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arXiv · 2305.03279

Stability of degree-2 Rossby-Haurwitz waves

Daomin Cao·Guodong Wang·Bijun Zuo
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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.

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Daomin Cao, Guodong Wang, Bijun Zuo. 2023-05-05. Stability of degree-2 Rossby-Haurwitz waves. https://arxiv.org/abs/2305.03279

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