Ensemble Simulations and Pullback Attractors of a Periodically Forced Double-Gyre System

Abstract

primitive equation ocean model has recently reproduced with reasonable realism the synchronization between the North Pacific Oscillation and the last two Kuroshio Extension decadal cycles observed from altimetry. However, the timing of the cycles is imperfect: could a different model initialization improve this fundamental aspect of the phenomenon? Ensemble simulations stemming from many initial conditions should be carried out to answer this question, but doing that with a primitive equation model is highly computationally expensive. A preliminary analysis is therefore performed here with a nonlinear low-order ocean model, which identifies a significant paradigm of intrinsic oceanic double-gyre low-frequency variability. The chaotic pullback attractors of the periodically forced model are first recognized to be periodic and cycloergodic. Two parameters are then introduced to analyze the topological structure of the pullback attractors as a function of the forcing period; their joint use allows one to identify four forms of sensitivity to initialization corresponding to different system behaviors. The model response under periodic forcing turns out to be, in most cases, very sensitive to initialization. Implications concerning the primitive equation model are finally discussed.