Comptes Rendus
no. 2
Third-order Elsässer moments in axisymmetric MHD turbulence
[Moments dʼElsässer du troisième ordre en turbulence MHD axisymétrique]
Sébastien Galtier1, 2
1 Univ Paris-Sud, institut dʼastrophysique spatiale, UMR 8617, bâtiment 121, 91405 Orsay cedex, France
2 Institut universitaire de France
Comptes Rendus. Physique, Volume 12 (2011) no. 2, pp. 151-159.

La turbulence MHD incompressible est étudiée en présence dʼun champ magnétique uniforme B0. Une telle situation est décrite dans lʼespace des corrélations par une relation de divergence qui exprime la conservation statistique du flux dʼénergie dʼElsässer à travers la zone inertielle. Nous faisons lʼansatz que lʼanisotropie, observée quand B0 est suffisamment fort, implique un feuilletage de lʼespace des corrélations. Une conséquence directe est la possibilité dʼobtenir une nouvelle loi vectorielle pour les moments dʼElsässer dʼordre trois qui est paramétrisée par lʼintensité de lʼanisotropie. Nous utilisons lʼhypothèse dʼéquilibre critique pour fixer ce paramètre et trouver une expression unique.

Incompressible MHD turbulence is investigated under the presence of a uniform magnetic field B0. Such a situation is described in the correlation space by a divergence relation which expresses the statistical conservation of the Elsässer energy flux through the inertial range. The ansatz is made that the development of anisotropy, observed when B0 is strong enough, implies a foliation of space correlation. A direct consequence is the possibility to derive a vectorial law for third-order Elsässer moments which is parametrized by the intensity of anisotropy. We use the so-called critical balance assumption to fix this parameter and find a unique expression.

Publié le :
DOI : 10.1016/j.crhy.2010.11.006
Keywords: MHD, Solar wind, Turbulence
Mot clés : MHD, Turbulence, Vent solaire
Sébastien Galtier 1, 2

1 Univ Paris-Sud, institut dʼastrophysique spatiale, UMR 8617, bâtiment 121, 91405 Orsay cedex, France
2 Institut universitaire de France 
@article{CRPHYS_2011__12_2_151_0,
     author = {S\'ebastien Galtier},
     title = {Third-order {Els\"asser} moments in axisymmetric {MHD} turbulence},
     journal = {Comptes Rendus. Physique},
     pages = {151--159},
     publisher = {Elsevier},
     volume = {12},
     number = {2},
     year = {2011},
     doi = {10.1016/j.crhy.2010.11.006},
     language = {en},
}
TY  - JOUR
AU  - Sébastien Galtier
TI  - Third-order Elsässer moments in axisymmetric MHD turbulence
JO  - Comptes Rendus. Physique
PY  - 2011
SP  - 151
EP  - 159
VL  - 12
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crhy.2010.11.006
LA  - en
ID  - CRPHYS_2011__12_2_151_0
ER  - 
%0 Journal Article
%A Sébastien Galtier
%T Third-order Elsässer moments in axisymmetric MHD turbulence
%J Comptes Rendus. Physique
%D 2011
%P 151-159
%V 12
%N 2
%I Elsevier
%R 10.1016/j.crhy.2010.11.006
%G en
%F CRPHYS_2011__12_2_151_0
Sébastien Galtier. Third-order Elsässer moments in axisymmetric MHD turbulence. Comptes Rendus. Physique, Volume 12 (2011) no. 2, pp. 151-159. doi : 10.1016/j.crhy.2010.11.006. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.11.006/

[1] U. Frisch Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge, 1995

[2] A.N. Kolmogorov Dissipation of energy in locally isotropic turbulence, Dokl. Akad. Nauk SSSR, Volume 32 (1941), pp. 16-18

[3] A.S. Monin; A.M. Yaglom, Statistical Fluid Mechanics, vol. 2, MIT Press, Cambridge MA, 1975

[4] A.M. Yaglom Local structure of the temperature field in a turbulent flow, Dokl. Akad. Nauk SSSR, Volume 69 (1949), pp. 743-746

[5] H. Politano; A. Pouquet Dynamical length scales for turbulent magnetized flows, Geophys. Res. Lett., Volume 25 (1998), pp. 273-276

[6] S. Galtier Exact scaling laws for 3D electron MHD turbulence, J. Geophys. Res., Volume 113 (2008), p. A01102

[7] S. Galtier von Kármán–Howarth equations for Hall magnetohydrodynamic flows, Phys. Rev. E, Volume 77 (2008), p. 015302(R)

[8] S. Galtier Exact vectorial law for axisymmetric MHD turbulence, Astrophys. J., Volume 704 (2009), pp. 1371-1384

[9] S. Galtier Consequence of space correlation foliation for EMHD turbulence, Phys. Plasmas, Volume 16 (2009), p. 112310

[10] P. Iroshnikov Turbulence of a conducting fluid in a strong magnetic field, Sov. Astron., Volume 7 (1964), pp. 566-571

[11] R.H. Kraichnan Inertial-range spectrum of hydromagnetic turbulence, Phys. Fluids, Volume 8 (1965), pp. 1385-1387

[12] S. Galtier et al. A weak turbulence theory for incompressible MHD, J. Plasma Phys., Volume 63 (2000), pp. 447-488

[13] J. Cho; E.T. Vishniac The anisotropy of MHD Alfvénic turbulence, Astrophys. J., Volume 539 (2000), pp. 273-282

[14] S. Boldyrev Spectrum of magnetohydrodynamic turbulence, Phys. Rev. Lett., Volume 96 (2006), p. 115002

[15] A. Alexakis; P.D. Mininni; A. Pouquet Turbulent cascades, transfer, and scale interactions in MHD, New J. Phys., Volume 9 (2007), pp. 298-318

[16] A. Alexakis et al. Anisotropic fluxes and nonlocal interactions in MHD turbulence, Phys. Rev. E, Volume 76 (2007), p. 056313

[17] B. Bigot; S. Galtier; H. Politano Energy decay laws in strongly anisotropic MHD turbulence, Phys. Rev. Lett., Volume 100 (2008), p. 074502

[18] B. Bigot; S. Galtier; H. Politano Development of anisotropy in incompressible MHD turbulence, Phys. Rev. E, Volume 78 (2008), p. 066301

[19] P. Goldreich; S. Sridhar Toward a theory of interstellar turbulence. II. Strong alfvénic turbulence, Astrophys. J., Volume 438 (1995), pp. 763-775

[20] S. Galtier; A. Pouquet; A. Mangeney On spectral scaling laws for incompressible anisotropic MHD turbulence, Phys. Plasmas, Volume 12 (2005), p. 092310

[21] J. Maron; P. Goldreich Simulations of incompressible MHD turbulence, Astrophys. J., Volume 554 (2001), pp. 1175-1196

[22] L.J. Milano et al. Local anisotropy in incompressible MHD turbulence, Phys. Plasmas, Volume 8 (2001), pp. 2673-2681

[23] C.S. Ng et al. Anisotropic fluid turbulence in the interstellar medium and solar wind, Phys. Plasmas, Volume 10 (2003), pp. 1954-1962

[24] J.J. Podesta; M.A. Forman; C.W. Smith Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric MHD turbulence, Phys. Plasmas, Volume 14 (2007), p. 092305

[25] S. Galtier Wave turbulence in incompressible Hall MHD, J. Plasma Phys., Volume 72 (2006), pp. 721-769

[26] S. Galtier Wave turbulence in magnetized plasmas, Nonlin. Processes Geophys., Volume 16 (2009), pp. 83-98

[27] L. Klein et al. Anisotropy and minimum variance of MHD fluctuations in the inner heliosphere, J. Geophys. Res., Volume 98 (1993), pp. 17461-17466

[28] J.W. Bieber; W. Wanner; W.H. Matthaeus Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport, J. Geophys. Res., Volume 101 (1996), pp. 2511-2522

[29] L. Sorriso-Valvo et al. Observation of inertial energy cascade in interplanetary space plasma, Phys. Rev. Lett., Volume 99 (2007), p. 115001

[30] V. Carbone et al. Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations, Phys. Rev. Lett., Volume 103 (2009), p. 061102

[31] R. Marino et al. Heating the solar wind by a MHD turbulent energy cascade, Astrophys. J., Volume 677 (2008), p. L71-L74

[32] R.A. Antonia et al. Analogy between predictions of Kolmogorov and Yaglom, J. Fluid Mech., Volume 332 (1997), pp. 395-409

[33] P.D. Mininni; A.G. Pouquet; D. Montgomery Small-scale structures in three-dimensional MHD turbulence, Phys. Rev. Lett., Volume 97 (2006), p. 244503

[34] J.J. Podesta et al. Scale-dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence, J. Geophys. Res., Volume 114 (2008), p. A01107

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

CFD for turbulence: from fundamentals to geophysics and astrophysics

Claude Cambon; Alejandro Alvarez Laguna; Ye Zhou

C. R. Méca (2022)

Observation and theoretical modeling of electron scale solar wind turbulence

Fouad Sahraoui; Melvyn L. Goldstein; K. Abdul-Kader; ...

C. R. Phys (2011)