Establish a rigorous theoretical basis for intermittency in magnetohydrodynamic turbulence

Establish a rigorous theoretical framework that explains intermittency in magnetohydrodynamic turbulence, demonstrating the fundamental principles and conditions under which intermittency arises and is maintained, analogous to or distinct from hydrodynamic turbulence, given that such a theoretical basis remains unproven.

Background

Intermittency—characterized by nonuniform, bursty dissipation and non-Gaussian statistics—is a central feature of both hydrodynamic and magnetohydrodynamic (MHD) turbulence. Empirical and simulation evidence links intermittency in MHD to structures such as current sheets and reconnection sites, but a rigorous theoretical foundation remains lacking.

A formal theory would unify phenomenological models and observations, clarify scaling relations, and support quantitative predictions across fluid and plasma environments, including the solar wind.

References

However, again one should note that the theoretical basis for intermittency in MHD remains unproven, as it is in hydrodynamics.

— Evaluation of scale-dependent kurtosis with HelioSwarm  (2407.06679 - Pecora et al., 2024) in Section 1: Introduction

The underlying open problem being intermittency, that is, the absence of statistical self-similarity across scales, a characteristic feature of strongly turbulent flows that so far eludes theoretical understanding and results in considerable difficulty in the derivation of a fundamental `theory of turbulence' and of high-fidelity turbulence models.

— Lagrangian Curvature Statistics from Gaussian Subensembles in Turbulent Flows  (2608.23198 - Hengster et al., 24 Aug 2026) in Section 1, Introduction

The variability of the Elsasser spectra is not fully explained theoretically as far as we are aware, and so far appears to be an indicator of the lack of universality in MHD and plasma turbulence.

— First Observation of a Polar Coronal Hole-like Fast Solar Wind Stream in the Sub-Alfvénic Solar Corona: an Analysis of Turbulence Properties  (2609.26720 - Bandyopadhyay et al., 22 Sep 2026) in Section 3, Discussion of Fig. 3 (the Elsasser spectra)