Eigenvalue Analysis of Atmospheric Free Oscillations under the Influence of a Zonal Mean Field

Abstract

Linear eigenvalue analysis of the primitive equations is performed to study atmospheric free oscillations under the influence of a zonal mean field. The model for the primitive equations is based on a three-dimensional spectral formulation, and the zonal mean field is produced by averaging reanalysis data over 10 years. The frequencies and latitudinal/vertical structures of the eigenmodes obtained by the analysis are compared with the results of the classical tidal theory and with those of the free oscillation modes detected from reanalysis data by a recent study. The frequencies and vertical structures of the eigenmodes obtained in the present study are consistent with those of the eigenmodes detected in the recent study, while the obtained latitudinal structures do not differ significantly from those of the classical tidal theory. It is shown that the deviation from the frequency obtained from the classical tidal theory is mainly due to the effect of the zonal mean flow, but partly also to the latitudinal variation of the temperature field. The present study also shows that the vertical phase structure of the obtained eigenmodes, which is inconsistent with the classical tidal theory, can be understood qualitatively by using the wave dispersion relation.