有旋空腔流自由边界的几何性质
The Geometric Properties of the Free Boundary of the Rotational Cavity Flow
DOI: 10.12677/pm.2026.165143, PDF,   
作者: 高 芬：成都理工大学数学科学学院，四川 成都
关键词: 有旋空腔流；自由边界；Euler方程组；几何性质；Rotational Cavity Flow； Free Boundaries； Euler System； Geometric Properties
摘要: 本文主要研究有旋空腔流自由边界的几何性质。通过建立无粘不可压缩有旋流的Euler方程组，结合滑移边界条件和质量通量条件，并引入流函数，将空腔流问题转化为自由边界问题，进一步发现，对于给定的平直的上管道壁，当障碍物对流体是凹的，那么自由边界对流体是严格凸的。本文的研究不仅完善了有旋空腔流的理论框架，还为相关工程应用提供了理论支持。通过严格的数学分析，揭示了有旋空腔流自由边界的几何特性，为相关领域的进一步研究奠定了基础。
Abstract: This paper primarily investigates the geometric properties of the free boundary of the rotational cavity flow. By formulating the Euler equations for inviscid, incompressible rotational flows, incorporating slip boundary conditions and mass flux conditions, and introducing a stream function, the cavity flow problem is transformed into a free boundary problem. Furthermore, we discover that the direction of fluid motion near the free boundary aligns with the geometric properties of the obstacle, and when the obstacle is concave to the flow field, the free boundary is convex. The research presented in this paper not only enhances the theoretical framework of rotational cavity flows but also provides theoretical support for related engineering applications. Through rigorous mathematical analysis, it reveals the geometric characteristics of the free boundary in rotational cavity flows, laying a foundation for further research in related fields.
文章引用：高芬. 有旋空腔流自由边界的几何性质[J]. 理论数学, 2026, 16(5): 192-203. https://doi.org/10.12677/pm.2026.165143

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