| According to Arnold (1966) ideal two-dimensional hydrodynamics can be formulated as
geodesics in the configuration space with a kinetic energy metric. Instability can be
assessed by the Jacobi equation, which describes the dynamics of infinitesimal
variations along the geodesics, and assuming a negative sectional curvature of the
Riemann manifold. Arnold suggested instability of the atmospheric flow based on a
double periodic plane (torus), while Dowker and Mo-zheng (1990) and Apps (2008)
argue that the spherical geometry stabilizes the flow. The aim of the present work is
to determine the stability properties of a variety of spherical background flows. |