508
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

A review of relaxation and structure in some turbulent plasmas: magnetohydrodynamics and related models

, , &
Article: N37 | Received 16 Apr 2012, Accepted 13 Jun 2012, Published online: 03 Sep 2012

References

  • Alexakis , A. , Mininni , P. D. and Pouquet , A. 2005 . Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence . Phys. Rev. , E 72 : 046301
  • Alexakis , A. , Bigot , B. , Politano , H. and Galtier , S. 2007 . Anisotropic fluxes and nonlocal interactions in magnetohydrodynamic turbulence . Phys. Rev. , E 76 : 056313
  • Alexandrova , O. , Saur , J. , Lacombe , C. , Mangeney , A. , Mitchell , J. , Schwartz , S. J. and Robert , P. 2009 . Universality of solar-wind turbulent spectrum from MHD to electron scales . Phys. Rev. Lett. , 103 : 165003
  • Bale , S. D. , Kasper , J. C. , Howes , G.G. , Quataert , E. , Salem , C. and Sundkvist , D. 2009 . Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind . Phys. Rev. Lett. , 103 : 211101
  • Balogh , A. , Carr , C. M. , Acuña , M. H. , Dunlop , M. W. , Beek , T. J. , Brown , P. , Fornacon , K.-H. , Georgescu , E. , Glassmeier , K.-H. , Harris , J. , Musmann , G. , Oddy , T. and Schwingenschuh , K. 2001 . The Cluster magnetic field investigation: overview of in-flight performance and initial results . Ann. Geophys. , 19 : 1207
  • Barnes , A. 1968 . Collisionless heating of the solar-wind plasma, 1. Theory of the heating of collisionless plasma by hydromagnetic waves . Astrophys. J. , 154 : 751
  • Barnes , A. 1979 . “ Hydromagnetic waves and turbulence in the solar wind ” . In Solar System Plasma Physics , Edited by: Parker , E. N. , Kennel , C. F. and Lanzerotti , L. J. 251 Amsterdam, North-Holland : Elsevier Science .
  • Batchelor , G. K. 1968 . Computation of the energy spectrum in homogeneous two-dimensional turbulence . Phys. Fluids , 12 : II – 233 .
  • Bavassano , B. , Dobrowolny , M. , Mariani , F. and Ness , N. F. 1982 . Radial evolution of power spectra of interplanetary Alfvénic turbulence . J. Geophys. Res. , 87 : 3617
  • Bavassano , B. , Dobrowolny , M. , Fanfoni , G. , Mariani , F. and Ness , N. F. 1982 . Statistical properties of MHD fluctuations associated with high-speed streams from Helios-2 observations . Sol. Phys. , 78 : 373
  • Bavassano , B. and Smith , E. J. 1986 . Radial variation of interplanetary alfvénic fluctuations: Pioneer 10 and 11 observations between 1 and 5 AU . J. Geophys. Res. , 91 : 1706
  • Belcher , J. W. and Davis , L. Jr . 1971 . Large-amplitude Alfvén waves in the interplanetary medium, 2 . J. Geophys. Res. , 76 : 3534
  • Beresnyak , A. and Lazarian , A. 2009 . Structure of stationary strong imbalanced turbulence . Astrophys. J. , 702 : 460
  • Bieber , J. W. , Matthaeus , W. H. , Smith , C. W. , Wanner , W. , Kallenrode , M. and Wibberenz , G. 1994 . Proton and electron mean free paths: The Palmer consensus revisited . Astrophys. J. , 420 : 294
  • Bieber , J. W. , Wanner , W. and Matthaeus , W. H. 1996 . Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport . J. Geophys. Res. , 101 : 2511
  • Biskamp , D. and Welter , H. 1989 . Dynamics of decaying two-dimensional magnetohydrodynamic turbulence . Phys. Fluids , B 1 : 1964
  • Biskamp , D. and Muller , W.-C. 2000 . Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence . Phys. Plasmas , 7 : 4889
  • Biskamp , D. 2003 . Magnetohydrodynamic Turbulence , Cambridge : Cambridge University Press .
  • Bondeson , A. , Marklin , G. , An , Z.G. , Chen , H.H. , Lee , Y.C. and Liu , C.S. 1981 . Tilting instability of a cylindrical spheromak . Phys. Fluids , 24 : 1682
  • Brachet , M. , Meneguzzi , M. , Politano , H. and Sulem , P.-L. 1988 . The dynamics of freely decaying two-dimensional turbulence . J. Fluid Mech. , 194 : 333
  • Brands , H. , Stulemeyer , J. , Pasmanter , R. A. and Schep , T. J. 1997 . A mean field prediction of the asymptotic state of decaying 2D turbulence . Phys. Fluids , 9 : 2815
  • Brands , H. , Chavanis , P. H. , Pasmanter , R. and Sommeria , J. 1999 . Maximum entropy verses minimum enstrophy vortices . Phys. Plasmas , 11 : 3465
  • Breech , B.B. , Matthaeus , W. H. , Minnie , J. , Bieber , J. W. , Oughton , S. , Smith , C. W. and Isenberg , P.A. 2008 . Turbulence transport throughout the heliosphere . J. Geophys. Res. , 113 : A08105
  • Breech , B. , Matthaeus , W. H. , Cranmer , S.R. , Kasper , J. C. and Oughton , S. 2009 . Electron and proton heating by solar wind turbulence . J. Greophys. Res. , 114 : A09103
  • Brown , M. R. 1996 . Experimental evidence of rapid relaxation to large scale structures in turbulent fluids: Selective decay and maximal entropy . J. Plasma Phys. , 57 : 203
  • Brown , M. R. 1999 . Experimental studies of magnetic reconnection . Phys. Plasmas , 6 : 1717
  • Bruno , R. , Bavassano , B. and Villante , U. 1985 . Evidence for long period Alfvén waves in the inner solar system . J. Geophys. Res. , 90 : 4373
  • Bruno , R. , Carbone , V. , Veltri , P. , Pietropaolo , E. and Bavassano , B. 2001 . Identifying intermittency events in the solar wind . Planet. Space Sci. , 49 : 1201
  • Bruno , R. and Carbone , V. 2005 . The solar wind as a turbulence laboratory . Living Rev. Sol. Phys. , 2 : 4 Available at http://www.livingreviews.org/lrsp-2005-4
  • Burlaga , L. F. 1968 . Micro-scale structures in the interplanetary medium . Sol. Phys. , 4 : 67
  • Burlaga , L. F. 1969 . Directional discontinuities in the interplanetary magnetic field . Sol. Phys., , 7 : 54
  • Burlaga , L. F. 1991 . Intermittent turbulence in the solar wind . J. Geophys. Res. , 96 : 5847
  • Carbone , V. , Veltri , P. and Mangeney , A. 1990 . Coherent structure formation and magnetic field line reconnection in magnetohydrodynamic turbulence . Phys. Fluids , A 2 : 1487
  • Chandrasekhar , S. and Woltjer , L. 1958 . On force-free magnetic fields . Proc. Natl. Acad. Sci. USA , 44 : 285
  • Chen , S. and Kraichnan , R. H. 1997 . Inhibition of turbulent cascade by sweep . J. Plasma Phys. , 57 : 187
  • Clercx , H.J. H. , Maassen , S. R. and van Heijst , G.J. F. 1998 . Spontaneous spin-up during the decay of of 2D turbulence in a square container with rigid boundaries . Phys. Rev. Lett. , 80 : 5129
  • Coleman , P. J. 1968 . Turbulence, viscosity, and dissipation in the solar-wind plasma . Astrophys. J. , 153 : 371
  • Cranmer , S.R. 2009 . Coronal holes . Living Rev. Sol. Phys. , 6
  • Cranmer , S. R. , Matthaeus , W. H. , Breech , B. A. and Kasper , J. C. 2009 . Empirical constraints on proton and electron heating in the fast solar wind . Astrophys. J. , 702 : 1604
  • Dmitruk , P. and Matthaeus , W. H. 2007 . Low-frequency 1/f fluctuations in hydrodynamic and magnetohydrodynamic turbulence . Phys. Rev. , E 76 : 036305
  • Dmitruk , P. , Mininni , P. D. , Pouquet , A. , Servidio , S. and Matthaeus , W. H. 2011 . Emergence of very long time fluctuations and 1/f noise in ideal flows . Phys. Rev. , E 83 : 066318
  • Dobrowolny , M. , Mangeney , A. and Veltri , P. 1980 . Fully developed anisotropic hydromagnetic turbulence in interplanetary space . Phys. Rev. Lett. , 45 : 144
  • Driscoll , C. F. and Fine , K. S. 1990 . Experiments on vortex dynamics in pure electron plasmas . Phys. Fluids , B 2 : 1359
  • Elsasser , W. M. 1950 . The hydromagnetic equations . Phys. Rev. , 79 : 183
  • Frisch , U. 1995 . Turbulence , Cambridge : Cambridge University Press .
  • Frisch , U. , Pouquet , A. , Léorat , J. and Mazure , A. 1975 . Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence . J. Fluid Mech. , 68 : 769
  • Meneguzzi , U.Frisch, A.Pouquet, P.-L.Sulem, M. 1983 . The dynamics of two-dimensional ideal MHD . J. Mech. Theor. Appl. , 2 : 191
  • Fyfe , D. and Montgomery , D. 1976 . High beta turbulence in two-dimensional magnetohydrodynamics . J. Plasma Phys. , 16 : 181 – 191 .
  • Fyfe , D. , Joyce , G. and Montgomery , D. 1977 . Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics . J. Plasma Phys. , 17 : 317
  • Fyfe , D. , Montgomery , D. and Joyce , G. 1977 . Dissipative, forced turbulence in two-dimensional magnetohydrodynamics . J. Plasma Phys. , 17 : 369
  • Gallay , T. and Wayne , C. E. 2005 . Global stability of vortex solutions of the twodimensional navier-stokes equation . Commun. Math. Phys. , 255 : 97
  • Galtier , S. , Politano , H. and Pouquet , A. 1997 . Self-similar energy decay in magnetohydrodynamic turbulence . Phys. Rev. Lett. , 79 : 2807
  • Galtier , S. 2009 . Exact vectorial law for axisymmetric magnetohydrodynamics turbulence . Astrophys. J. , 704 : 1371
  • Goldreich , P. and Sridhar , S. 1995 . Toward a theory of interstellar turbulence: II. Strong Alfvénic turbulence . Astrophys. J. , 438 : 763
  • Grappin , R. , Frisch , U. , Léorat , J. and Pouquet , A. 1982 . Alfvénic fluctuations as asymptotic states of MHD turbulence . Astron. Astrophys. , 105 : 6
  • Greco , A. , Chuychai , P. , Matthaeus , W. H. , Servidio , S. and Dmitruk , P. 2008 . Intermittent MHD structures and classical discontinuities . Geophys. Res. Lett. , 35 : L19111
  • Greco , A. , Matthaeus , W. H. , Servidio , S. , Chuychai , P. and Dmitruk , P. 2009 . Statistical analysis of discontinuities in solar wind ACE data and comparison with intermittent MHD turbulence . Astrophys. J. , 691 : L111
  • Hamilton , K. , Smith , C. W. , Vasquez , B.J. and Leamon , R.J. 2008 . Anisotropies and helicities in the solar wind inertial and dissipation ranges at 1  AU . J. Geophys. Res. , 113 : A01106
  • van Heijst , G.J. F. , Clercx , H.J. H. and Molenaar , D. 2006 . The effects of solid boundaries on confined two-dimensional turbulence . J. Fluid Mech. , 554 : 411
  • Hollweg , J. V. 1973 . Alfvén waves in the solar wind: Wave pressure, Poynting flux, and angular momentum . J. Geophys. Res. , 78 : 3643
  • Horbury , T. A. , Balogh , A. , Forsyth , R. J. and Smith , E. J. 1997 . Ulysses observations of intermittent heliospheric turbulence . Adv. Space Phys. , 19 : 847
  • Horton , W. 1999 . Drift waves and transport . Rev. Mod. Phys. , 71 : 735
  • Hossain , M. , Gray , P. C. , Pontius , D. H. , Matthaeus , Jr, W.H. and Oughton , S. 1995 . Phenomenology for the decay of energy-containing eddies in homogeneous MHD turbulence . Phys. Fluids , 7 : 2886
  • Huang , X.-P. and Driscoll , C. F. 1994 . Relaxation of 2D turbulence to a metaequilibrium near the minimum enstrophy state . Phys. Rev. Lett. , 72 : 2187
  • Iroshnikov , P. S. 1964 . Turbulence of a conducting fluid in a strong magnetic field . Sov. Astron. , 7 : 566
  • de Kármán , T. and Howarth , L. 1938 . On the statistical theory of isotropic turbulence . Proc. R. Soc. Lond. , A 164 : 192
  • Kerr , R. M. 1987 . Histograms of helicity and strain in numerical turbulence . Phys. Rev. Lett. , 59 : 783
  • Kolmogorov , A.N. 1941 . Dissipation of energy in the locally isotropic turbulence . C. R. Acad. Sci. U.R.S.S. , 32 : 16 [Reprinted in Proc. R. Soc. London, Ser. A 434 (1991), p. 15]
  • Kolmogorov , A. N. 1962 . A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number . J. Fluid Mech. , 12 : 82
  • Kraichnan , R. H. 1973 . Helical turbulence and absolute equilibrium . J. Fluid Mech. , 59 : 745
  • Kraichnan , R. H. 1965 . Inertial-range spectrum of hydromagnetic turbulence . Phys. Fluids , 8 : 1385
  • Kraichnan , R. H. 1967 . Inertial ranges in two-dimensional turbulence . Phys. Fluids , 10 : 1417
  • Kraichnan , R. H. and Nagarajan , S. 1967 . Growth of turbulent magnetic fields . Phys. Fluids , 10 : 859
  • Kraichnan , R. H. 1975 . Statistical dynamics of two-dimensional flow . J. Fluid Mech. , 67 : 155
  • Kraichnan , R. H. and Panda , R. 1988 . Depression of nonlinearity in decaying isotropic turbulence . Phys. Fluids , 31 : 2395
  • Kriesel , J. M. and Driscoll , C. F. 2001 . Measurements of viscosity in pure-electron plasmas . Phys. Rev. Lett. , 87 : 135003
  • Leamon , R. J. , Smith , C. W. , Ness , N. F. , Matthaeus , W. H. and Wong , H. K. 1998 . Observational constraints on the dynamics of the interplanetary magnetic field dissipation range . J. Geophys. Res. , 103 : 4775
  • Leamon , R.J. , Smith , C. W. , Ness , N.F. and Wong , H.K. 1999 . Dissipation range dynamics: Kinetic Alfvén waves and the importance of β e . J. Geophys. Res. , 104 : 22331
  • Leamon , R. J. , Matthaeus , W. H. , Smith , C. W. , Zank , G. P. , Mullan , D. J. and Oughton , S. 2000 . MHD-driven kinetic dissipation in the solar wind and corona . Astrophys. J. , 537 : 1054
  • Lee , T. D. 1952 . On some statistical properties of hydrodynamical and magneto-hydrodynamical fields . Q. Appl. Math. , 10 : 69
  • Lee , E. , Brachet , M.E. , Pouquet , A. , Mininni , P. D. and Rosenberg , D. 2010 . Lack of universality in decaying magnetohydrodynamic turbulence . Phys. Rev. , E 81 : 016318
  • Lesieur , M. 1990 . Turbulence in Fluids , 2nd ed. Kluwer, Dordrecht , , The Netherlands
  • Li , S. and Montgomery , D.C. 1996 . Decaying two-dimensional turbulence with rigid walls . Phys. Lett. A 218 , : 281 A222, 461 (1996) (erratum).
  • Li , S. , Montgomery , D. C. and Jones , W.B. 1997 . Two dimensional turbulence with rigid, circular walls . Theor. Comput. Fluid Dyn. , 9 : 167
  • MacBride , B. T. , Forman , M. A. and Smith , C. W. 2005 . “ Turbulence and third moment of fluctuations: Kolmogorov’s 4/5 law and its MHD analogues in the solar wind ” . In Proceedings Solar Wind 11: Connecting Sun and Heliosphere , Edited by: Fleck , B. and Zurbuchen , T.H. 613 EuropeanSpaceAgency , , TheNetherlands : (ESASP-592) .
  • MacBride , B. T. , Smith , C. W. and Forman , M. A. 2008 . The turbulent cascade at 1 AU: Energy transfer and the third-order scaling for MHD . Astrophys. J. , 679 : 1644
  • Marsch , E. and Tu , C.-Y. 1994 . Non-Gaussian probability distributions of solar wind fluctuations . Ann. Geophys. , 12 : 1127
  • Marsch , E. 2006 . Kinetic physics of the solar corona and solar wind . Living Rev. Solar Phys. , 3 : 1 Available at http://www.livingreviews.org/lrsp-2006-1
  • Mason , J. , Cattaneo , F. and Boldyrev , S. 2006 . Dynamic alignment in driven magnetohydrodynamic turbulence . Phys. Rev. Lett. , 97 : 255002
  • Matthaeus , W. H. and Montgomery , D. 1980 . Selective decay hypothesis at high mechanical and magnetic reynolds numbers . Ann. New York Acad. Sci. , 357 : 203
  • Matthaeus , W. H. and Goldstein , M. L. 1982 . Measurement of the rugged invariants of magnetohydrodynamic turbulence . J. Geophys. Res. , 87 : 6011
  • Matthaeus , W. H. and Montgomery , D. 1984 . “ Dynamic alignment and selective decay in MHD ” . In Statistical Physics and Chaos in Fusion Plasmas , Edited by: Horton , C. W. and Reichl , Jr., L.E. 285 – 291 . New York : Wiley .
  • Matthaeus , W. H. , Goldstein , M.L. and Roberts , D. A. 1990 . Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind . J. Geophys. Res. , 95 : 20673
  • Matthaeus , W. H. , Stribling , W. T. , Martínez , D. , Oughton , S. and Montgomery , D. 1991 . Selective decay and coherent vortices in two-dimensional incompressible turbulence . Phys. Rev. Lett. , 66 : 2731
  • Matthaeus , W. H. , Dasso , S. , Weygand , J. M. , Milano , L. J. , Smith , C. W. and Kivelson , M.G. 2005 . Spatial correlation of solar-wind turbulence from two-point measurements . Phys. Rev. Lett. , 95 : 231101
  • Matthaeus , W. H. , Breech , B. , Dmitruk , P. , Bemporad , A. , Poletto , G. , Velli , M. and Romoli , M. 2007 . Density and magnetic field signatures of interplanetary 1/f noise . Astrophys. J. , 657 : L121
  • Matthaeus , W. H. , Pouquet , A. , Mininni , P. D. , Dmitruk , P. and Breech , B. 2008 . Rapid alignment of velocity and magnetic field in magnetohydrodynamic turbulence . Phys. Rev. Lett. , 100 : 085003
  • McWilliams , J. C. 1984 . Emergence of isolated coherent vortices in turbulent flow . J. Fluid Mech. , 146 : 21
  • Merrifield , J.A. , Müller , W.-C. , Chapman , S.C. and Dendy , R.O. 2005 . The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence . Phys. Plasmas , 12 : 022301
  • Mininni , P. D. , Gómez , D.O. and Mahajan , S.M. 2002 . Dynamo action in hall magnetohydrodynamics . Astrophys. J. , 567 : L81
  • Mininni , P. D. , Montgomery , D. and Pouquet , A. 2005 . A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows . Phys. Fluids , 17 : 035112
  • Mininni , P. D. and Pouquet , A. 2009 . Finite dissipation and intermittency in magnetohydrodynamics . Phys. Rev. , E 80 : 025401
  • Mininni , P. 2011 . Scale interactions in magnetohydrodynamic turbulence . Ann. Rev. Fluid Mech. , 43 : 377
  • Mininni , P. D. , Dmitruk , P. , Matthaeus , W. H. and Pouquet , A. 2011 . Large-scale behavior and statistical equilibria in rotating flows . Phys. Rev. , E 83 : 016309
  • Mitchell , T.B. , Wang , X.J. and Rossi , L.F. October 2006 . “ Stability of elliptical electron vortices ” . In Non-Neutral Plasma Physics VI , Edited by: Drewsen , M. , Uggerhoj , U. and Knudsen , H. Vol. 862 , 29 – 38 . American Institute of Physics Conference Series .
  • Moffatt , H. K. 1978 . Magnetic Field Generation in Electrically Conducting Fluids , New York : CUP .
  • Monin , A.S. and Yaglom , A.M. 1971, 1975 . “ Statistical Fluid Mechanics ” . Vol. 1 and 2 , Cambridge , MA : MIT Press .
  • Joyce , G. and Montgomery , D. 1973 . Negative temperature states for the two-dimensional guiding-centre plasma . J. Plasma Phys. , 10 : 107
  • Montgomery , D. , Turner , L. and Vahala , G. 1978 . Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry . Phys. Fluids , 21 : 757
  • Montgomery , D. , Turner , L. and Vahala , G. 1979 . Most probable states in magnetohydrodynamics . J. Plasma Phys. , 21 : 239
  • Montgomery , D. C. 1982 . Major disruptions, inverse cascades, and the strauss equations . Phys. Scr. , T2 : 83
  • Montgomery , D. C. , Shan , X. and Matthaeus , W. H. 1993 . Navier-stokes relaxation to sinh-poisson states at finite reynolds numbers . Phys. Fluids , A 5 : 2207
  • Montgomery , D. , Matthaeus , W. H. , Stribling , W. T. , Martinez , D. and Oughton , S. 1992 . Relaxation in two dimensions and the sinh-poisson equation . Phys. Fluids , A 4 : 3
  • Montgomery , D. C. and Bates , J. W. 1999 . The geometry and symmetries of magnetohydrodynamic turbulence: Anomalies of spatial periodicity . Phys. Plasmas , 6 : 2727
  • Montgomery , D.C. and Matthaeus , W. H. 2011 . Oseen vortex as a maximum entropy state of a two dimensional fluid . Phys. Fluids , 23 : 075104
  • Ness , N.F. and Burlaga , L.F. 2001 . Spacecraft studies of the interplanetary magnetic field . J. Geophys. Res. , 106 : 15803
  • Neugebauer , M. 2006 . Comment on the abundances of rotational and tangential discontinuities in the solar wind . J. Geophys. Res. , 111 : A04103
  • Nelkin , M. 1994 . Universality and scaling in fully developed turbulence . Adv. Phys. , 43 : 143
  • Ohsaki , S. and Yoshida , Z. 2005 . Variational principle with singular perturbation of hall magnetohydrodynamics . Phys. Plasmas , 12 : 064505
  • Orszag , S. A. 1970 . Analytical theories of turbulence . J. Fluid Mech. , 41 : 363
  • Osman , K.T. , Matthaeus , W. H. , Greco , A. and Servidio , S. 2011 . Evidence for inhomogeneous heating in the solar wind . Astrophys. J. , 727 : L11
  • Osman , K. T. , Wan , M. , Matthaeus , W. H. , Breech , B. and Oughton , S. 2011 . Directional alignment and non-gaussian statistics in solar wind turbulence . Astrophys. , J 741 : 75
  • Osman , K.T. , Wan , M. , Matthaeus , W. H. , Weygand , J. M. and Dasso , S. 2011 . Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using multi-spacecraft data . Phys. Rev. Lett. , 107 : 165001
  • Oughton , S. , Priest , E. R. and Matthaeus , W. H. 1994 . The influence of a mean magnetic field on three dimensional magnetohydrodynamic turbulence . J. Fluid Mech. , 280 : 95
  • Parker , E. N. 1979 . Cosmical Magnetic Fields: Their Origin and Activity , Oxford , , UK : Oxford University Press .
  • Pelz , R. B. , Yakhot , V. , Orszag , S. A. , Shtilman , L. and Levich , E. 1985 . Velocity-vorticity patterns in turbulent flow . Phys. Rev. Lett. , 54 : 2505
  • Podesta , J. , Forman , M. A. and Smith , C. W. 2007 . Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric . Phys. Plasmas , 14 : 092305
  • Podesta , J. J. 2009 . Dependence of solar-wind power spectra on the direction of the local mean magnetic field . Astrophys. J. , 698 : 986
  • Politano , H. , Pouquet , A. and Sulem , P.-L. 1989 . Inertial ranges and resistive instabilities in two-dimensional magnetohydrodynamic turbulence . Phys. Fluids , B 1 : 2990
  • Politano , H. and Pouquet , A. 1998 . Dynamical length scales for turbulent magnetized flows . Geophys. Res. Lett. , 25 : 273
  • Politano , H. , Pouquet , A. and Carbone , V. 1998 . Determination of anomalous exponents of structure functions in two-dimensional magnetohydrodynamic turbulence . Europhys. Lett. , 43 : 516
  • Ponty , Y. , Politano , H. and Pinton , J.-F. 2004 . Simulation of induction at low magnetic prandtl number . Phys. Rev. Lett. , 92 : 144503
  • Pouquet , A. , Frisch , U. and Léorat , J. 1976 . Strong MHD helical turbulence and the nonlinear dynamo effect . J. Fluid Mech. , 77 : 321
  • Pouquet , A. , Meneguzzi , M. and Frisch , U. 1986 . Growth of correlations in magnetohydrodynamic turbulence . Phys. Rev. , A 33 : 4266
  • Robert , R. and Sommeria , J. 1991 . Statistical equilibrium states for two-dimensional flows . J. Fluid Mech. , 229 : 291
  • Robert , R. and Sommeria , J. 1992 . Relaxation towards a statistical equilibrium state in two-dimensional perfect fluid dynamics . Phys. Rev. Lett. , 69 : 2776
  • Roberts , D.A. , Klein , L.W. , Goldstein , M.L. and Matthaeus , W. H. 1987 . The nature and evolution of magnetohydrodynamic fluctuations in the solar wind: Voyager observations . J. Geophys. Res. , 92 : 11021
  • Roberts , D.A. , Goldstein , M. A. , Matthaeus , W. H. and Ghosh , S. 1992 . Velocity sheer generation of soler wind turbulence . J. Geophys. Res. , 97 : 17115
  • Robinson , D. C. and Rusbridge , M. G. 1971 . Structure of turbulence in the zeta plasma . Phys. Fluids , 14 : 2499
  • Rodgers , D.J. , Servidio , S. , Matthaeus , W. H. , Montgomery , D.C. , Mitchell , T.B. and Aziz , T. 2009 . Hydrodynamic relaxation of an electron plasma to a near-maximum entropy state . Phys. Rev. Lett. , 102 : 244501
  • Rodgers , D.J. , Matthaeus , W. H. , Mitchell , T.B. and Montgomery , D.C. 2010 . Similarity decay of enstrophy in an electron fluid . Phys. Rev. Lett. , 105 : 234501
  • Ruzmaikin , A. A. , Sokoloff , D. D. and Shukurov , A. M. 1989 . The dynamo origin of magnetic fields in galaxy clusters . Mon. Not. R. Astron. Soc. , 241 : 1
  • Sahraoui , F. , Goldstein , M. L. , Robert , P. and Khotyaintsev , Y.V. 2009 . Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale . Phys. Rev. Lett. , 102 : 231102
  • Servidio , S. , Matthaeus , W. H. and Dmitruk , P. 2008 . Depression of nonlinearity in decaying isotropic MHD turbulence . Phys. Rev. Lett. , 100 : 095005
  • Servidio , S. , Matthaeus , W. H. and Carbone , V. 2008 . Statistical properties of ideal three-dimensional hall magnetohydrodynamics: The spectral structure of the equilibrium ensemble . Phys. Plasmas , 15 : 042314
  • Servidio , S. , Matthaeus , W. H. , Shay , M. A. , Cassak , P.A. and Dmitruk , P. 2009 . Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence . Phys. Rev. Lett. , 102 : 115003
  • Servidio , S. , Matthaeus , W. H. , Dmitruk , P. and Carbone , V. 2011 . Time decorrelation in isotropic magnetohydrodynamic turbulence . Europhys. Lett. , 96 : 55003
  • Schalchi , A. 2009 . Nonlinear Cosmic Ray Diffusion Theories, Astrophysics Space Science Library Vol. 362 , Springer, Berlin
  • Shebalin , J. V. , Matthaeus , W. H. and Montgomery , D. 1983 . Anisotropy in MHD turbulence due to a mean magnetic field . J. Plasma Phys. , 29 : 525
  • Smith , C. W. , L’Heureux , J. , Ness , N. F. , Acuna , M. H. , Burlaga , L. F. and Scheifele , J. 1998 . The ACE magnetic fields experiment . Space Sci. Rev. , 86 : 611
  • Smith , C. W. , Hamilton , K. , Vasquez , B.J. and Leamon , R.J. 2006 . Dependence of the dissipation range spectrum of interplanetary magnetic fluctuationson the rate of energy cascade . Astrophys. J. , 645 : L85
  • Sorriso-Valvo , L. , Marino , R. , Carbone , V. , Noullez , A. , Lepreti , F. , Veltri , P. , Bruno , R. , Bavassano , B. and Pietropaolo , E. 2007 . Observation of inertial energy cascade in interplanetary space plasma . Phys. Rev. Lett. , 99 : 115001
  • Sorriso-Valvo , L. , Carbone , V. , Veltri , P. , Consolini , G. and Bruno , R. 1999 . Intermittency in the solar wind turbulence through probability distribution functions of fluctuations . Geoph. Res. Lett. , 26 : 1801
  • Antonia , K.R. Sreenivasan, R.A. 1997 . The phenomenon of small-scale turbulence . Annu. Rev. Fluid Mech. , 29 : 435
  • Stawarz , J. E. , Smith , C. W. , Vasquez , B. J. , Forman , M. A. and MacBride , B. T. 2009 . The turbulent cascade and proton heating in the solar wind at 1 au . Astrophys. J. , 697 : 1119
  • Strauss , H.R. 1976 . Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks . Phys. Fluids , 19 : 134
  • Stribling , T. and Matthaeus , W. H. 1990 . Statistical properties of ideal three-dimensional magnetohydrodynamics . Phys. Fluids , B 2 : 1979
  • Stribling , T. and Matthaeus , W. H. 1991 . Relaxation processes in a low-order three-dimensional magnetohydrodynamics model . Phys. Fluids , B 3 : 1848
  • Taylor , J. B. 1974 . Relaxation of toroidal plasma and generation of reverse magnetic fields . Phys. Rev. Lett. , 33 : 1139
  • Taylor , J. B. 1986 . Relaxation and magnetic reconnection in plasmas . Rev. Mod. Phys. , 58 : 741
  • Ting , A. C. , Matthaeus , W. H. and Montgomery , D. 1986 . Turbulent relaxation processes in magnetohydrodynamics . Phys. Fluids , 29 : 3261
  • Tsurutani , B. T. and Smith , E. J. 1979 . Interplanetary discontinuities - Temporal variations and the radial gradient from 1 to 8.5 AU . J. Geophys. Res. , 84 : 2773
  • Vasquez , B.J. , Smith , C. W. , Hamilton , K. , MacBride , B. T. and Leamon , R.J. 2007 . Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU . J. Geophys. Res. , 112 : A07101
  • Veltri , P. and Mangeney , A. 1999 . “ Scaling laws and intermittent structures in solar wind MHD turbulence ” . In Solar Wind IX, AIP Conference Proceedings 471 543 Nantucket , MA
  • Veltri , P. 1999 . MHD turbulence in the solar wind: Self-similarity, intermittency and coherent structures . Plasma Phys. Control. Fusion , 41 : A787
  • Verdini , A. , Velli , M. , Matthaeus , W. H. , Oughton , S. and Dmitruk , P. 2010 . A turbulence-driven model for heating and acceleration of the fast wind in coronal holes . Astrophys. J. Lett. , 708 : L116
  • Wan , M. , Oughton , S. , Servidio , S. and Matthaeus , W. H. 2009 . Generation of non-Gaussian statistics and coherent structures in ideal magnetohydrodynamics . Phys. Plasmas , 16 : 080703
  • Wan , M. , Oughton , S. , Servidio , S. and Matthaeus , W. H. 2012 . von Karman self-preservation hypothesis for MHD turbulence and its consequences for universality . J. Fluid Mech. , 697 : 296
  • Weygand , L. M. , Matthaeus , W. H. , El-Alaoui , M. , Dasso , S. and Kivelson , M.G. 2010 . Anisotropy of the taylor scale and the correlation scale in plasma sheet magnetic field fluctuations as a function of auroral electrojet activity . J. Geophys. Res. , 115 : A12250
  • Woltjer , L. 1958 . A theorem on force-free magnetic fields . Proc. Natl. Acad. Sci. USA , 44 : 489
  • Yokoi , N. , Rubenstein , R. , Hamba , F. and Yoshizawa , A. 2008 . A turbulence model for magnetohydrodynamic plasmas . J. Turb. , 9 : 1
  • Yoshizawa , A. 1990 . Three equation modeling of inhomogeneous compressible turbulence based on a two-scale direct-interaction approximations . Phys. Fluids , A 2 : 838
  • Zank , G. P. and Matthaeus , W. H. 1992 . The equations of reduced magnetohydrodynamics . J. Plasma Phys. , 48 : 85
  • Zank , G. P. , Oughton , S. , Neubauer , F.M. and Webb , G.M. 1992 . Properties of mass-loading shocks 2. Magnetohydrodynamics . J. Geophys. Res. , 97 : 17051
  • Zank , G. P. , Matthaeus , W. H. and Smith , C. W. 1996 . Evolution of turbulent magnetic fluctuation power with heliocentric distance . J. Geophys. Res. , 101 : 17093
  • Zhou , Y. and Matthaeus , W. H. 1990 . Transport and turbulence modeling of solar wind fluctuations . J. Geophys. Res. , 95 : 10291
  • Zhou , Y. , Matthaeus , W. H. and Dmitruk , P. 2004 . Magnetohydrodynamic turbulence and time scales in astrophysical and space plasmas . Rev. Mod. Phys. , 76 : 1015
  • Zweben , S. J. and Taylor , R. J. 1981 . Phenomenological comparison of magnetic and electrostatic fluctuations in the Macrotor tokamak . Nucl. Fusion , 21 : 193
  • Wells , D. R. 1970 . Dynamic stability of closed plasma configurations . J. Plasma Phys. , 4 : 645

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.