The computation of the free barotropic oscillations of a global ocean model including friction and loading effects

A set of 61 normal modes with periods between 7.8 and 133.1 h has been calculated, using a 1 degrees model of the global ocean, including the Arctic Ocean. The model explicitly considers frictional forces and ocean self-attraction and loading effects. The latter effects have generally been taken into account by parameterization, but for some modes the effects have also been considered fully. Due to friction, the computed eigenfrequencies are complex, exhibiting also the varying dissipative properties of the modes and their dependence on the distribution of potential and kinetic energies over the oceanic regions. In detail, gravity modes having periods less then 80 h and dominating the semi-diurnal and the diurnal tides, topographically controlled vorticity modes with periods longer than diurnal, and two planetary vorticity modes with periods of 96.8 and 119.4 h have been identified. These planetary vorticity modes have their energies distributed over Pacific, Atlantic, and Indian Oceans, while the other modes with periods longer than 80 h, as vorticity modes, have their energies concentrated on topographic structures of restricted extension. The modes are discussed with respect to their wave properties, e.g., concerning quasi-standing-wave resonances and to the appearance of Kelvin waves of different orders and trapped by different coastlines. In particular, the relevance of specific modes for the development of the fields of the most important semi-diurnal and diurnal tidal constituents is investigated.