The Non-zonal Rossby-Haurwitz Solutions of the 2D Euler Equations on a Rotating Ellipsoid
Analysis of PDEs
2023-10-30 v1
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.
Keywords
Cite
@article{arxiv.2310.17854,
title = {The Non-zonal Rossby-Haurwitz Solutions of the 2D Euler Equations on a Rotating Ellipsoid},
author = {Chenghao Xu},
journal= {arXiv preprint arXiv:2310.17854},
year = {2023}
}