Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes

An attempt has been made to apply Arnol’d type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the po-tential vorticity of the observed atmosphere are analyzed, which indicates that Arnol'd second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the sta-ble and unstable zonal flows, Arnol’d second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol'd second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.