Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model

TL;DR

This paper uses a shell model to explore multiscaling behaviors in 3D Hall-MHD turbulence, revealing complex scaling laws and aiding interpretation of solar wind data.

Contribution

It introduces a shell-model approach to study multiscaling in Hall-MHD turbulence, providing new insights into structure function scaling behaviors.

Findings

Shell model captures multiscaling in velocity and magnetic fields.

Extended-self-similarity helps reveal multiscaling in high-$k$ regimes.

Results relate to observed solar-wind turbulence features.

Abstract

We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-$k$ and high-$k$ power-law ranges of 3D Hall-MHD, and find that the extended-self-similarity (ESS) procedure is helpful in extracting the multiscaling nature of structure functions in the high-$k$ regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.