Norman Cao will speak at the Courant PIs Workshop on Wednesday, November 30th at 3:15pm
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 conducts a computational and theoretical study of coherence in turbulent flows in the stochastically forced barotropic β-plane quasigeostrophic (QG) equations. These equations serve as a prototypical two-dimensional model for turbulent flows in Jovian atmospheres, and can also be extended to study flows in magnetically confined fusion plasmas. 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 reveals that Lagrangian flows induced by the zonal flows plus large-scale waves exhibit localized chaotic regions bounded by invariant tori, manifesting as Rossby wave breaking in the absence of critical layers. The resulting inhomogeneous mixing is linked to a form of stability for certain eigenmodes under the large-scale flow, suggesting a self-organization principle for large-scale flows that accounts for the resilience of the observed large-amplitude Rossby waves.