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The Von Karman Sodium Experiment The von Karman Sodium experiment: Turbulent dynamical dynamos Romain Monchaux, Michaël Berhanu, Sébastien Aumaître, Arnaud Chiffaudel, François Daviaud, Bérengère Dubrulle, Florent Ravelet, Stéphan Fauve, Nicolas Mordant, François Pétrélis, et al. To cite this version: Romain Monchaux, Michaël Berhanu, Sébastien Aumaître, Arnaud Chiffaudel, François Daviaud, et al.. The von Karman Sodium experiment: Turbulent dynamical dynamos. Physics of Fluids, American Institute of Physics, 2010, 21 (3), pp.035108. 10.1063/1.3085724. hal-00492266 HAL Id: hal-00492266 https://hal.archives-ouvertes.fr/hal-00492266 Submitted on 15 Jun 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICS OF FLUIDS 21, 035108 ͑2009͒ The von Kármán Sodium experiment: Turbulent dynamical dynamos Romain Monchaux,1 Michael Berhanu,2 Sébastien Aumaître,1 Arnaud Chiffaudel,1 François Daviaud,1 Bérengère Dubrulle,1 Florent Ravelet,1 Stephan Fauve,2 Nicolas Mordant,2 François Pétrélis,2 Mickael Bourgoin,3 Philippe Odier,3 Jean-François Pinton,3 Nicolas Plihon,3 and Romain Volk3 1CEA, IRAMIS, Service de Physique de l’Etat Condensé, CNRS URA 2464, CEA Saclay, F-91191 Gif-sur-Yvette, France 2Laboratoire de Physique Statistique, CNRS and École Normale Supérieure, 24 rue Lhomond, F-75005 Paris, France 3Laboratoire de Physique de l’École Normale Supérieure de Lyon, CNRS and Université de Lyon, F-69364 Lyon, France ͑Received 7 July 2008; accepted 19 January 2009; published online 30 March 2009; publisher error corrected 2 April 2009͒ The von Kármán Sodium ͑VKS͒ experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers ͑the von Kármán geometry͒. We first report observations related to the self-generation of a stationary dynamo when the flow forcing is ␲-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities.R The bifurcation is found to be supercritical with a neutral mode whose geometry is predominantly axisymmetric. We then report the different dynamical dynamo regimes observed when the flow forcing is not symmetric, including magnetic field reversals. We finally show that these dynamics display characteristic features of low dimensional dynamical systems despite the high degree of turbulence in the flow. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3085724͔ I. INTRODUCTION Roberts’ scheme11 and again the dynamo onset and magnetic A. Experimental dynamos field characteristics have been accurately predicted numerically.12–15 1 Although it was almost a century ago that Larmor pro- The approach adopted in the von Kármán Sodium ͑VKS͒ posed that a magnetic field could be self-sustained by the 2 experiments builds up on the above results. In order to access motions of an electrically conducting fluid, the experimental various dynamical regimes above dynamo onset,16–18 it uses demonstrations of this principle are quite recent. Using solid less constrained flow generators but keeps helicity and dif- rotor motions, Lowes and Wilkinson realized the first ͑nearly 3 ferential rotation as the main ingredients for the generation homogeneous experimental dynamo in 1963; a subcritical 19,20 ͒ of magnetic field. It does not rely on analytical predic- bifurcation to a stationary magnetic field was generated and tions from model flows, although, as discussed later, many of oscillations were later observed in an improved setup in its magnetohydrodynamics ͑MHD͒ features have been dis- which the angle between the rotors could be adjusted.4 In this cussed using kinematic or direct simulations of model situa- experiment, the main induction source lies in the axial dif- tions. In the first versions of VKS experiment—VKS1, be- ferential rotation between the rotor and the stationary soft tween 2000 and 2002 and VKS2, between 2005 and July iron. Observations of fluid dynamos, however, did not occur before 2000 with the Riga and Karlsruhe experiments. In 2006—all materials used had the same magnetic permeabil- Riga, the dynamo is generated by the screw motion of liquid ity ͑␮r Ӎ1͒. However none of these configurations suc- sodium. The flow is a helicoidal jet confined within a bath of ceeded in providing dynamo action: the present paper ana- liquid sodium at rest.5 The induction processes are the dif- lyzes dynamo regimes observed in the VKS2 setup when the ferential rotation and the shear associated with the screw liquid sodium is stirred with pure soft-iron impellers ͑␮r motion at the lateral boundary. The dynamo field has a heli- ϳ100͒. Although the VKS2 dynamo is therefore not fully cal geometry and is time periodic. The bifurcation threshold homogeneous, it involves fluid motions that are much more and geometry of the neutral mode trace back to Ponomaren- fluctuating than in previous experiments. The role of the fer- ko’s analytical study6 and have been computed accurately romagnetic impellers is at present not fully understood, but is with model velocity profiles7 or from Reynolds-averaged thoroughly discussed in the text. Navier–Stokes numerical simulations.8,9 The Karlsruhe Below, we will first describe the experimental setup and dynamo10 is based on scale separation, the flow being gen- flow features. We then describe and discuss in detail in Sec. erated by motions of liquid sodium in an array of screw II our observations of the dynamo generated when the im- generators with like-sign helicity. The magnetic field at onset pellers that drive the flow are in exact counter-rotation. In is stationary and its large scale component is transverse to this case the self-sustained magnetic field is statistically sta- the axis of the flow generators. The arrangement follows tionary in time. We describe in Sec. III the dynamical re- 1070-6631/2009/21͑3͒/035108/21/$25.0021, 035108-1 © 2009 American Institute of Physics Downloaded 20 May 2009 to 194.254.66.253. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp 035108-2 Monchaux et al. Phys. Fluids 21, 035108 ͑2009͒ gimes observed for asymmetric forcing conditions, i.e., when Oil cooling circulation the impeller rotation rates differ. Concluding remarks are P1 given in Sec. IV. P2 z B. The VKS experiment P3 P4 155 0.75 The VKS experiment studies MHD in a sodium flow y x generated inside a cylinder by counter-rotation of impellers R 1.00 located near the end plates. This flow has two main charac- 206 teristics which have motivated its choice. First, its time- 5 78 averaged velocity field has both helicity and differential ro- Na at rest 0.4 tation, as measured in Refs. 21–23, two features that have 2 41 long been believed to favor dynamo action. Second, the von 40 61 185 0.90 0.30 Kármán geometry generates a very intense turbulence in a 16 24–31 r θ compact volume of space. x P The topology of the time-averaged velocity field has re- z ceived much attention because it is similar to the s2t2 flow 32 y x considered in a sphere by Dudley and James. This topology 1 2 generates a stationary kinematic dynamo33–35 whose main component is a dipole perpendicular to the rotation axis ͑an z “m=1” mode in cylindrical coordinates . The threshold, in 3 4 ͒ y x magnetic Reynolds number, for kinematic dynamo genera- 5 tion is very sensitive to details of the mean flow such as the poloidal to toroidal velocity ratio,33–35 the electrical bound- ary conditions,34–38 or the details of the velocity profile near the impellers.38 Specific choices in the actual flow configu- ration have been based on a careful optimization of the ki- 22,35 nematic dynamo capacity of the VKS mean flow. The FIG. 1. ͑Color online͒ Experimental setup. Note the curved impellers, the above numerical studies do not take into account the fully inner copper cylinder which separates the flow volume from the blanket of developed turbulence of the von Kármán flows, for which surrounding sodium, and the thin annulus in the midplane. Also shown are the holes through which the 3D Hall probes are inserted into the copper velocity fluctuations can be on the order of the mean. In vessel for magnetic measurements. Location in ͑r/R,␪,x/R͒ coordinates actual laboratory conditions the magnetic Prandtl number of of available measurement points: P1͑1,␲/2,0͒, P2͑1,␲/2,0.53͒, −5 the fluid is very small ͑about 10 for sodium͒ so that the P3͑0.25,␲/2,−0.53͒, P4͑0.25,␲/2,0.53͒, and P5͑1,␲,0͒͑see Table I for details concerning available measurements in different experimental runs͒. kinetic Reynolds number must be indeed huge in order to When referring to the coordinates of magnetic field vector B measured in generate even moderate magnetic Reynolds numbers. A fully the experiment at these different points, we will use either the Cartesian realistic numerical treatment of the von Kármán flows is out projection ͑Bx ,By ,Bx͒ on the frame ͑x,y,z͒ or the cylindrical projection of reach. The influence of turbulence on the dynamo onset ͑Br ,B␪ ,Bx͒ on the frame ͑r,␪,x͒͑B␪ =−By and Br =Bz for measurements at 39–41 points P1, P2, and P3͒. We will use in figures the following color code for has thus been studied using model behaviors or numeri- the magnetic field components: axial ͑x͒ in blue, azimuthal ͑y͒ in red, and 42–44 cal simulations in the related Taylor–Green ͑TG͒ flow.
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