Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux

TL;DR

This paper develops turbulence models for quasi-static MHD that incorporate variable energy flux caused by Joule dissipation, explaining the steeper spectra observed experimentally and numerically.

Contribution

It introduces two models based on energy flux variations to explain the steeper spectra in quasi-static MHD turbulence across different interaction parameters.

Findings

Power-law spectrum with steeper than -5/3 exponent at small interaction parameters

Exponential energy spectrum at large interaction parameters

Model predictions agree well with numerical simulations

Abstract

In quasi-static MHD, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explain this observation, we construct turbulence models based on variable energy flux, which is caused by the Joule dissipation. In the first model, which is applicable to small interaction parameters, the energy spectrum is a power law, but with a spectral exponent steeper than -5/3. In the other limit of large interaction parameters, the second model predicts an exponential energy spectrum and flux. The model predictions are in good agreement with the numerical results.