Baroclinic modes in a two-layer basin

The objective of this study is to investigate the time-dependent circulation in a closed basin where the steady circulation is included and long Rossby wave speeds are consistent with observations. Specifically, the large-scale baroclinic eigenmodes of a two-layer rectangular basin forced by surface wind stress in the limit of small dissipation are examined. Low-frequency modes with small decay rates independent of friction result when the constraint of mass conservation is enforced. The magnitude of the wind stress is found to be critical to the eigenspectrum. For all forcing magnitudes, including forcings with closed geostrophic contours, oscillatory modes with decay rates independent of friction emerge. For forcings with closed geostrophic contours, two important classes of eigenmodes with comparable decay rates emerge: purely decaying modes confined to the region of closed contours, and basin-scale oscillatory modes. The purely decaying modes also exist without the constraint of total mass conservation but their decay rates depend on the magnitude of friction to leading order.