Two different aperiodic phases of wind-driven ocean circulation in a double-gyre, two-layer shallow-water model

A two-layer shallow-water model is used to investigate the transition of wind-driven double-gyre circulation from laminar flow to turbulence as the Reynolds number (Re) is systematically increased. Two distinctly different phases of turbulent double-gyre patterns and energy trajectories are exhibited before and after at Re = 95: deterministic and fully developed turbulent circulations. In the former phase, the inertial subgyres vary between an asymmetric solution and an antisymmetric solution and the double-gyre circulations reach the aperiodic solution mainly due to their barotropic instability. An integrated kinetic energy in the lower layer is slight and the generated mesoscale eddies are confined in the upper layer. The power spectrum of energies integrated over the whole domain at Re = 70 has peaks at the interannual periods (4-7 yr) and the interdecadal period (10-20 yr). The loops of the attractors take on one cycle at those periods and display the blue-sky catastrophe. At Re = 95, the double-gyre circulation reaches a metastable state and the attracters obtained from the three energies form a topological manifold. In the latter, as Re increases, the double-gyre varies from a metastable state to a chaotic state because of the barotropic instability of the eastward jet and the baroclinic instability of recirculation retrograde flow, and the eastward jet meanders significantly with interdecadal variability. The generated eddies cascade to the red side of the power spectrum as expected in the geostrophic turbulence. The main results in the simulation may indicate essential mechanisms for the appearance of multiple states of the Kuroshio and for low-frequency variations in the midlatitude ocean.