一种能量一致的浅层欧拉系统：推导与性质
An energy-consistent depth-averaged Euler system: derivation and properties
AI总结：
本文推导了一个非静力浅水型模型，用于近似具有自由表面的不可压缩欧拉和纳维-斯托克斯系统，通过最小能量约束代替渐近展开，并与欧拉系统的旋转流解析解进行对比。
摘要：
在本文中，我们提出了一种非静力浅水型模型的原始推导过程，旨在近似具有自由表面的不可压缩欧拉和纳维-斯托克斯系统。闭合关系通过最小能量约束而不是渐近展开来获得。该模型与著名的格林-纳赫迪模型略有不同，并与欧拉系统的静态和解析解相对应于旋转流。在本文的最后部分，我们给出了欧拉系统的时变解析解，这些解也是所提出模型的解析解，但不是格林-纳赫迪模型的解。我们还给出了两种非静力浅水模型的解析解并进行比较。
英文摘要：
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by aminimal energy constraint instead of an asymptotic expansion. The model slightly differs from thewell-known Green-Naghdi model and is confronted with stationary andanalytical solutions of the Euler system corresponding to rotationalflows. At the end of the paper, we givetime-dependent analytical solutions for the Euler system that are alsoanalytical solutions for the proposed model but that are not solutionsof the Green-Naghdi model. We also give and compare analytical solutions of thetwo non-hydrostatic shallow water models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
