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

Instability of Planetary Flows using Riemann Curvature: a Numerical Study