For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta...For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta-plane, and to verify it, one needs only to find out the least eigenvalue of a boundary value problem for the 2-D Laplacian. By more accurate estimate and more detailed analysis, this note establishes a new展开更多
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 result...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.展开更多
基金Project supported by the National Natural Science Foundation of China the French-Chinese Cooperation Programme
文摘For three-dimensional quasigeostrophic motion, Mu and Wang first established a nonlinear stability criterion analogous to Arnold’s second theorem when the horizontal domain at each depth is a bounded domain on a beta-plane, and to verify it, one needs only to find out the least eigenvalue of a boundary value problem for the 2-D Laplacian. By more accurate estimate and more detailed analysis, this note establishes a new
文摘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.
