Low-frequency variability of a two-layer ocean forced by periodic winds

To seek the variability of the oceanic subtropical gyre on interannual and longer time scales we have conducted numerical experiments with a two-layer quasigeostrophic model in a square basin bounded by no-slip walls. We find that when the amplitude of annually periodic wind forcing is increased, the time series of the total energy exhibit a transition to chaos in such a manner that the response frequency constitutes a quasi-devil's staircase against the forcing amplitude; in particular, the n-cycles appear in descending order of n. The low-frequency modes may thus be produced by seasonal winds. Since, however, the power of the subharmonics is much weaker than that with the forcing frequency, their energy would be concealed by noise in the presence of stochastic wind forcing. The present result is in contrast with the case of the time-independent forcing in which we observe the intrinsic frequencies probably associated with the wave propagation, frequency locking and a cascade of period-doubling bifurcations.