The influence of periodic forcing on the time dependence of western boundary currents: Phase locking, chaos, and mechanisms of low-frequency variability

In this study an idealized gyre is put into a temporally periodic state by a steady wind stress curl forcing, and its nonlinear response to variable forcing is investigated by a detailed parameter survey varying the time-mean component of the wind and the amplitude and frequency of a periodic component. Periodic wind variations exceeding ~0.5% profoundly affect the western boundary current (WBC) time dependence, yielding regime diagrams with intricately interleaved regions of phase locking, quasiperiodicity, and chaos. In phase-locked states, the WBC period is locked to a rational multiple of the forcing period and can be shifted far outside its natural range. Quasiperiodic states can exhibit long intervals of near-synchrony interrupted periodically by brief slips out of phase with the forcing. Hysteresis and a period-doubling route to chaos are also found. The nonlinear WBC response can include variability at long time scales that are absent from both the forcing and the steadily driven current; this is a new mechanism for the generation of low-frequency WBC variability. These behaviors and their parameter dependence resemble the Devil's staircase found in the "circle map" model of a periodically forced nonlinear oscillator, but with differences attributable to higher-dimensional dynamics. These nonlinear effects occur with forcing amplitudes in the observed range of the annual wind stress curl cycle and therefore should be considered when inferring the cause of observed WBC time scales. These results suggest that studies omitting either forcing variation or nonlinearity provide an unrealistically narrow view of the possible origins of time dependence in WBCs.