[Étude linéaire et non linéaire d'une dynamo produite par un forçage de Taylor–Green]
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.
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.
Mot clés : Dynamo, Magnétohydrodynamique, Turbulence, Taylor–Green
@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] Magnetic Field Generation in Electrically Conducting Fluids, Cosmical Magnetic Fields, Cambridge University Press, Cambridge, 1978
[2] Advection of a magnetic field by a turbulent swirling flow, Phys. Rev. E, Volume 58 (1998), pp. 7397-7401
[3] Toward a self-generating magnetic dynamo, Phys. Rev. E, Volume 61 (2000), p. 5287
[4] MHD measurements in the von Kármán sodium experiment, Phys. Fluids, Volume 14 (2002), p. 3046
[5] Intermittent magnetic field excitation by a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 97 (2006), p. 044503
[6] Induction, helicity, and alpha effect in a toroidal screw flow of liquid gallium, Phys. Rev. E, Volume 73 (2006), p. 046310
[7] Fluctuation of magnetic induction in von Kármán swirling flows, Phys. Fluids, Volume 18 (2006), p. 085105
[8] Magnetic field saturation in the Riga dynamo experiment, Phys. Rev. Lett., Volume 86 (2001), p. 3024
[9] Experimental demonstration of a homogeneous two-scale dynamo, Phys. Fluids, Volume 13 (2001), p. 561
[10] Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 98 (2007), p. 044502
[11] Magnetic field reversals in an experimental turbulent dynamo, Europhys. Lett., Volume 77 (2007), p. 59001
[12] A new finite Element Method for magneto-dynamical problems: two-dimensional results, Eur. J. Mech. B/Fluids, Volume 22 (2003), p. 555
[13] 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] An interior penalty Galerkin method for the MHD equations in heterogeneous domains, J. Comput. Phys., Volume 221 (2007), pp. 349-369
[15] Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, 1996
[16] Numerical simulation of three-dimensional homogeneous isotropic turbulence, Phys. Rev. Lett., Volume 28 (1972), pp. 76-79
[17] The spatial structure and the statistical properties of homegeneous turbulence, J. Fluid Mech., Volume 225 (1991), pp. 1-25
[18] Small-scale structure of the Taylor–Green vortex, J. Mech. Fluids, Volume 130 (1983), pp. 411-452
[19] Turbulence in Fluids, Kluwer, 1997
[20] Simulation of induction at low magnetic Prandtl number, Phys. Rev. Lett., Volume 92 (2004) no. 14, p. 144503
[21] Numerical study of dynamo action at low magnetic Prandtl numbers, Phys. Rev. Lett., Volume 94 (2005), p. 164512
[22] An alternative interpretation for the Holm alpha model, Phys. Fluids, Volume 14 (2002), p. 3365
[23] Numerical solutions of the three-dimensional magnetohydrodynamic alpha model, Phys. Rev. E, Volume 71 (2005), p. 046304
[24] 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] Direct observation of the intermittency of intense vorticity filaments in turbulence, Phys. Rev. Lett., Volume 67 (1991), p. 983
[27] Dynamo action in the Taylor–Green vortex near threshold, Phys. Plasmas, Volume 4 (1997), p. 1
[28] 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] 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] Bifurcations and dynamo action in a Taylor–Green flow, New J. Phys., Volume 9 (2007), p. 308
[31] Dynamo action at low magnetic Prandtl numbers: mean flow versus fully turbulent motions, New J. Phys., Volume 9 (2007), p. 296
[32] Influence of turbulence on the dynamo threshold, Phys. Rev. Lett., Volume 96 (2006), p. 204503
[33] Numerical study of homogeneous dynamo based on experimental von Karman type flows, Eur. Phys. J. B, Volume 33 (2003), p. 469
[34] Toward an experimental von Kármán dynamo: Numerical studies for an optimized design, Phys. Fluids, Volume 17 (2005), p. 117104
[35] Dynamo regimes with a non-helical forcing, Astrophys. J., Volume 626 (2005), pp. 853-863
[36] Linear and nonlinear dynamo properties of time-dependent ABC flows, Fluid Dynam. Res., Volume 28 (2001), pp. 237-265
[37] Subcritical dynamo bifurcation in the Taylor–Green flow, Phys. Rev. Lett., Volume 99 (2007), p. 224501
[38] Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence, Phys. Rev. E, Volume 72 (2005), p. 046301
[39] Shell-to-shell energy transfer in magnetohydrodynamics. II. Kinematic dynamo, Phys. Rev. E, Volume 72 (2005), p. 046302
[40] Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics, New J. Phys., Volume 9 (2007), p. 298
[41] Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers, New J. Phys., Volume 9 (2007), p. 300
[42] Numerical modeling of the geodynamo: A systematic parameter study, Geophys. J. Int., Volume 138 (1999), p. 393
[43] 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
Cité par Sources :
Commentaires - Politique
Interplay between experimental and numerical approaches in the fluid dynamo problem
Jacques Léorat; Caroline Nore
C. R. Phys (2008)
The VKS experiment: turbulent dynamical dynamos
Sébastien Aumaître; Michael Berhanu; Mickael Bourgoin; ...
C. R. Phys (2008)