The von Kármán Sodium experiment: Turbulent dynamical dynamos

The von Karman Sodium (VKS) experiment studies dynamo action in the flow generated inside a cylinder filled with liquid sodium by the rotation of coaxial impellers (the von Karman geometry). We first report observations related to the self-generation of a stationary dynamo when the flow forcing is R-pi-symmetric, i.e., when the impellers rotate in opposite directions at equal angular velocities. 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.

[1]  Sasa Kenjeres,et al.  Numerical insights into magnetic dynamo action in a turbulent regime , 2007 .

[2]  J. Duistermaat,et al.  Geomagnetic reversals and the stochastic exit problem , 2004 .

[3]  C. Jones,et al.  A convection driven geodynamo reversal model , 1999 .

[4]  H. K. Moffatt.  Magnetic Field Generation in Electrically Conducting Fluids , 1978 .

[5]  J. Pinton,et al.  Fluctuation of magnetic induction in von Kármán swirling flows , 2005, physics/0511204.

[6]  J. Valet.  Time variations in geomagnetic intensity , 2003 .

[7]  M D Nornberg,et al.  Turbulent diamagnetism in flowing liquid sodium. , 2007, Physical review letters.

[8]  R. Stepanov,et al.  Mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  F. Daviaud,et al.  Experimental measurement of the scale-by-scale momentum transport budget in a turbulent shear flow , 2004 .

[10]  J. Larmor.  17. How Could a Rotating Body such as the Sun Become a Magnet , 1979 .

[11]  L. Meynadier,et al.  Geomagnetic dipole strength and reversal rate over the past two million years , 2005, Nature.

[12]  M D Nornberg,et al.  Intermittent magnetic field excitation by a turbulent flow of liquid sodium. , 2006, Physical review letters.

[13]  F. Daviaud,et al.  Supercritical transition to turbulence in an inertially driven von Kármán closed flow , 2008, Journal of Fluid Mechanics.

[14]  Wetting and particle adsorption in nanoflows , 2004, cond-mat/0406291.

[15]  G. Roberts,et al.  Dynamo action of fluid motions with two-dimensional periodicity , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[16]  M. Brachet,et al.  Dynamo action in the Taylor-Green vortex near threshold , 1997 .

[17]  S Kenjeres,et al.  Numerical simulation of a turbulent magnetic dynamo. , 2007, Physical review letters.

[18]  J. McWilliams,et al.  Critical magnetic Prandtl number for small-scale dynamo. , 2003, Physical review letters.

[19]  J. Pinton,et al.  Characterization of Turbulence in a Closed Flow , 1997 .

[20]  Patrick Tabeling,et al.  Statistics of Turbulence between Two Counterrotating Disks in Low-Temperature Helium Gas , 1994 .

[21]  S. Fauve,et al.  On the magnetic fields generated by experimental dynamos , 2007, 0709.0234.

[22]  A. Tilgner.  A kinematic dynamo with a small scale velocity field , 1997 .

[23]  B. Dubrulle,et al.  Magnetic field reversals in an experimental turbulent dynamo , 2007, physics/0701076.

[24]  Romain Monchaux.  Mécanique statistique et effet dynamo dans un écoulement de von Karman turbulent , 2007 .

[25]  Thomas M. Antonsen,et al.  Blowout bifurcations and the onset of magnetic dynamo action , 2001 .

[26]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[27]  J. Pinton,et al.  Dynamo action in an annular array of helical vortices , 2008 .

[28]  F. Plunian,et al.  Subharmonic Dynamo Action in the Roberts Flow , 2002 .

[29]  P. Chossat,et al.  Dynamo and dynamics, a mathematical challenge , 2001 .

[30]  D. Lathrop,et al.  Characterization of experimental dynamos , 2000 .

[31]  B. Dubrulle,et al.  Bifurcations and dynamo action in a Taylor–Green flow , 2007 .

[32]  R. Stieglitz,et al.  Experimental demonstration of a homogeneous two-scale dynamo , 2000 .

[33]  S. Fauve,et al.  Inhibition of the dynamo effect by phase fluctuations , 2006 .

[34]  F. Lowes,et al.  Geomagnetic Dynamo: An Improved Laboratory Model , 1968, Nature.

[35]  Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model. , 2004, Physical review letters.

[36]  S. I. Braginskii.  KINEMATIC MODELS OF THE EARTH'S HYDROMAGNETIC DYNAMO , 1964 .

[37]  S. Fauve,et al.  Saturation of the magnetic field above the dynamo threshold , 2001 .

[38]  Walden,et al.  Traveling waves and chaos in convection in binary fluid mixtures. , 1985, Physical review letters.

[39]  J. Burguete,et al.  Numerical study of homogeneous dynamo based on experimental von Kármán type flows , 2003, physics/0301032.

[40]  V. Kirk,et al.  Chaotically modulated stellar dynamos , 1995 .

[41]  E. Dormy,et al.  Numerical models of the geodynamo and observational constraints , 2000 .

[42]  Jean-François Pinton,et al.  Simulation of induction at low magnetic Prandtl number. , 2004, Physical review letters.

[43]  W. Shew,et al.  Laboratory experiments on the transition to MHD dynamos , 2001 .

[44]  G. Gerbeth,et al.  Riga Dynamo Experiment , 2001 .

[45]  Jean-François Pinton,et al.  Correction to the Taylor hypothesis in swirling flows , 1994 .

[46]  Y. Ponty,et al.  Dynamo Regimes with a Nonhelical Forcing , 2005 .

[47]  Yu. B. Ponomarenko,et al.  Theory of the hydromagnetic generator , 1973 .

[48]  J. Guermond,et al.  Impact of impellers on the axisymmetric magnetic mode in the VKS2 dynamo experiment. , 2008, Physical review letters.

[49]  F. Stefani,et al.  Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment , 2006 .

[50]  B. Dubrulle,et al.  Properties of steady states in turbulent axisymmetric flows. , 2006, Physical review letters.

[51]  L. Marié.  Transport de moment cinétique et de champ magnétique par un écoulement tourbillonnaire turbulent : influence de la rotation , 2003 .

[52]  Florent Ravelet.  Bifurcations globales hydrodynamiques et magnetohydrodynamiques dans un ecoulement de von Karman turbulent , 2005 .

[53]  A. Chiffaudel,et al.  Toward an experimental von Kármán dynamo: Numerical studies for an optimized design , 2004, physics/0411213.

[54]  S. Fauve,et al.  Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows , 2008, 0804.1923.

[55]  Florent Ravelet,et al.  Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium , 2009, Journal of Fluid Mechanics.

[56]  Y. Couder,et al.  Direct observation of the intermittency of intense vorticity filaments in turbulence. , 1991, Physical review letters.

[57]  Perrin,et al.  Competing instabilities in a rotating layer of mercury heated from below. , 1985, Physical review letters.

[58]  R. W. James,et al.  Time-dependent kinematic dynamos with stationary flows , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[59]  J. Pinton,et al.  Transport of magnetic field by a turbulent flow of liquid sodium. , 2006, Physical review letters.

[60]  E. Parker.  Hydromagnetic Dynamo Models , 1955 .

[61]  J. Pinton,et al.  An iterative study of time independent induction effects in magnetohydrodynamics , 2004 .

[62]  B Dubrulle,et al.  Influence of turbulence on the dynamo threshold. , 2006, Physical review letters.

[63]  T Gundrum,et al.  Magnetic field saturation in the Riga dynamo experiment. , 2001, Physical review letters.

[64]  S. Fauve,et al.  The Dynamo Effect , 2003 .

[65]  Matthias Rheinhardt,et al.  The Karlsruhe Dynamo Experiment. A Mean Field Approach , 1998 .

[66]  Dynamics of polar reversals in spherical dynamos , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[67]  S. Fauve,et al.  Pressure fluctuations in swirling turbulent flows , 1993 .

[68]  R Volk,et al.  Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. , 2007, Physical review letters.

[69]  C. B. Forest,et al.  Measurements of the magnetic field induced by a turbulent flow of liquid metal , 2006 .

[70]  G. Hammett,et al.  A model of nonlinear evolution and saturation of the turbulent MHD dynamo , 2002, astro-ph/0207503.

[71]  Lathrop,et al.  Toward a self-generating magnetic dynamo: the role of turbulence , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[72]  M. Proctor,et al.  A Heteroclinic model of geodynamo reversals and excursions , 2001 .

[73]  Y. Ponty,et al.  Numerical study of dynamo action at low magnetic Prandtl numbers. , 2004, Physical review letters.

[74]  I. Wilkinson,et al.  Geomagnetic Dynamo: A Laboratory Model , 1963, Nature.

[75]  E. Ott,et al.  Blowout bifurcations and the onset of magnetic activity in turbulent dynamos. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  Slow dynamics in a turbulent von Kármán swirling flow. , 2007, Physical review letters.

[77]  J. Pinton,et al.  Magnetohydrodynamics measurements in the von Kármán sodium experiment , 2002 .

[78]  J. Pinton,et al.  Induction, helicity, and alpha effect in a toroidal screw flow of liquid gallium. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[79]  F. Plunian,et al.  Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[80]  E. Knobloch,et al.  A new model of the solar cycle , 1996 .

[81]  J. Pinton,et al.  ADVECTION OF A MAGNETIC FIELD BY A TURBULENT SWIRLING FLOW , 1998 .

[82]  J. Pinton,et al.  Chaotic dynamos generated by a turbulent flow of liquid sodium. , 2008, Physical review letters.

[83]  J. Pinton,et al.  An experimental Bullard–von Kármán dynamo , 2006 .

[84]  G. Gerbeth,et al.  The Riga Dynamo Experiment , 2003 .

[85]  M. Brachet.  Direct simulation of three-dimensional turbulence in the Taylor–Green vortex , 1991 .

[86]  Florent Ravelet,et al.  Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. , 2004, Physical review letters.

[87]  F. Daviaud,et al.  Galerkin analysis of kinematic dynamos in the von Kármán geometry , 2006 .

[88]  Rehberg,et al.  Experimental observation of a codimension-two bifurcation in a binary fluid mixture. , 1985, Physical review letters.

[89]  B. Dubrulle,et al.  Normalized kinetic energy as a hydrodynamical global quantity for inhomogeneous anisotropic turbulence , 2009 .

[90]  J. Pinton,et al.  Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow. , 2003, Physical review letters.

[91]  J. Pinton,et al.  Power Fluctuations in Turbulent Swirling Flows , 1996 .