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.

On the nonlinear stability of three-dimensional quasigeostrophic motions in spherical geometry

Nonlinear stability 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 approximation of vertically integrated nondivergency, criteria corresponding to Arnol’d’s second theorem are first established by a detailed analysis. This research was supported by the National Natural Science Foundation of China.