Stability of degree-2 Rossby-Haurwitz waves
Abstract
Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability of degree-2 RH waves, which confirms a conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech. Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with the main challenge being to establish suitable variational characterizations for the solutions under consideration. In this process, the set of rearrangements of a fixed function plays a vital role. We also apply our approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and zonal flows with monotone absolute vorticity.
Keywords
Cite
@article{arxiv.2305.03279,
title = {Stability of degree-2 Rossby-Haurwitz waves},
author = {Daomin Cao and Guodong Wang and Bijun Zuo},
journal= {arXiv preprint arXiv:2305.03279},
year = {2023}
}
Comments
In this version, we showed that Theorem 2.3 is optimal for any $\omega\in\mathbb R$ by introducing the generalized RH waves. Stability of zonal flows with monotone absolute vorticity has also been added