To interpret dynamically these oscillations, we use a shallow water axisymmetric model, driven by a zonal force with latitudinal and temporal variations following the 1/2 diurnal and the diurnal components of the zonal mean barotropic pressure force produced by the mountains in the GCM.
When our shallow water model has a mean depth representative of the equivalent depth of the atmosphere (between 8km and 10km), it predicts diurnal and semi-diurnal motions that resemble the first and second eigensolutions of the Laplace's tidal equations with zero zonal wavenumber respectively. The first does not affect the mass AAM while the second does. We verify that comparable motions occur in the GCM at the corresponding periodicities, hence explaining the semi-diurnal cycle in mass AAM that occurs in the GCM. Our shallow water model nevertheless fails in explaining the diurnal cycle in the GCM mass AAM, and which is also associated with an axisymmetric motion resembling to the second Eigensolution of the Laplace's tidal equations.
The significance of our results is discussed in the context of the theory of the tides with zero-zonal wavenumber. Some consequences for geodesy are also given.