The Non-zonal Rossby–Haurwitz Solutions of the 2D Euler Equations on a Rotating Ellipsoid

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2024-10-01 DOI:10.1007/s00021-024-00884-1

Chenghao Xu

引用次数: 0

Abstract

In this article, we investigate the incompressible 2D Euler equations on a rotating biaxial ellipsoid, which model the dynamics of the atmosphere of a Jovian planet. We study the non-zonal Rossby–Haurwitz solutions of the Euler equations on an ellipsoid, while previous works only considered the case of a sphere. Our main results include: the existence and uniqueness of the stationary Rossby–Haurwitz solutions; the construction of the traveling-wave solutions; and the demonstration of the Lyapunov instability of both the stationary and the traveling-wave solutions.

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旋转椭球体上二维欧拉方程的非纵向罗斯比-豪尔维茨解

在本文中，我们研究了旋转双轴椭球体上的不可压缩二维欧拉方程，该方程模拟了一颗类木行星的大气动力学。我们研究了欧拉方程在椭球体上的非正交 Rossby-Haurwitz 解，而之前的研究只考虑了球体的情况。我们的主要成果包括：静态罗斯比-霍尔维茨解的存在性和唯一性；行波解的构造；以及静态解和行波解的 Lyapunov 不稳定性的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.