Abstract
In this study, eigenmodes and singular modes are analyzed for a dynamical system of the atmosphere, linearized about a winter basic state in order to understand the dynamics of the Arctic Oscillation (AO). Since the fluctuations of the sea-level pressure are dynamically linked with the barotropic component of the atmosphere, the AO is investigated in the framework of a barotropic model.
As a result of the analysis, we find multiple eigenmodes which are similar to the AO, with a negative pole in the Arctic, and positive poles in the Pacific and Atlantic sectors. Since some of the eigenmodes are unstable, a linear drag is introduced to shift the eigenvalues in order to pick up different eigenmodes as a singular mode with resonant behavior.
It is demonstrated that the singular eigenmode of the dynamical system emerges resonantly as the AO, in response to the arbitrary forcing. The resonant growth is allowed for multiple eigenmodes, including the unstable modes, and therefore the AO described by the neutral mode under the strong friction is recognized as the least damping mode excited by the tail of the resonant response curve of the singular eigenmode. In reference to the result of the nonlinear simulation of the AO, using the same barotropic model, we may conclude that the AO is a physical mode ofa dynamical system for the global atmosphere.
