On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

Nonlinear Mobility criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol’d’s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol’d’s second theorem and better than the known results. Especially, under the approxima-tion of vertically integrated nondivergency, criteria corresponding to Arnol’d’s second theorem are first established by a detailed analysis.