The spectrum of linear free modes of a reduced-gravity ocean in a closed basin with weak dissipation is examined. The constraint of total mass conservation, 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 presence of dissipation.

These weakly damped modes can be quasi-resonantly excited by time-dependent forcing near the eigenperiods, or during the process of adjustment to Sverdrup balance with a steady wind from arbitrary initial conditions. In both cases the frequency of the oscillations is a multiple of 2π/t₀, where t₀ is the long Rossby wave transit time, which is of the order of decades for midlatitude, large-scale basins. These oscillatory modes are missed when the global mass conservation constraint is overlooked.

A model for the interaction between the midlatitude ocean gyres and the wind stress is formulated for a shallow-water, spherical hemisphere with finite thermocline displacement and the latitudinal dependence of the long Rossby wave speed. The oceanic currents create a temperature front at the midlatitude intergyre boundary that is strongest near the western part of the basin. The intergyre temperature front affects the atmospheric temperature gradient in the storm track region, increasing the eddy transport of heat and the surface westerlies. The delayed adjustment of the gyres to the wind stress causes the westerly maximum to migrate periodically in time with a decadal period. The behavior of the model in a spherical geometry is qualitatively similar to that in a quasigeostrophic setting except that here the coupled oscillation involves oceanic temperature anomalies that circulate around the subpolar gyre, whereas the quasigeostrophic calculations favor the subtropical gyre. Another difference is that here there is a linear relationship between the period of the coupled oscillation and the delay time for the adjustment of ocean gyres to changes in the wind stress. This result departs from the quasigeostrophic result, in which the advection timescale also influences the period of the decadal oscillation.