Under the extremely cold climate conditions characteristic of the glacial states that were a recurrent 100,000 year quasi-periodic characteristic of the most recent million years of Earth history, there existed intense climate variability on a millennium timescale. This variability consisted of either clusters of such millennium scale events or of single such oscillations. This oscillatory behavior was first identified over 30 years ago by Willi Dansgaard of the Niels Boer Institute in Copenhagen and by Hans Oeschger of the University of Bern, based upon analyses of oxygen isotopic data from deep Greenland ice cores.

This phenomenon has only very recently become explicable in terms of detailed mathematical/numerical  models. As I will discuss, the explanation involves the thermohaline overturning component of the ocean general circulation. From the perspective of this Fields Institute programme on multi-scale processes, the Meridional Overturning Circulation (MOC) of the oceans is especially interesting because it exists only because the volume of the global oceans is filled with small scale density stratified turbulence generated by the breaking of hydrodynamic waves, the net consequence of which is to effect a vertical flux of mass. The MOC is therefore an extreme example of a multi-scale phenomenon in nature.

As I will show on the basis of coupled climate system analyses which include appropriate parameterizations of the turbulence, the Dansgaard--Oeschger oscillation phenomenon is associated with an intrinsically time dependent mode of operation of the MOC, one that exists only under cold climate conditions. This demonstration involves the integration of a comprehensive model of climate system behavior when modern boundary conditions of topography, land-sea distribution, continental ice cover, atmospheric greenhouse gas concentrations, and solar insolation forcing are replaced by those appropriate to the glacial state. When this model is ``spun-up" from an entirely quiescent ocean state with modern ocean heat content, it is shown to eventually enter a cold oscillatory state following a final sharp cooling event (Peltier and Vettoretti, 2014, GRL). The oscillations are of ``relaxation oscillator" form in which transition from the cold stadial phase of the oscillation into the warm interstadial phase occurs on an extremely fast timescale compared to the millennium timescale period of the oscillation itself (Vettoretti and Peltier, 2016, GRL). The process that governs this fast timescale will also be discussed.