Relaxation Oscillations as a Mechanism of Abrupt Climate Change

Climate variability at the millennial time scale is difficult to rationalize, as the frequency 0.001 1/yr falls near the middle of a wide gap in the spectrum of external forcing on the climate system (between the low-frequency orbital components and the high-frequency tidal components). This situation prompted interest in the possibility for the climate system to undergo self-sustained or self-excited oscillations. Our contribution will comprise two parts. First, we will review elements from the theory of non-linear vibrations that provide a framework for the discussion of the fundamental mechanisms responsible for millennial-scale climate variability. Particular emphasis will be put on the self-sustained oscillations that occur in physical systems with one degree of freedom. In such systems self-sustained oscillations arise from the nonlinear dependence of the damping force on velocity. In the limit of very large nonlinearity, the oscillator stores energy for a relatively long period of time and releases this energy in a relatively short time, i.e., the oscillations are strongly asymmetric (relaxation oscillations). Second, we will examine the self-sustained oscillations of the meridional overturning circulation simulated by an ocean circulation model when subject to large freshwater forcing (salt addition at low latitudes and salt extraction at high latitudes). A scaling analysis provides evidence that these oscillations can be fundamentally interpreted as relaxation oscillations : the model ocean stores potential energy in the form of an unstable vertical temperature gradient for a relatively long period of time (phase of reduced MOC) and converts this potential energy into kinetic energy (phase of intense MOC) when the unstable vertical temperature gradient dominates the stable vertical salinity gradient in the density stratification. The merits and weaknesses of the hypothesis of relaxation oscillations as a mechanism of abrupt climate change will be discussed.