Relaxation oscillations in an idealized ocean circulation model

Abstract

This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting model is a piecewise-smooth, three time-scale system. The model is analyzed using geometric singular perturbation theory to demonstrate the existence of attracting periodic orbits. The system is capable of producing classical relaxation oscillations as expected, but there is also a parameter regime in which the model exhibits small amplitude oscillations known as canard cycles. Forcing the model with obliquity variations from the last 100,000 years produces oscillations that are modulated in amplitude and frequency. The output shows similarities with important features of the climate proxy data of the same period.