Centennial oscillations of the ocean thermohaline circulation are studied in a 2-D latitude-depth model under mixed boundary conditions (i.e. restoring surface temperature and prescribed freshwater flux). The oscillations are revealed through linear stability analysis of a steady state obtained in a single hemisphere configuration. A density variance budget is performed and helps determine the physical processes sustaining these oscillations: the restoring surface temperature appears as a source of density variance - this is a consequence of positively-correlated temperature and salinity anomalies. A minimal model, the Howard-Malkus loop oscillator, enables us to understand physically the oscillatory and growth mechanisms. The centennial oscillation is connected to the advection of salinity anomaly around the loop; it is also related to the salinity feedback on the overturning which reinforces anomalies through a change of residence time in the freshwater flux regions. Analytical solutions of this loop model show that these centennial oscillations exist in a specific parameter regime in terms of the freshwater flux amplitude F0: oscillations are damped if F0 is too weak, but if F0 is too large, the instability grows exponentially without oscillating-the latter regime is known as the positive salinity feedback. The robustness of these oscillations is then analyzed in more realistic bihemispheric configurations, some including a highly idealized Antarctic Circumpolar Current: oscillations are then always damped. These results are rationalized with the loop model, and compared to the oscillations found in general circulation models.