Stability of magnetohydrodynamic zonal flows on a sphere

作者：Adrian Constantin, Zhiwu Lin, Hao Zhu · 发表于：Discrete and Continuous Dynamical Systems · 年份：2026 · DOI：10.3934/dcds.2026143 · 研究领域：Geomagnetism and Paleomagnetism Studies、Solar and Space Plasma Dynamics、Fluid Dynamics and Turbulent Flows

We study the linear stability of a magnetohydrodynamic zonal flow which consists of a zonal velocity field coupled to a toroidal magnetic field on the surface of a sphere. We derive a Howard-type semicircle theorem, which provides bounds for the phase speed of unstable modes. We show that in spherical coordinates, the magnetic field can only reduce the radii of the semicircles corresponding to the purely hydrodynamic case. This leads to a sufficient condition for spectral stability if the magnitude of the toroidal magnetic field is larger than that of the zonal flow. In particular, a magnetostatic equilibrium is always spectrally stable. While numerical evidence indicates that the hydrodynamically stable 2-jet and 3-jet zonal flows can be driven unstable by certain toroidal magnetic fields, we prove that the 1-jet zonal flow with an arbitrary toroidal magnetic field is spectrally stable.