Nonlinear dynamo action in a precessing cylindrical container

It is numerically demonstrated by means of a magnetohydrodynamics (MHD) code that precession can trigger the dynamo effect in a cylindrical container. This result adds credit to the hypothesis that precession can be strong enough to be one of the sources of the dynamo action in some astrophysical bodies.Comment: 5 pages, 5 figures including subfigure

Towards an experimental von Karman dynamo: numerical studies for an optimized design

Numerical studies of a kinematic dynamo based on von Karman type flows between two counterrotating disks in a finite cylinder are reported. The flow has been optimized using a water model experiment, varying the driving impellers configuration. A solution leading to dynamo action for the mean flow has been found. This solution may be achieved in VKS2, the new sodium experiment to be performed in Cadarache, France. The optimization process is described and discussed, then the effects of adding a stationary conducting layer around the flow on the threshold, on the shape of the neutral mode and on the magnetic energy balance are studied. Finally, the possible processes involved into kinematic dynamo action in a von Karman flow are reviewed and discussed. Among the possible processes we highlight the joint effect of the boundary-layer radial velocity shear and of the Ohmic dissipation localized at the flow/outer-shell boundary

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present 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 high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence

Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of Mechanics B/Fluid

Dynamo action in finite cylinders

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

The purpose of this note is to analyze the long term stability of the Navier-Stokes equations supplemented with the Coriolis force and the stress-free boundary condition. It is shown that, if the flow domain is axisymmetric, spurious stability behaviors can occur depending whether the Coriolis force is active or not

Lagrangian particle paths and ortho-normal quaternion frames

Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an orthonormal frame attached to each Lagrangian fluid particle undergoing three-axis rotations, by using quaternions in combination with Ertel's theorem for frozen-in vorticity. The method is applicable to a wide range of Lagrangian flows including the three-dimensional Euler equations and its variants such as ideal MHD. The applicability of the quaterionic frame description to Lagrangian averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise