Abstract

Abstract. The rapid rotation of planets causes cyclonic thermal turbulence in their cores which may generate the large-scale magnetic fields observed outside the planets. We investigate numerically a model based on the geodynamo equations in simplified geometry, which enables us to reproduce the main features of small-scale geostrophic flows in physical and wave vector spaces. We find fluxes of kinetic and magnetic energy as a function of the wave number and demonstrate the co-existence of forward and inverse cascades. We also explain the mechanism of magnetic field saturation at the end of the kinematic dynamo regime.

Highlights

  • Many astrophysical objects such as galaxies, stars, the Earth, and some planets have large-scale magnetic fields that are believed to be generated by a common universal mechanism – the conversion of kinetic energy into magnetic energy in a turbulent rotating shell

  • We examine the origin of the magnetic energy on scale 1/k: Is it connected with the energy transfer from the other scales or is it a product of real generation on this scale?

  • In contrast to TK, TN has no positive regions at small k, i.e. the inverse cascade of the magnetic energy, related to the advective term in this region is absent

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Summary

Introduction

Many astrophysical objects such as galaxies, stars, the Earth, and some planets have large-scale magnetic fields that are believed to be generated by a common universal mechanism – the conversion of kinetic energy into magnetic energy in a turbulent rotating shell. Calculations for an entire planet are done using either spectral models (Kono and Roberts, 2002) finite-volume methods (Hejda and Reshetnyak, 2004; Harden and Hansen, 2005) or finite differences (Kageyama and Sato, 1997) and have demonstrated beyond reasonable doubt that the turbulent 3-D convection of the conductive fluid can generate a large-scale magnetic field similar to the one associated with small random fluctuations. Both of these methods cannot cover the enormous span of scales required for a realistic parameter set.

Equations in physical space
Equations in wave space
Basic properties of the fields
Energy fluxes
Findings
Conclusions
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