Nonnormal Perturbation Growth of Pure Thermohaline Circulation Using a 2D Zonally Averaged Model

Abstract

Generalized linear stability theory is used to calculate the optimal initial conditions that result in transient amplification of the thermohaline circulation (THC) in a zonally averaged single-basin ocean model. The eigenmodes of the tangent linear model verify that the system is asymptotically stable, but the nonnormality of the system permits the growth of perturbations for a finite period through the interference of nonorthogonal eigenmodes. It is found that the maximum amplification of the THC anomalies occurs after 6 yr with both the thermally and salinity-driven components playing major roles in the amplification process. The transient amplification of THC anomalies is due to the constructive and destructive interference of a large number of eigenmodes, and the evolution over time is determined by how the interference pattern evolves. It is found that five of the most highly nonnormal eigenmodes are critical to the initial cancellation of the salinity and temperature contributions to the THC, while 11 oscillating modes with decay time scales ranging from 2 to 6 yr are the major contributors at the time of maximum amplification. This analysis demonstrates that the different dynamics of salinity and temperature anomalies allow the dramatic growth of perturbations to the THC on relatively short (interannual to decadal) time scales.