Global fluctuations in magnetohydrodynamic dynamos

TL;DR

This paper investigates the spectral properties of magnetic energy fluctuations in various magnetohydrodynamic dynamo models, revealing colored noise behavior and explaining it through phenomenological models and turbulence theory.

Contribution

It provides new simulation results for the G.O. Roberts dynamo and convective dynamos, and links the observed spectral features to turbulence theory and phenomenological explanations.

Findings

Magnetic energy fluctuations exhibit colored noise at low frequencies.

Simulations of Roberts and convective dynamos support the spectral analysis.

Turbulence theory predicts the inertial range spectra of energy fluctuations.

Abstract

The spectrum of temporal fluctuations of total magnetic energy for several dynamo models is different from white noise at frequencies smaller than the inverse of the turnover time of the underlying turbulent velocity field. Examples for this phenomenon are known from previous work and we add in this paper simulations of the G.O. Roberts dynamo and of convectively driven dynamos in rotating spherical shells. The appearance of colored noise in the magnetic energy is explained by simple phenomenological models. The Kolmogorov theory of turbulence is used to predict the spectrum of kinetic and magnetic energy fluctuations in the inertial range.