2014/12/19 by Richard Blender, Blender, Richard
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Astro and Planetary Science #Classical mechanics #Curvature #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Geomagnetism and Paleomagnetism Studies #Geometry #Geophysics and Gravity Measurements #Ideal (ethics) #Instability #Mathematical analysis #Mathematics #Mechanics #Optics #Physics #Rotation (mathematics) #Wavenumber #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1412.6317
3 pages, 3 figures
arxiv created 2014/12/19 · openalex publication_date 2014/12/19 · arxiv updated 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The instability of ideal non-divergent zonal flows on the sphere is\ndetermined numerically by the instability criterion of Arnol'd (1966) for the\nsectional curvature. Zonal flows are unstable for all perturbations besides for\na small set which are in approximate resonance. The sectional curvature scales\nwith m/\ℓ for large total and zonal wave numbers \ℓ and m of the\nperturbations. The planetary rotation is stable and the presence of rotation\nreduces the instability of perturbations.\n