Comptes Rendus
The dynamo effect/L'effet dynamo
Linear and non-linear features of the Taylor–Green dynamo
Comptes Rendus. Physique, Volume 9 (2008) no. 7, pp. 749-756.

The Taylor–Green flow is a model flow sharing many properties with the von Kármán flow, in which experimental turbulent dynamo action has recently been achieved. We present here recent numerical results on the Taylor–Green dynamo instability, both in the linear and non-linear regime. Various properties are considered, such as the influence of turbulence, the energy transfer between different scales, the spatial structure of the neutral mode, the nature of the bifurcation and the saturation mechanisms. We also discuss the role of the velocity fluctuations on the dynamo onset.

Un écoulement turbulent forçé par un tourbillon de type Taylor–Green, partage de nombreuses propriétés avec l'écoulement de von Kármán dans lequel une dynamo turbulente a été récemment mise en évidence expérimentalement. Nous présentons des résultats récents de dynamos numériques engendrées par des tourbillons de Taylor–Green dans les régimes linéaire et non linéaire. Nous discutons certaines de ses propriétés comme l'influence de la turbulence, le transfert d'énergie entre différentes échelles, la structure du mode neutre, la nature de la bifurcation et les mécanismes de saturation. Nous discutons également le rôle joué par les fluctuations de vitesse sur le seuil de la dynamo.

Published online:
DOI: 10.1016/j.crhy.2008.07.007
Keywords: Dynamo, Magnetohydrodynamics, Turbulence, Taylor–Green
Mot clés : Dynamo, Magnétohydrodynamique, Turbulence, Taylor–Green

Yannick Ponty 1; Pablo D. Mininni 2, 3; Jean-Philipe Laval 4; Alexandros Alexakis 1, 3; Julien Baerenzung 1, 3; François Daviaud 5; Bérengère Dubrulle 5; Jean-François Pinton 6; Héléne Politano 1; Annick Pouquet 3

1 Observatoire de la Côte d'Azur, CNRS and Université de Nice Sophia-Antipolis, BP 4229, Nice cedex 04, France
2 Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
3 NCAR, P.O. Box 3000, Boulder, Colorado 80307-3000, USA
4 Laboratoire de mécanique de Lille, CNRS, boulevard Paul-Langevin, 59655 Villeneuve d'Asq, France
5 Service de physique de l'état condensé, CNRS et CEA-Saclay, 91191 Gif-sur-Yvette, France
6 Laboratoire de physique, de l'École normale supérieure de Lyon, CNRS et Université de Lyon, 46, allée d'Italie, 69007 Lyon, France
@article{CRPHYS_2008__9_7_749_0,
     author = {Yannick Ponty and Pablo D. Mininni and Jean-Philipe Laval and Alexandros Alexakis and Julien Baerenzung and Fran\c{c}ois Daviaud and B\'ereng\`ere Dubrulle and Jean-Fran\c{c}ois Pinton and H\'el\'ene Politano and Annick Pouquet},
     title = {Linear and non-linear features of the {Taylor{\textendash}Green} dynamo},
     journal = {Comptes Rendus. Physique},
     pages = {749--756},
     publisher = {Elsevier},
     volume = {9},
     number = {7},
     year = {2008},
     doi = {10.1016/j.crhy.2008.07.007},
     language = {en},
}
TY  - JOUR
AU  - Yannick Ponty
AU  - Pablo D. Mininni
AU  - Jean-Philipe Laval
AU  - Alexandros Alexakis
AU  - Julien Baerenzung
AU  - François Daviaud
AU  - Bérengère Dubrulle
AU  - Jean-François Pinton
AU  - Héléne Politano
AU  - Annick Pouquet
TI  - Linear and non-linear features of the Taylor–Green dynamo
JO  - Comptes Rendus. Physique
PY  - 2008
SP  - 749
EP  - 756
VL  - 9
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crhy.2008.07.007
LA  - en
ID  - CRPHYS_2008__9_7_749_0
ER  - 
%0 Journal Article
%A Yannick Ponty
%A Pablo D. Mininni
%A Jean-Philipe Laval
%A Alexandros Alexakis
%A Julien Baerenzung
%A François Daviaud
%A Bérengère Dubrulle
%A Jean-François Pinton
%A Héléne Politano
%A Annick Pouquet
%T Linear and non-linear features of the Taylor–Green dynamo
%J Comptes Rendus. Physique
%D 2008
%P 749-756
%V 9
%N 7
%I Elsevier
%R 10.1016/j.crhy.2008.07.007
%G en
%F CRPHYS_2008__9_7_749_0
Yannick Ponty; Pablo D. Mininni; Jean-Philipe Laval; Alexandros Alexakis; Julien Baerenzung; François Daviaud; Bérengère Dubrulle; Jean-François Pinton; Héléne Politano; Annick Pouquet. Linear and non-linear features of the Taylor–Green dynamo. Comptes Rendus. Physique, Volume 9 (2008) no. 7, pp. 749-756. doi : 10.1016/j.crhy.2008.07.007. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2008.07.007/

[1] H.K. Moffatt; E.N. Parker Magnetic Field Generation in Electrically Conducting Fluids, Cosmical Magnetic Fields, Cambridge University Press, Cambridge, 1978

[2] P. Odier; J.-F. Pinton; S. Fauve Advection of a magnetic field by a turbulent swirling flow, Phys. Rev. E, Volume 58 (1998), pp. 7397-7401

[3] N.L. Peffley; A.B. Cawthorne; D.P. Lathrop Toward a self-generating magnetic dynamo, Phys. Rev. E, Volume 61 (2000), p. 5287

[4] M. Bourgoin; L. Marié; F. Pétrélis; C. Gasquet; A. Guiguon; J.-B. Luciani; M. Moulin; F. Namer; J. Burguete; F. Daviaud; A. Chiffaudel; S. Fauve; Ph. Odier; J.-F. Pinton MHD measurements in the von Kármán sodium experiment, Phys. Fluids, Volume 14 (2002), p. 3046

[5] M.D. Nornberg; E.J. Spence; R.D. Kendrick; C.M. Jacobson; C.B. Forest Intermittent magnetic field excitation by a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 97 (2006), p. 044503

[6] R. Stepanov; R. Volk; S. Denisov; P. Frick; V. Noskov; J.-F. Pinton Induction, helicity, and alpha effect in a toroidal screw flow of liquid gallium, Phys. Rev. E, Volume 73 (2006), p. 046310

[7] R. Volk; P. Odier; J.-F. Pinton Fluctuation of magnetic induction in von Kármán swirling flows, Phys. Fluids, Volume 18 (2006), p. 085105

[8] A. Gailitis; O. Lielausis; S. Dement'ev; A. Cifersons; G. Gerbeth; T. Gundrum; F. Stefani; M. Christen; H. Hãnel; G. Will Magnetic field saturation in the Riga dynamo experiment, Phys. Rev. Lett., Volume 86 (2001), p. 3024

[9] R. Stieglitz; U. Müller Experimental demonstration of a homogeneous two-scale dynamo, Phys. Fluids, Volume 13 (2001), p. 561

[10] R. Monchaux; M. Berhanu; M. Bourgoin; M. Moulin; Ph. Odier; J.-F. Pinton; R. Volk; S. Fauve; N. Mordant; F. Pétrélis; A. Chiffaudel; F. Daviaud; B. Dubrulle; C. Gasquet; L. Marié; F. Ravelet Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 98 (2007), p. 044502

[11] M. Berhanu; R. Monchaux; S. Fauve; N. Mordant; F. Pétrélis; A. Chiffaudel; F. Daviaud; F. Ravelet; M. Bourgoin; Ph. Odier; J.-F. Pinton; R. Volk; B. Dubrulle; L. Marie Magnetic field reversals in an experimental turbulent dynamo, Europhys. Lett., Volume 77 (2007), p. 59001

[12] J.L. Guermond; J. Léorat; C. Nore A new finite Element Method for magneto-dynamical problems: two-dimensional results, Eur. J. Mech. B/Fluids, Volume 22 (2003), p. 555

[13] A.B. Iskakov; S. Descombes; E. Dormy An integro-differential formulation for magnetic induction in bounded domains: boundary element-finite volume method, J. Comput. Phys., Volume 197 (2004), pp. 540-554

[14] J.L. Guermond; R. Laguerre; J. Léorat; C. Nore An interior penalty Galerkin method for the MHD equations in heterogeneous domains, J. Comput. Phys., Volume 221 (2007), pp. 349-369

[15] U. Frisch Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, 1996

[16] S.A. Orszag; J.S. Patterson Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys. Rev. Lett., Volume 28 (1972), pp. 76-79

[17] A. Vincent; M. Meneguzzi The spatial structure and the statistical properties of homegeneous turbulence, J. Fluid Mech., Volume 225 (1991), pp. 1-25

[18] M.E. Brachet; D.I. Meiron; S.A. Orszag; B.G. Nickel; R.H. Morf; U. Frisch Small-scale structure of the Taylor–Green vortex, J. Mech. Fluids, Volume 130 (1983), pp. 411-452

[19] M. Lesieur Turbulence in Fluids, Kluwer, 1997

[20] Y. Ponty; J.F. Pinton; H. Politano Simulation of induction at low magnetic Prandtl number, Phys. Rev. Lett., Volume 92 (2004) no. 14, p. 144503

[21] Y. Ponty; P.D. Minnini; A. Pouquet; H. Politano; D.C. Montgomery; J.-F. Pinton Numerical study of dynamo action at low magnetic Prandtl numbers, Phys. Rev. Lett., Volume 94 (2005), p. 164512

[22] D.C. Montgomery; A. Pouquet An alternative interpretation for the Holm alpha model, Phys. Fluids, Volume 14 (2002), p. 3365

[23] P.D. Mininni; D.C. Montgomery; A. Pouquet Numerical solutions of the three-dimensional magnetohydrodynamic alpha model, Phys. Rev. E, Volume 71 (2005), p. 046304

[24] J. Baerenzung; H. Politano; Y. Ponty; A. Pouquet Spectral modeling of turbulent flows and the role of helicity, Phys. Rev. E, Volume 77 (2008), p. 046303

[25] J. Baerenzung, H. Politano, Y. Ponty, A. Pouquet, Spectral modeling of magnetohydrodynamic turbulent flows, Phys. Rev. E (2008), in press

[26] S. Douady; Y. Couder; M.-E. Brachet Direct observation of the intermittency of intense vorticity filaments in turbulence, Phys. Rev. Lett., Volume 67 (1991), p. 983

[27] C. Nore; M. Brachet; H. Politano; A. Pouquet Dynamo action in the Taylor–Green vortex near threshold, Phys. Plasmas, Volume 4 (1997), p. 1

[28] C. Nore; M.-E. Brachet; H. Politano; A. Pouquet Dynamo action in a forced Taylor–Green vortex, Cargèse, France, 21–26 August 2000 (P. Chossat; D. Armbruster; I. Oprea, eds.) (Nato Science Series II), Volume vol. 26, Kluwer Academic, Dordrecht (2001), pp. 51-58 (Proceedings of the Nato Advanced Research Workshop)

[29] J. Clyne; P.D. Mininni; A. Norton; M. Rast Interactive desktop analysis of high resolution simulations: application to turbulent plume dynamics and current sheet formation, New J. Phys., Volume 9 (2007), p. 301

[30] B. Dubrulle; P. Blaineau; O. Mafra Lopes; F. Daviaud; J.-P. Laval; R. Dolganov Bifurcations and dynamo action in a Taylor–Green flow, New J. Phys., Volume 9 (2007), p. 308

[31] Y. Ponty; P.D. Minnini; J.-F. Pinton; H. Politano; A. Pouquet Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions, New J. Phys., Volume 9 (2007), p. 296

[32] J.-P. Laval; P. Blaineau; N. Leprovost; B. Dubrulle; F. Daviaud Influence of turbulence on the dynamo threshold, Phys. Rev. Lett., Volume 96 (2006), p. 204503

[33] L. Marié; J. Burgete; F. Daviaud; J. Léorat Numerical study of homogeneous dynamo based on experimental von Karman type flows, Eur. Phys. J. B, Volume 33 (2003), p. 469

[34] F. Ravelet; A. Chiffaudel; F. Daviaud; J. Léorat Toward an experimental von Kármán dynamo: Numerical studies for an optimized design, Phys. Fluids, Volume 17 (2005), p. 117104

[35] P.D. Mininni; Y. Ponty; D.C. Montgomery; J.-F. Pinton; H. Politano; A. Pouquet Dynamo regimes with a non-helical forcing, Astrophys. J., Volume 626 (2005), pp. 853-863

[36] N.H. Brummell; F. Cattaneo; S.M. Tobias Linear and nonlinear dynamo properties of time-dependent ABC flows, Fluid Dynam. Res., Volume 28 (2001), pp. 237-265

[37] Y. Ponty; J.-P. Laval; B. Dubrulle; F. Daviaud; J.-F. Pinton Subcritical dynamo bifurcation in the Taylor–Green flow, Phys. Rev. Lett., Volume 99 (2007), p. 224501

[38] A. Alexakis; P.D. Mininni; A. Pouquet Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence, Phys. Rev. E, Volume 72 (2005), p. 046301

[39] P. Mininni; A. Alexakis; A. Pouquet Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo, Phys. Rev. E, Volume 72 (2005), p. 046302

[40] A. Alexakis; P.D. Mininni; A. Pouquet Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics, New J. Phys., Volume 9 (2007), p. 298

[41] A.A. Schekochihin; A.B. Iskakov; S.C. Cowley; J.C. McWilliams; M.R.E. Proctor; T.A. Yousef Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers, New J. Phys., Volume 9 (2007), p. 300

[42] U.R. Christensen; P. Olson; G.A. Glatzmaier Numerical modeling of the geodynamo: A systematic parameter study, Geophys. J. Int., Volume 138 (1999), p. 393

[43] S. Stellmach; U. Hansen Cartesian convection driven dynamos at low Ekman number, Phys. Rev. E, Volume 70 (2004), p. 056312

[44] V. Morin, Ph.D. Thesis, University Paris VI, 2005

[45] M. Berhanu, R. Monchaux, M. Bourgoin, Ph. Odier, J.-F. Pinton, N. Plihon, R. Volk, S. Fauve, N. Mordant, F. Pétrélis, S. Aumaître, A. Chiffaudel, F. Daviaud, B. Dubrulle, F. Ravelet, Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium, Europhys. Lett. (03/2008), submitted for publication

Cited by Sources:

Comments - Policy