Low-frequency variability, coherence resonance and phase selection in a low-order model of the wind-driven ocean circulation

In this paper, a low-order spectral quasigeostrophic (QG) model of the wind-driven ocean circulation is derived and used to analyze the low-order character of the intrinsic low-frequency variability of the midlatitude double-gyre ocean circulation and of the related coherence resonance and phase selection phenomena. The model includes an exponential in the basis functions that allows for westward intensification, retains only four modes in the Galerkin projection, is defined in a rectangular domain, and is forced by deterministic and stochastic winds, thus extending previous low-order QG ocean models. The solution under steady forcing is first obtained, and the results are also analyzed in terms of dynamical systems theory. A homoclinic bifurcation (with the wind amplitude chosen as the control parameter) leads to intrinsic decadal relaxation oscillations (ROs) similar in several respects to those obtained with primitive equation models. The system is then forced with an additional red noise wind, and, in a parameter range preceding the global bifurcation, a coherence resonance scenario very similar to the one found with a primitive equation model of the Kuroshio Extension is obtained: this suggests that such a phenomenon is of low-order character. To study the RO excitation mechanism, a method denoted as phase selection is proposed. The system is forced with additional fictitious periodic winds that produce an emergence of ROs yielding strong phase dependence with the periodic forcing. The subsequent analysis reveals the character of the wind forcing that is most likely to excite a RO. All the results are discussed within the general framework of climate dynamics.