Arnol'd Nonlinear Stability Theorems and their Application to the Atmosphere and Oceans |
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Authors: | Mu Mu Yong-Hui Wu |
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Affiliation: | (1) LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, P. R. China;(2) Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo, 060-0812, Japan |
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Abstract: | Within the context of atmospheric and oceanic fluid dynamicsthe problems of nonlinear stability and instability, particularlythe Arnol'd second type nonlinear stability, are surveyed.The stability criteria obtained by means of the energy-Casimirand energy-Lagrange methods are presented for a varietyof models, the estimates for various generalized perturbationenergy and enstrophy are given. Potential applications of thesecriteria are shown in the estimation of bounds on the perturbationenergy and enstrophy, in the diagnostic study of the persistence orbreakdown of jet flows in the middle and high latitudes, and in theverification of the validity of the tangent linear model in bothatmospheric dynamics and oceanography.Some further research results are also highlighted. |
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Keywords: | energy-Casimir energy-Lagrange Linear stability nonlinear stability normal mode |
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