A nested polyhedra model of isotropic MHD turbulence

TL;DR

This paper introduces a nested polyhedra model for isotropic MHD turbulence that produces a stationary $k^{-5/3}$ spectrum and maintains statistical isotropy without biasing helicity or scale interactions.

Contribution

The paper presents a novel nested polyhedra model for MHD turbulence that naturally enforces isotropy and avoids helicity bias, providing insights into energy spectra and scale interactions.

Findings

Achieves a stationary $k^{-5/3}$ energy spectrum for kinetic and magnetic energies.

Demonstrates isotropy and scale interaction properties of the model.

Shows a $k^{-1/2}$ scaling for the time scale of equipartition offset.

Abstract

A nested polyhedra model has been developed for magnetohydrodynamic (MHD) turbulence. Driving only the velocity field at large scales with random, divergence free forcing results in a clear, stationary $k^{-5/3}$ spectrum for both kinetic and magnetic energies. Since the model naturaly effaces disparate scale interactions, does not have a guide field and avoids injecting any sign of helicity by random forcing, the resulting three dimensional k-spectrum is statistically isotropic. The strengths and weaknesses of the model are demonstrated by considering large or small magnetic Prandtl numbers. It was also observed that the time scale for the equipartition offset with those of the smallest scales shows a $k^{-1/2}$ scaling.