Transitions of zonal flows in a two-layer quasi-geostrophic ocean model

We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by steady Kolmogorov wind stress in periodic channel domain, which allows to mathematically study nonlinear development of resulting flow. The supports parallel shear flow as response stress. As maximal velocity (equivalently amplitude forcing) exceeds critical threshold, zonal jet destabilizes due baroclinic instability and we numerically demonstrate that first transition occurs. obtain reduced equations system using formalism dynamic theory establish two scenarios completely describe this transition. generic scenario conjugate pair modes loses stability Hopf bifurcation occurs result. Under an appropriate set parameters describing related midlatitude oceanic flows, show continuous: supercritical stable time solution bifurcates. also investigate case double bifurcations occur when four linear problem simultaneously destabilize jet. In case, prove that, relevant parameter regime, exhibits continuous accompanied bifurcated attractor homeomorphic \(S^3\). topological structure analyzed detail shown depend on parameters. particular, contains (stable or unstable) time-periodic solutions quasi-periodic solution.