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

TL;DR

This paper investigates the transition from near-integrability to chaos in plasma turbulence within the Dimits shift regime, linking dynamical systems theory to observed intermittency and coherent structures in turbulence.

Contribution

It introduces a theoretical framework based on generalized Liouville integrability to explain the emergence of chaos and intermittency in plasma edge turbulence.

Findings

Turbulence is dominated by zonal flows and drift-wave vortices with strong linear character.

Transition to chaos occurs via chaotic tangles in Lagrangian flow, linked to intermittency.

Theoretical link between integrability, chaos, and turbulent intermittency in plasma systems.

Abstract

Transitionally turbulent flows frequently exhibit spatiotemporal intermittency, reflecting a complex interplay between driving forces, dissipation, and transport present in these systems. When this intermittency manifests as observable structures and patterns in the flow, the characterization of turbulence in these systems becomes challenging due to the nontrivial correlations introduced into the statistics of the turbulence by these structures. In this work, we use tools from dynamical systems theory to study intermittency in the Dimits shift regime of the flux-balanced Hasegawa-Wakatani (BHW) equations, which models a transitional regime of resistive drift-wave turbulence relevant to magnetically confined fusion plasmas. First, 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 observed zonal flows plus drift waves in the BHW system 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 observed turbulent dissipation. This illustrates how utilizing tools from deterministic dynamical systems theory to study convective nonlinearities can explain aspects of intermittent spatiotemporal structure exhibited by the statistics of turbulent fields.