Francky Luddens

Nonlinear dynamo action in a precessing cylindrical container.

It is numerically demonstrated by means of a magnetohydrodynamics code that precession can trigger the dynamo effect in a cylindrical container. When the Reynolds number, based on the radius of the cylinder and its angular velocity, increases, the flow, which is initially centrosymmetric, loses its stability and bifurcates to a quasiperiodic motion. This unsteady and asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field thus generated is unsteady and quadrupolar. These numerical evidences of dynamo action in a precessing cylindrical container may be useful for an experiment now planned at the Dresden sodium facility for dynamo and thermohydraulic studies in Germany.

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-Kármán-Sodium (VKS) dynamo experiment. The material properties of the flow driving impellers are modeled by means of high-conducting and high-permeability disks in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the disks are thin. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high-permeability disks yield a reduction of the critical magnetic Reynolds number Rmc for the onset of dynamo action of the simplest non-axisymmetric field mode. However, this threshold reduction is not sufficient to fully explain the VKS experiment. We show that this reduction of Rmc is influenced by small variations in the flow configuration so that the observed reduction may be changed with respect to small modifications of setup and properties of turbulence.

Effects of discontinuous magnetic permeability on magnetodynamic problems

A novel approximation technique using Lagrange finite elements is proposed to solve magneto-dynamics problems involving discontinuous magnetic permeability and non-smooth interfaces. The algorithm is validated on benchmark problems and is used for kinematic studies of the Cadarache von Karman Sodium 2 (VKS2) experimental fluid dynamo.

Nonlinear dynamo in a short Taylor–Couette setup

It is numerically demonstrated by means of a magnetohydrodynamics code that a short Taylor–Couette setup with a body force can sustain dynamo action. The magnetic threshold is comparable to what is usually obtained in spherical geometries. The linear dynamo is characterized by a rotating equatorial dipole. The nonlinear regime is characterized by fluctuating kinetic and magnetic energies and a tilted dipole whose axial component exhibits aperiodic reversals during the time evolution. These numerical evidences of dynamo action in a short Taylor–Couette setup may be useful for developing an experimental device.

Remarks on the stability of the Navier–Stokes equations supplemented with stress boundary conditions

Abstract The purpose of this note is to analyze the long term stability of the Navier–Stokes equations augmented with the Coriolis force and supplemented stress boundary conditions. It is shown that spurious stability behaviors can occur depending whether the Coriolis force is active or not when the flow domain is axisymmetric.

Nonlinear dynamo action in a cylindrical container driven by precession

Precession, which results simply from the composition of two rotations with distinct axes, is an efficient way to drive a 3D flow in a closed rigid container. Are such flows relevant to dynamo action in some astrophysical bodies? Positive answers are available for a spherical and a spheroidal containers, using parameters which are, however, not realistic. An experimental approach could be relevant to natural dynamos and seems within reach using a cylindrical container (cf. the experiment now planned at the DREsden Sodium facility for DYNamo and thermohydraulic studies in Germany (DRESDYN), F. Stefani, personal communication, 2011). Using a nonlinear magnetohydrodynamics (MHD) code (SFEMaNS), we numerically demonstrate that precession is able to drive a cylindrical dynamo.