The Problem of Marginality in Model Reductions of Turbulence

TL;DR

This paper evaluates the accuracy of reduced quasilinear and nonlinear turbulence models in magnetised plasmas, highlighting their limitations near marginal stability and proposing improvements for better flux prediction.

Contribution

It compares reduced and nonlinear models across different turbulence regimes, revealing their strengths and weaknesses, especially near marginal stability.

Findings

Reduced models agree well above threshold.

Near marginality, reduced models underpredict fluxes.

Mesoscale flow organization is crucial for accurate flux modeling.

Abstract

Reduced quasilinear (QL) and nonlinear (gradient-driven) models with scale separations, commonly used to interpret experiments and to forecast turbulent transport levels in magnetised plasmas are tested against nonlinear models without scale separations (flux-driven). Two distinct regimes of turbulence -- either far above threshold or near marginal stability -- are investigated with Boltzmann electrons. The success of reduced models especially hinges on the reproduction of nonlinear fluxes. Good agreement between models is found above threshold whilst reduced models would significantly underpredict fluxes near marginality, overlooking mesoscale flow organisation and turbulence self-advection. Constructive prescriptions whereby to improve reduced models is discussed.