The Influence of Periodic Forcing on the Time Dependence of Western Boundary Currents: Phase Locking, Chaos, and Mechanisms of Low-Frequency Variability

Abstract

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.

Wind Forced Variability in Eddy Formation, Eddy Shedding, and the Separation of the East Australian Current

“…In comparison to steady forcing, we find that variability in the local forcing field creates: a rectified subsurface enhancement of the EAC with increased eddy variance in the upstream EAC, a shorter eddy shedding time scale, and a time‐mean EAC extension that extends further south toward Tasmania. Although we find no evidence of phase‐locking (e.g., Kiss & Frankcombe, ) between the seasonal cycle of the forcing field and EAC eddy shedding, we do see a reduction in the variability of the eddy‐shedding timing under variable surface forcing (supporting information Figure S3). Additional experiments (Figure ) reveal that regional variability in the wind stress field shorter than 56 days accounts for the enhancement of the mean EAC extension, and that variability at longer time scales and/or in other surface fluxes is unimportant for this feature.…”

“…In contrast, the contemporary view via observational and modeling studies (Bowen et al, ; Mata et al, ; Wilkin & Zhang, ) suggests eddies arise from locally generated mixed baroclinic and barotropic instabilities propagating southward along Australia's east coast with little involvement from Rossby waves at the eddy‐shedding time scale. Although idealized models show that variable forcing can control the timing of intrinsic WBC variability (e.g., Kiss & Frankcombe, ), it remains an open question whether variable forcing can influence the timing of EAC eddy shedding or change the relative importance of barotropic/baroclinic instability in the EAC.…”

Frequency-Domain Analysis of the Energy Budget in an Idealized Coupled Ocean–Atmosphere Model

“…In other words, is the low-frequency variability in the ocean or atmosphere ''free'' (intrinsic), ''forced'' (by the opposing fluid), or intrinsically coupled? This question, with particular interest in showing the existence and importance of low-frequency intrinsic ocean variability, has been addressed by many previous studies (e.g., Dewar 2003;Dijkstra and Ghil 2005;Kravtsov et al 2006;Hogg and Blundell 2006;Berloff et al 2007a,b;Penduff et al 2011;Quattrocchi et al 2012;Sérazin et al 2015;Huck et al 2015; Kiss and Frankcombe 2016). Recently there has been interest in diagnosing intrinsic versus forced ocean variability using spectral energy budget techniques, as in Arbic et al (2012), O'Rourke et al (2018, and Sérazin et al (2018).…”