Nonlinear dynamics of the elongation-contraction mode of the Gulf-Stream and Kuroshio extension systems

Satellite based observations of sea surface height in the regions of strong air-sea heat flux that flank the Gulf Stream and Kuroshio extension systems are beginning to reveal large-scale patterns of variability on inter-annual to decadal time scales. One of the striking results from these observations is the similarity between the observed changes in the structure of the recirculation regions with those produced in highly idealized wind-driven ocean models. In both the simple models and the observations, the dominant mode of variability can be described as a low-frequency oscillation between a state in which the recirculation gyres are in an elongated state and one in which the recirculation gyres are in a contracted state.

In a previous study we showed using a quasigeostrophic model that the origin of the elongation-contraction variability can be traced back to the existence of multiple steady equilibria: some with contracted recirculation gyres and others with elongated recirculation gyres. However, other published numerical bifurcation studies of the more accurate shallow-water equations did not find the solutions with the elongated recirculation gyres. In this study we use a shallow-water model and compute steady-state solutions using an arc-length continuation methodology based on two control parameters: one that controls the dissipation and a second that controls the relative input of vorticity in the subpolar and subtropical gyres.

Only by performing the analysis in a two-parameter space can we identify successive cusps in parameter space. These successive cusps produce folds in the solution surface that lead to the coexistence of solutions with progressively more elongated recirculation gyres with solutions having contracted gyres. These cusps are the generic manifestation of the pitchfork bifurcations that produced the multiple equilibria in the QG model.

We also present time-dependent solutions that show low-frequency variability associated with spontaneous and irregular transitions between the elongated and contracted modes of circulation. The modeled variability is conjectured to correspond to the elongation-contraction regimes observed in the Kuroshio and Gulf-Stream extension systems