I'll talk about some recent work (in collaboration with Leela Frankcombe, CCRC UNSW) on the origins of time-dependence in ocean circulation, in particular in western boundary currents (WBCs) such as the East Australian Current and Gulf Stream. These currents are driven by the surface winds and are present at the west of every ocean basin; in the subtropics each one carries about 100 Amazon's worth of warm water towards the poles, thereby contributing to the heat transport in the global climate system. WBCs are highly variable on timescales of months to decades, and dynamical systems theory applied to idealised ocean models has provided many insights into the origins of this variability, which typically arises in a series of bifurcations from steady to periodic and ultimately to chaotic states as the wind forcing is made stronger. Such studies have almost all used steady wind forcing, but in reality the winds also have an annual cycle superimposed on an almost white spectrum of variation. Studies with variable wind typically use linear models with no intrinsic time-dependence.
We have therefore conducted a series of experiments to determine the response of a simple nonlinear ocean model to wind forcing which has a time-periodic component in addition to a steady component. The steady component puts the WBC into a periodic oscillation and we survey the temporal behaviour of the model WBC as a function the forcing frequency and amplitude. We find that very weak forcing variations of O(0.1%) are sufficient to phase-lock the WBC period to a rational multiple of the forcing period. At larger forcing variations the frequency range over which this locking occurs increases, and period-doubling cascades and chaos also appear. Unlocked states can also exhibit periods of near-synchrony interrupted periodically by brief slips out of phase with the forcing. There is an intricate dependence on parameters, with locked regions arranged similarly to Arnold tongues in the circle map, although with some differences. These results suggest that the variability timescales identified under steady forcing could be significantly modified by the annual cycle: phase-locking to the annual cycle can shift the oscillation frequency far from its natural value, and chaos, phase slipping and multiple period doublings induced by periodic forcing all exhibit long timescales which are not present in the forcing or intrinsic to the current itself.