Drift-Rossby waves past the breaking point in zonally-dominated turbulence

The spontaneous emergence of structure is a ubiquitous process observed in fluid and plasma turbulence. These structures typically manifest as flows which remain coherent over a range of spatial and temporal scales, which resist statistically homogeneous description. This work considers the stochastically forced barotropic β-plane quasigeostrophic equations, a prototypical two-dimensional model for turbulent flows in Jovian atmospheres and a special case of the Charney-Hasegawa-Mima equations. First, analysis of direct numerical simulations demonstrate that a significant fraction of the flow energy is organized into coherent large-scale Rossby wave eigenmodes, comparable to the total energy in the zonal flows. A characterization is given for Rossby wave eigenmodes as nearly-integrable perturbations to Lagrangian flow trajectories, linking finite-dimensional deterministic Hamiltonian chaos in the plane to a laminar-to-turbulent flow transition. Poincaré section analysis of the wave-induced Lagrangian flow demonstrates that the observed large-scale Rossby waves combined with zonal flows induce flows with localized chaotic regions bounded by invariant tori, manifesting as Rossby wave breaking in the absence of critical layers. The resulting inhomogeneous mixing suggests a paradigm for the self-organization of large-scale flows beyond a zonally-averaged sense that accounts for the resilience of the observed Rossby waves. Possible extensions of the method to other plasma systems are also given.