Dynamos in precessing cubes

O Goepfert,A Tilgner

doi:10.1088/1367-2630/18/10/103019

Abstract

We investigate with numerical simulations the dynamo properties of liquid flows in precessing cubes. There are some similarities with the flow in precessing spheres. Instabilities in the form of triad resonances are observed. The flow is turbulent far above the onset of instability but simplifies to a single vortex for certain control parameters. The critical magnetic Reynolds numbers for the onset of magnetic field generation are lower than, but comparable to, the numbers known for precessing spheres, and are larger than the Reynolds numbers realizable in an experiment currently under construction in Dresden.

Highlights

The dynamo mechanism is generally believed to be responsible for the generation of magnetic fields in planets and stars
Precession driven motion was demonstrated numerically to allow for dynamo action in spheres [1, 2], ellipsoids [3], plane layers [4] and cylinders [5], and tidally [6], libration [7] and collision driven dynamos [8] exist, too
The study of convection driven dynamos is far more advanced than the investigation of mechanically forced dynamos. This is partly due to the fact that numerical simulations of convective dynamos are less demanding

Summary

Introduction

The dynamo mechanism is generally believed to be responsible for the generation of magnetic fields in planets and stars In this scenario, the kinetic energy of the motion of an electrically conducting fluid is transformed into magnetic energy. The study of convection driven dynamos is far more advanced than the investigation of mechanically forced dynamos. Precession on the contrary is unable to maintain a stationary state with a non-trivial motion in a liquid filled container with stress free boundaries rotating about an axis of symmetry [9]. The rationale of the present paper is to find a system which allows to investigate precession dynamos in laminar and if possible turbulent states with minimal numerical effort, which means with stress free boundaries. The subsequent sections will study in turn the laminar flow, its hydrodynamic instability, and the kinematic dynamo effect

Mathematical model and numerical methods

W cos a

Hydrodynamics

Kinematic dynamos

Findings

Conclusions