Dissipative selection of low-frequency modes in a reduced-gravity basin

The spectrum of linear free modes of a reduced-gravity ocean in a closed ba sin with weak dissipation is examined. The constraint of total mass conserv ation, which in the quasigeostrophic formulation determines the pressure on the boundary as a function of time, allows the existence of selected large -scale, low-frequency basin modes that are very weakly damped in the presen ce of dissipation. These weakly damped modes can be quasi-resonantly excite d by time-dependent forcing near the eigenperiods, or during the process of adjustment to Sverdrup balance with a steady wind from arbitrary initial c onditions. In both cases the frequency of the oscillations is a multiple of 2 pi /t(0), where t(0) is the long Rossby wave transit time, which is of t he order of decades for midlatitude, large-scale basins. These oscillatory modes are missed when the global mass conservation constraint is overlooked .