Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow

水力冲击和横滚波对倾斜浅水流场有很大的影响，这对渠道和大坝溢洪道的设计尤为重要。 首席研究员（PI）将使用理论和计算方法来研究旋转和多维对倾斜浅水流中流型的存在和稳定性的影响。 这些结果预计会引起水利工程师的兴趣，他们希望通过防止异常大浪的出现，或者通过建立现有和发展中理论所要求的尺寸和强度的补救结构来防止异常大浪造成的损害。PI将研究一系列关于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）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，同时提供浅水流动/水利工程中滚波行为的坚实框架。 将在该项目中使用的研究方法包括混合数值，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律的专业技术。 浅水中滚波稳定性简单判据的验证以及新的渐近方法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具有广泛的应用。同样，计算常见流动的所有参数稳定性图也具有基本的基础科学价值。该奖项反映了NSF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.