schematic of the THC. (from here)

Stability of the THC and its possible proximity to an instability threshold: The THC has been remarkably stable and its variability quite small over the Holocene (past 10,000 years). The much stronger climate instability and high frequency variability seen in high resolution ice and deep sea cores throughout the preceding 150,000 years has been linked to similarly stronger past THC variability (most likely amplified by sea ice feedbacks, see our paleo climate activities). We proposed that present day climate may be close to a "stability threshold" such that the THC may become unstable if it reduces by about 25%. Once unstable, the THC may rapidly increase, collapse, or display strong oscillations. This idea was examined in both simple conceptual models, ocean general circulation models, and "realistic" coupled ocean-atmosphere general circulation models. [e.g., 1, 2]
The existence of a weak unstable THC regime may account for the larger THC and climate variability prior to the Holocene. The implicationsto greenhouse scenarios that predict a weakening of the THC are clearly an important yet open issue. (With collaborators from GFDL/ Princeton University).

time series of the THC from a coupled ocean-atmosphere runs demonstrating that a strong THC tends to be stable (remain near its initial conditions) while a weak THC is unstable.

THC variability: Although generally stable over the past 10,000 years, the THC still varies on time scales of decades to centuries. This variability may have been a factor in the "little ice age" (1550-1850), or "medieval warm period" (from the 10th century to about the 14th century), for example. We have examined possible mechanisms for such variability, from a linear oscillatory THC mode excited by stochastic atmospheric forcing, to a strong "transient amplification" of THC anomalies by what's known as "non normal" dynamics [1, 2, 3]

Transient amplification of the THC in a simple model: the THC and other quantities start with small amplitude and are amplified to a maximum after about 40 years. Panel (c) shows the THC as function of latitude and time, showing how it first increases dramatically and then decays. The other panels show the ocean temperature, salinity and density at the surface and at depth, and the atmospheric temperature and humidity. (with Laure Zanna).