摘要
Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper. The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories, since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest growing perturbation.
Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper. The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories, since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest growing perturbation.
基金
the National Key Basic Research Project, "Research on the FormationMechanism and Prediction Theory of Severe Synoptic Disasters in China" (Grand No. G1998040910), the National Natural Science Foundation of China (Grand Nos. 49775262 and 49823002) and t
关键词
单个向量
单个价值
非线性
可预测性
singular vector
singular value
nonlinear
predictability