BxC: a swift generator for 3D magnetohydrodynamic turbulence

TL;DR

This paper introduces a fast, analytic generator for realistic 3D magnetohydrodynamic turbulence fields, enabling quick simulations that match detailed numerical results and facilitate turbulence research.

Contribution

The authors present a novel, efficient model for generating realistic 3D MHD turbulence fields that closely replicate DNS results, reducing computational costs significantly.

Findings

Generated fields match DNS in structural and spectral properties

Model reproduces statistical distributions of magnetic and current fields

Allows for synthetic, time-evolving turbulent data simulations

Abstract

Magnetohydrodynamic turbulence is central to laboratory and astrophysical plasmas, and is invoked for interpreting many observed scalings. Verifying predicted scaling law behaviour requires extreme-resolution direct numerical simulations (DNS), with needed computing resources excluding systematic parameter surveys. We here present an analytic generator of realistically looking turbulent magnetic fields, that computes 3D ${\cal{O}}(1000^3)$ solenoidal vector fields in minutes to hours on desktops. Our model is inspired by recent developments in 3D incompressible fluid turbulence theory, where a Gaussian white noise vector subjected to a non-linear transformation results in an intermittent, multifractal random field. Our $B\times C$ model has only few parameters that have clear geometric interpretations. We directly compare a (costly) DNS with a swiftly $B\times C$-generated realization, in terms of its (i) characteristic sheet-like structures of current density, (ii) volume-filling aspects across current intensity, (iii) power-spectral behaviour, (iv) probability distribution functions of increments for magnetic field and current density, structure functions, spectra of exponents, and (v) partial variance of increments. The model even allows to mimic time-evolving magnetic and current density distributions and can be used for synthetic observations on 3D turbulent data cubes.