同时为浅水流动/水力工程中的横摇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/转折点工具的混合，以及来自爆炸理论和双曲守恒定律的专门技术。浅水流中横摇波简单稳定性判据的验证以及新的渐近和数值方法的引入，在水利工程、双曲激波理论和边值问题中都有广泛的应用。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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.