拉格朗日坐标系下二维和三维Euler-Boussinesq方程精确解的一种方法

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Tomi Saleva, Jukka Tuomela
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引用次数: 0

摘要

利用拉格朗日描述研究了不可压缩欧拉方程的Boussinesq近似。在这种情况下,导出了拉格朗日流体图的条件,并给出了在二维和三维情况下求精确流体流动的一般方法。用这种方法可以得到大量的解,这里我们只能展示一些有趣的例子,包括二维Euler-Boussinesq方程的Gerstner型解。在之前的两篇论文中,我们使用了相同的方法来找到齐次欧拉方程的精确拉格朗日解,本文作为一个例子,说明了如何将这些相同的想法扩展到提供相关的、更复杂的模型的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates

A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates

We study the Boussinesq approximation for the incompressible Euler equations using Lagrangian description. The conditions for the Lagrangian fluid map are derived in this setting, and a general method is presented to find exact fluid flows in both the two-dimensional and the three-dimensional case. There is a vast amount of solutions obtainable with this method and we can only showcase a handful of interesting examples here, including a Gerstner type solution to the two-dimensional Euler–Boussinesq equations. In two earlier papers we used the same method to find exact Lagrangian solutions to the homogeneous Euler equations, and this paper serves as an example of how these same ideas can be extended to provide solutions also to related, more involved models.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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