Instability of Planetary Flows using Riemann Curvature: a Numerical Study

Richard Blender

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arXiv · 1412.6317

Instability of Planetary Flows using Riemann Curvature: a Numerical Study

Richard Blender

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Abstract

The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnol'd (1966) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The sectional curvature scales with $m/\ell$ for large total and zonal wave numbers $\ell$ and $m$ of the perturbations. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.

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Richard Blender. 2014-12-19. Instability of Planetary Flows using Riemann Curvature: a Numerical Study. https://arxiv.org/abs/1412.6317

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