Nearly-integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence

Turbulent flows frequently exhibit spatiotemporal intermittency, reflecting a complex interplay between driving forces, dissipation, and transport. This intermittency often manifests as observable structures and patterns in the flow, introducing nontrivial statistical correlations that are challenging to understand and model. In this work, we use dynamical systems techniques to study the Dimits shift regime of the flux-balanced Hasegawa-Wakatani (BHW) equations, which models a transitional regime of resistive drift-wave turbulence. We show in direct numerical simulations that turbulence in this regime is dominated by strong zonal flows and coherent drift-wave vortex structures which maintain a strong linear character despite their large amplitude. Using the framework of generalized Liouville integrability, we develop a theory of integrable Lagrangian flows in generic fluid and plasma systems and discuss how the zonal flows plus drift waves exhibit a form of "near-integrability" originating from a fluid element relabeling symmetry. We further demonstrate that the BHW flows transition from integrability to chaos via the formation of chaotic tangles in the aperiodic Lagrangian flow, and establish a direct link between the 'lobes' associated with these tangles and intermittency in the turbulence statistics. This illustrates how studying the convective nonlinearity with dynamical systems theory can explain aspects of spatiotemporal intermittency in complex turbulent flows.