Long Rossby Wave Basin Modes For The Southern Ocean

The basin modes of the linear free long Rossby wave of the Southern Ocean are investigated in the frameworks of quasi-geostrophy and the planetary geostrophy. The constraint of total mass conservation, which determines the pressure on the boundary as a function of time, allows the existence of selected large-scale, low-frequency and weak dissipative modes.Global 1°×1°climatology of the first baroclinic Rossby radius of deformationλ1 is computed from climatological annual mean temperature and salinity profiles by solving a Sturm-Liouville eigenvalue problem. Under the quasi-geostrophic approximation and ignoring bottom slope, the phase speed of the first baroclinic Rossby wave isβλ1 2. Using width of each basin and the phase speed, we obtain the basin-crossing time of the first baroclinic Rossby wave in the global basins. The Drake Passage (DP) appears to be the controlling area of the global Rossby wave adjustment. Analysis of the one-dimensional quasi-geostrophic potential vorticity equation demonstrated, the resonant mode mainly presents the westward propagation of the low-frequency long Rossby wave when the forcing frequency is close to that of the gravest mode. Sensitivity tests for the resonant mode to the relative vorticity term reveal, eigen modes are insensitive to the relative vorticity term when the relative vorticity term is very small; but when the relative vorticity term is large enough, the amplitude of the resonant mode obviously becomes small. These two chapters serve as the theoretical basis for the main chapters of dissertation.For the quasi-geostrophic case, the long Rossby wave basin modes for the Southern Ocean are studied under three different basin geometries. Results indicate that the closing or the opening of the DP can significantly affect the eigen modes. When the DP is closed, the eigen periods (the e-folding times) become much longer (shorter) than those with the DP open; and the eigen functions can fill up the whole basin. When the DP is open, the e-folding times can become noticeably larger as the tips of...