Existence and Stability of the Lamb Dipoles for the Quasi-Geostrophic Shallow-Water Equations

2022/06/05 by Lai, Shanfa, Qin, Guolin, Zhan, Weicheng
#35A02 #35Q31 (Secondary) #76B03 #76B47 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.02174

Abstract

In this paper, we prove the nonlinear orbital stability of vortex dipoles for the quasi-geostrophic shallow-water (QGSW) equations. The vortex dipoles are explicit travelling wave solutions to the QGSW equations, which are analogues of the classical circular vortex of Lamb and Chaplygin for the steady planar Euler equations. We establish a variational characterization of these vortex poles, which provides a basis for the stability result.

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• Stability of Lamb dipoles
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• Smooth travelling-wave solutions to the inviscid surface quasi-geostrophic equation
• Vortex rigid motion in quasi-geostrophic shallow-water equations
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