The different nature of the interdecadal variability of the thermohaline circulation under mixed and flux boundary conditions

The differences between the interdecadal variability under mixed and constant flux boundary conditions are investigated using a coarse-resolution ocean model in an idealized flat-bottom single-hemisphere basin. Objective features are determined that allow one type of oscillation to be distinguished versus the other. First, by performing a linear stability analysis of the steady state obtained under restoring boundary conditions, it is shown that the interdecadal variability under constant flux and mixed boundary conditions arises, respectively, from the instability of a linear mode around the mean stratification and circulation and from departure from the initial state. Based on the budgets of density variance, it is shown next that the two types of oscillations have different energy sources: Under the constant-flux boundary condition (the thermal mode), the downgradient meridional eddy heat flux in the western boundary current regions sustains interdecadal variability, whereas under mixed boundary conditions (the salinity mode), a positive feedback between convective adjustment and restoring surface heat flux is at the heart of the existence of the decadal oscillation. Furthermore, the positive correlations between temperature and salinity anomalies in the forcing layer are shown to dominate the forcing of density variance. In addition, the vertical structure of perturbations reveals vertical phase lags at different depths in all tracer fields under constant flux, while under mixed boundary conditions only the temperature anomalies show a strong dipolar structure. The authors propose that these differences will allow one to identify which type of oscillation, if any, is at play in the more exhaustive climate models