Instability of Planetary Flows using Riemann Curvature: a Numerical Study

Richard Blender

Instability of Planetary Flows using Riemann Curvature: a Numerical Study

Fluid Dynamics 2014-12-22 v1

Authors: Richard Blender

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.

Keywords

hydrodynamic instability fluid dynamics planetary dynamics

Cite

@article{arxiv.1412.6317,
  title  = {Instability of Planetary Flows using Riemann Curvature: a Numerical Study},
  author = {Richard Blender},
  journal= {arXiv preprint arXiv:1412.6317},
  year   = {2014}
}