Space Science Reviews

, Volume 178, Issue 2–4, pp 163–200 | Cite as

Astrophysical Hydromagnetic Turbulence



Recent progress in astrophysical hydromagnetic turbulence is being reviewed. The physical ideas behind the now widely accepted Goldreich–Sridhar model and its extension to compressible magnetohydrodynamic turbulence are introduced. Implications for cosmic ray diffusion and acceleration is being discussed. Dynamo-generated magnetic fields with and without helicity are contrasted against each other. Certain turbulent transport processes are being modified and often suppressed by anisotropy and inhomogeneities of the turbulence, while others are being produced by such properties, which can lead to new large-scale instabilities of the turbulent medium. Applications of various such processes to astrophysical systems are being considered.


Magnetic fields Turbulence Sun: magnetic fields ISM: magnetic fields 


  1. J.W. Armstrong, B.J. Rickett, S.R. Spangler, Electron density power spectrum in the local interstellar medium. Astrophys. J. 443, 209–221 (1995) ADSGoogle Scholar
  2. R. Banerjee, K. Jedamzik, Evolution of cosmic magnetic fields: from the very early universe, to recombination, to the present. Phys. Rev. D 70, 123003 (2004) ADSGoogle Scholar
  3. S. Banerjee, S. Galtier, Exact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence. Phys. Rev. E 87, 013019 (2013) ADSGoogle Scholar
  4. G.K. Batchelor, On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. R. Soc. Lond. A 201, 405–416 (1950) MathSciNetADSMATHGoogle Scholar
  5. R. Beck, A. Brandenburg, D. Moss, A. Shukurov, D. Sokoloff, Galactic magnetism: recent developments and perspectives. Annu. Rev. Astron. Astrophys. 34, 155–206 (1996) ADSGoogle Scholar
  6. A.R. Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Mon. Not. R. Astron. Soc. 353, 550–558 (2004) ADSGoogle Scholar
  7. A. Beresnyak, Spectral slope and Kolmogorov constant of MHD turbulence. Phys. Rev. Lett. 106, 075001 (2011) ADSGoogle Scholar
  8. A. Beresnyak, Basic properties of magnetohydrodynamic turbulence in the inertial range. Mon. Not. R. Astron. Soc. 422, 3495–3502 (2012) ADSGoogle Scholar
  9. A. Beresnyak, A. Lazarian, Strong imbalanced turbulence. Astrophys. J. Lett. 682, 1070–1075 (2008) ADSGoogle Scholar
  10. A. Beresnyak, A. Lazarian, Comparison of spectral slopes of magnetohydrodynamic and hydrodynamic turbulence and measurements of alignment effects. Astrophys. J. Lett. 702, 1190–1198 (2009) ADSGoogle Scholar
  11. A. Beresnyak, A. Lazarian, Scaling laws and diffuse locality of balanced and imbalanced magnetohydrodynamic turbulence. Astrophys. J. Lett. 722, L110–L113 (2010) ADSGoogle Scholar
  12. A. Beresnyak, A. Lazarian, J. Cho, Density scaling and anisotropy in supersonic magnetohydrodynamic turbulence. Astrophys. J. Lett. 624, L93–L96 (2005) ADSGoogle Scholar
  13. A. Beresnyak, T.W. Jones, A. Lazarian, Turbulence-induced magnetic fields and structure of cosmic ray modified shocks. Astrophys. J. 707, 1541–1549 (2009) ADSGoogle Scholar
  14. P. Bhat, K. Subramanian, Fluctuation dynamos and their Faraday rotation signatures. Mon. Not. R. Astron. Soc. 429, 2469–2481 (2013) ADSGoogle Scholar
  15. D. Biskamp, Magnetohydrodynamic Turbulence (Cambridge University Press, Cambridge, 2003) MATHGoogle Scholar
  16. D. Biskamp, W.-C. Müller, Decay laws for three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 83, 2195–2198 (1999) ADSGoogle Scholar
  17. E.G. Blackman, A. Brandenburg, Doubly helical coronal ejections from dynamos and their role in sustaining the solar cycle. Astrophys. J. Lett. 584, L99–L102 (2003) ADSGoogle Scholar
  18. E.G. Blackman, G.B. Field, Dimensionless measures of turbulent magnetohydrodynamic dissipation rates. Mon. Not. R. Astron. Soc. 386, 1481–1486 (2008) ADSGoogle Scholar
  19. S. Boldyrev, On the spectrum of magnetohydrodynamic turbulence. Astrophys. J. Lett. 626, L37–L40 (2005) ADSGoogle Scholar
  20. S. Boldyrev, Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96, 115002 (2006) ADSGoogle Scholar
  21. S.A. Boldyrev, F. Cattaneo, Magnetic-field generation in Kolmogorov turbulence. Phys. Rev. Lett. 92, 144501 (2004) ADSGoogle Scholar
  22. S. Boldyrev, Å. Nordlund, P. Padoan, Scaling relations of supersonic turbulence in star-forming molecular clouds. Astrophys. J. 573, 678–684 (2002) ADSGoogle Scholar
  23. S. Boldyrev, J.C. Perez, J.E. Borovsky, J.J. Podesta, Spectral scaling laws in magnetohydrodynamic turbulence simulations and in the solar wind. Astrophys. J. 741, L19 (2011) ADSGoogle Scholar
  24. A. Brandenburg, The case for a distributed solar dynamo shaped by near-surface shear. Astrophys. J. 625, 539–547 (2005) ADSGoogle Scholar
  25. A. Brandenburg, Nonlinear small-scale dynamos at low magnetic Prandtl numbers. Astrophys. J. 741, 92 (2011a) ADSGoogle Scholar
  26. A. Brandenburg, Å. Nordlund, Astrophysical turbulence modeling. Rep. Prog. Phys. 74, 046901 (2011b) ADSGoogle Scholar
  27. A. Brandenburg, K. Subramanian, Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209 (2005) MathSciNetADSGoogle Scholar
  28. A. Brandenburg, K. Enqvist, P. Olesen, Large-scale magnetic fields from hydromagnetic turbulence in the very early universe. Phys. Rev. D 54, 1291–1300 (1996) ADSGoogle Scholar
  29. A. Brandenburg, P. Käpylä, A. Mohammed, Non-Fickian diffusion and tau-approximation from numerical turbulence. Phys. Fluids 16, 1020–1027 (2004) ADSGoogle Scholar
  30. A. Brandenburg, K.-H. Rädler, M. Rheinhardt, K. Subramanian, Magnetic quenching of alpha and diffusivity tensors in helical turbulence. Astrophys. J. 676, 740-L52 (2008a) ADSGoogle Scholar
  31. A. Brandenburg, K.-H. Rädler, M. Schrinner, Scale dependence of alpha effect and turbulent diffusivity. Astron. Astrophys. 482, 739–746 (2008b) ADSMATHGoogle Scholar
  32. A. Brandenburg, N. Kleeorin, I. Rogachevskii, Large-scale magnetic flux concentrations from turbulent stresses. Astron. Nachr. 331, 5–13 (2010) ADSMATHGoogle Scholar
  33. A. Brandenburg, N. Kleeorin, I. Rogachevskii, Self-assembly of shallow magnetic spots through strongly stratified turbulence. Astrophys. J. Lett. (2013, submitted). arXiv:1306.4915
  34. A. Brandenburg, K. Subramanian, A. Balogh, M.L. Goldstein, Scale-dependence of magnetic helicity in the solar wind. Astrophys. J. 734, 9 (2011a) ADSGoogle Scholar
  35. A. Brandenburg, K. Kemel, N. Kleeorin, D. Mitra, I. Rogachevskii, Detection of negative effective magnetic pressure instability in turbulence simulations. Astrophys. J. 740, L50 (2011b) ADSGoogle Scholar
  36. A. Brandenburg, K. Kemel, N. Kleeorin, I. Rogachevskii, The negative effective magnetic pressure in stratified forced turbulence. Astrophys. J. 749, 179 (2012a) ADSGoogle Scholar
  37. A. Brandenburg, K.-H. Rädler, K. Kemel, Mean-field transport in stratified and/or rotating turbulence. Astron. Astrophys. 539, A35 (2012b) ADSGoogle Scholar
  38. A. Brandenburg, D. Sokoloff, K. Subramanian, Current status of turbulent dynamo theory: from large-scale to small-scale dynamos. Space Sci. Rev. 169, 123–157 (2012c) ADSGoogle Scholar
  39. B.P. Brown, M.K. Browning, A.S. Brun, M.S. Miesch, J. Toomre, Persistent magnetic wreaths in a rapidly rotating sun. Astrophys. J. 711, 424–438 (2010) ADSGoogle Scholar
  40. B.P. Brown, M.S. Miesch, M.K. Browning, A.S. Brun, J. Toomre, Magnetic cycles in a convective dynamo simulation of a young solar-type star. Astrophys. J. 731, 69 (2011) ADSGoogle Scholar
  41. G. Brunetti, A. Lazarian, Compressible turbulence in galaxy clusters: physics and stochastic particle re-acceleration. Mon. Not. R. Astron. Soc. 378, 245–275 (2007) ADSGoogle Scholar
  42. B. Burkhart, A. Lazarian, V. Ossenkopf, J. Stutzki, The turbulence power spectrum in optically thick interstellar clouds. Astrophys. J. 771, 123 (2013) ADSGoogle Scholar
  43. A.M. Bykov, A. Brandenburg, M.A. Malkov, S.M. Osipov, Microphysics of cosmic ray driven plasma instabilities. Space Sci. Rev. (2013). doi:10.1007/s11214-013-9988-3 MATHGoogle Scholar
  44. S. Candelaresi, A. Brandenburg, How much helicity is needed to drive large-scale dynamos? Phys. Rev. E 87, 043104 (2013) ADSGoogle Scholar
  45. B.D.G. Chandran, Scattering of energetic particles by anisotropic magnetohydrodynamic turbulence with a Goldreich-Sridhar power spectrum. Phys. Rev. Lett. 85, 4656–4659 (2000) ADSGoogle Scholar
  46. B.D.G. Chandran, S.C. Cowley, Thermal conduction in a tangled magnetic field. Phys. Rev. Lett. 80, 3077–3080 (1998) ADSGoogle Scholar
  47. L. Chamandy, K. Subramanian, A. Shukurov, Galactic spiral patterns and dynamo action. I. A new twist on magnetic arms. Mon. Not. R. Astron. Soc. 428, 3569–3589 (2013) ADSGoogle Scholar
  48. P. Chatterjee, G. Guerrero, A. Brandenburg, Magnetic helicity fluxes in interface and flux transport dynamos. Astron. Astrophys. 525, A5 (2011) ADSGoogle Scholar
  49. A. Chepurnov, A. Lazarian, Turbulence spectra from Doppler-broadened spectral lines: tests of the velocity channel analysis and velocity coordinate spectrum techniques. Astrophys. J. 693, 1074–1083 (2009) ADSGoogle Scholar
  50. A. Chepurnov, A. Lazarian, Extending the big power law in the sky with turbulence spectra from Wisconsin Hα mapper data. Astrophys. J. 710, 853–858 (2010) ADSGoogle Scholar
  51. J. Cho, A. Lazarian, Compressible sub-Alfvénic MHD turbulence in low-β plasmas. Phys. Rev. Lett. 88, 245001 (2002). CL02 ADSGoogle Scholar
  52. J. Cho, A. Lazarian, Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications. Mon. Not. R. Astron. Soc. 345, 325–339 (2003). CL03 ADSGoogle Scholar
  53. J. Cho, A. Lazarian, Thermal conduction in magnetized turbulent gas. J. Korean Astron. Soc. 37, 557–562 (2004) ADSGoogle Scholar
  54. J. Cho, A. Lazarian, Grain alignment by radiation in dark clouds and cores. Astrophys. J. 631, 361–370 (2005) ADSGoogle Scholar
  55. J. Cho, A. Lazarian, E.T. Vishniac, Simulations of magnetohydrodynamic turbulence in a strongly magnetized medium. Astrophys. J. 564, 291–301 (2002) ADSGoogle Scholar
  56. J. Cho, E.T. Vishniac, The generation of magnetic fields through driven turbulence. Astrophys. J. 538, 217–225 (2000) ADSGoogle Scholar
  57. J. Crovisier, J.M. Dickey, The spatial power spectrum of galactic neutral hydrogen from observations of the 21-cm emission line. Astron. Astrophys. 122, 282–296 (1983) ADSGoogle Scholar
  58. R.M. Crutcher, B. Wandelt, C. Heiles, E. Falgarone, T.H. Troland, Magnetic fields in interstellar clouds from Zeeman observations: inference of total field strengths by Bayesian analysis. Astrophys. J. 725, 466–479 (2010) ADSGoogle Scholar
  59. F. Del Sordo, G. Guerrero, A. Brandenburg, Turbulent dynamo with advective magnetic helicity flux. Mon. Not. R. Astron. Soc. 429, 1686–1694 (2013) ADSGoogle Scholar
  60. R.L. Dickman, S.C. Kleiner, Large-scale structure of the Taurus molecular complex. Part 3. Methods for turbulence. Astrophys. J. 295, 479–484 (1985) ADSGoogle Scholar
  61. W. Dobler, N.E.L. Haugen, T.A. Yousef, A. Brandenburg, Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E 68, 026304 (2003) ADSGoogle Scholar
  62. T.A. Enßlin, C. Vogt, Magnetic turbulence in cool cores of galaxy clusters. Astron. Astrophys. 453, 447–458 (2006) ADSGoogle Scholar
  63. A. Esquivel, A. Lazarian, S. Horibe, J. Cho, V. Ossenkopf, J. Stutzki, Statistics of velocity centroids: effects of density-velocity correlations and non-Gaussianity. Mon. Not. R. Astron. Soc. 381, 1733–1744 (2007) ADSGoogle Scholar
  64. G.L. Eyink, A. Lazarian, E.T. Vishniac, Fast magnetic reconnection and spontaneous stochasticity. Astrophys. J. 743, 51 (2011) ADSGoogle Scholar
  65. B.G. Elmegreen, J. Scalo, Interstellar turbulence. I. Observations and processes. Annu. Rev. Astron. Astrophys. 42, 211–273 (2004) ADSGoogle Scholar
  66. G. Falkovich, Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414 (1994) ADSMATHGoogle Scholar
  67. S. Galtier, S. Banerjee, Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107, 134501 (2011) ADSGoogle Scholar
  68. S. Galtier, S.V. Nazarenko, A.C. Newell, A. Pouquet, A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63, 447–488 (2000) ADSGoogle Scholar
  69. M. Ghizaru, P. Charbonneau, P.K. Smolarkiewicz, Magnetic cycles in global large-eddy simulations of solar convection. Astrophys. J. 715, L133–L137 (2010) ADSGoogle Scholar
  70. P.A. Gilman, Dynamically consistent nonlinear dynamos driven by convection in a rotating spherical shell. II. Dynamos with cycles and strong feedbacks. Astrophys. J. Suppl. Ser. 53, 243–268 (1983) ADSGoogle Scholar
  71. P. Goldreich, S. Sridhar, Toward a theory of interstellar turbulence. 2. Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995). GS95 ADSGoogle Scholar
  72. P. Goldreich, S. Sridhar, Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680–688 (1997) ADSGoogle Scholar
  73. G.A. Glatzmaier, Numerical simulations of stellar convective dynamos. II. Field propagation in the convection zone. Astrophys. J. 291, 300–307 (1985) ADSGoogle Scholar
  74. J. Goodman, R. Narayan, Slow pulsar scintillation and the spectrum of interstellar electron density fluctuations. Mon. Not. R. Astron. Soc. 214, 519–537 (1985) ADSGoogle Scholar
  75. D.A. Green, A power spectrum analysis of the angular scale of galactic neutral hydrogen emission towards L=140, B=0, Monthly Notices Roy. Mon. Not. R. Astron. Soc. 262, 327–342 (1993) ADSGoogle Scholar
  76. A. Gruzinov, S. Cowley, R. Sudan, Small-scale-field dynamo. Phys. Rev. Lett. 77, 4342–4345 (1996) ADSGoogle Scholar
  77. N.E.L. Haugen, A. Brandenburg, Hydrodynamic and hydromagnetic energy spectra from large eddy simulations. Phys. Fluids 18, 075106 (2006) ADSGoogle Scholar
  78. N.E.L. Haugen, A. Brandenburg, W. Dobler, Is nonhelical hydromagnetic turbulence peaked at small scales? Astrophys. J. 597, L141–L144 (2003) ADSGoogle Scholar
  79. N.E.L. Haugen, A. Brandenburg, W. Dobler, Simulations of nonhelical hydromagnetic turbulence. Phys. Rev. E 70, 016308 (2004) ADSGoogle Scholar
  80. J.C. Higdon, Density fluctuations in the interstellar medium: evidence for anisotropic magnetogas turbulence. I. Model and astrophysical sites. Astrophys. J. 285, 109–123 (1984) ADSGoogle Scholar
  81. A. Hubbard, A. Brandenburg, Memory effects in turbulent transport. Astrophys. J. 706, 712–726 (2009) ADSGoogle Scholar
  82. A. Hubbard, A. Brandenburg, Magnetic helicity fluxes in an α 2 dynamo embedded in a halo. Geophys. Astrophys. Fluid Dyn. 104, 577–590 (2010) MathSciNetADSGoogle Scholar
  83. R.S. Iroshnikov, Turbulence of a conducting fluid in a strong magnetic field. Sov. Astron. 7, 566–571 (1963) MathSciNetADSGoogle Scholar
  84. A.B. Iskakov, A.A. Schekochihin, S.C. Cowley, J.C. McWilliams, M.R.E. Proctor, Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers. Phys. Rev. Lett. 98, 208501 (2007) ADSGoogle Scholar
  85. J.R. Jokipii, Pitch-angle scattering of charged particles in a random magnetic field. Astrophys. J. 194, 465–469 (1974) ADSGoogle Scholar
  86. T. Kahniashvili, A. Brandenburg, A.G. Tevzadze, B. Ratra, Numerical simulations of the decay of primordial magnetic turbulence. Phys. Rev. D 81, 123002 (2010) ADSGoogle Scholar
  87. T. Kahniashvili, A.G. Tevzadze, A. Brandenburg, A. Neronov, Evolution of primordial magnetic fields from phase transitions. Phys. Rev. D 87, 083007 (2013) ADSGoogle Scholar
  88. P.J. Käpylä, M.J. Korpi, A. Brandenburg, D. Mitra, R. Tavakol, Convective dynamos in spherical wedge geometry. Astron. Nachr. 331, 73–81 (2010) ADSMATHGoogle Scholar
  89. P.J. Käpylä, M.J. Mantere, A. Brandenburg, Cyclic magnetic activity due to turbulent convection in spherical wedge geometry. Astrophys. J. Lett. 755, L22 (2012a) ADSGoogle Scholar
  90. P.J. Käpylä, A. Brandenburg, N. Kleeorin, M.J. Mantere, I. Rogachevskii, Negative effective magnetic pressure in turbulent convection. Mon. Not. R. Astron. Soc. 422, 2465–2473 (2012b) ADSGoogle Scholar
  91. A.P. Kazantsev, Enhancement of a magnetic field by a conducting fluid. Sov. Phys. JETP 26, 1031–1034 (1968) ADSGoogle Scholar
  92. K. Kemel, A. Brandenburg, N. Kleeorin, D. Mitra, I. Rogachevskii, Spontaneous formation of magnetic flux concentrations in stratified turbulence. Sol. Phys. 280, 321–333 (2012) ADSGoogle Scholar
  93. K. Kemel, A. Brandenburg, N. Kleeorin, D. Mitra, I. Rogachevskii, Active region formation through the negative effective magnetic pressure instability. Sol. Phys. (2013). doi:10.1007/s11207-012-0031-8 Google Scholar
  94. S. Kida, S. Yanase, J. Mizushima, Statistical properties of MHD turbulence and turbulent dynamo. Phys. Fluids A 3, 457–465 (1991) ADSGoogle Scholar
  95. L.L. Kitchatinov, A. Brandenburg, Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors. Astron. Nachr. 333, 230–236 (2012) ADSGoogle Scholar
  96. N. Kleeorin, I. Rogachevskii, Effective Ampère force in developed magnetohydrodynamic turbulence. Phys. Rev. E 50, 2716–2730 (1994) ADSGoogle Scholar
  97. N.I. Kleeorin, I.V. Rogachevskii, A.A. Ruzmaikin, Negative magnetic pressure as a trigger of large-scale magnetic instability in the solar convective zone. Sov. Astron. Lett. 15, 274–277 (1989) ADSGoogle Scholar
  98. N.I. Kleeorin, I.V. Rogachevskii, A.A. Ruzmaikin, Magnetic force reversal and instability in a plasma with advanced magnetohydrodynamic turbulence. Sov. Phys. JETP 70, 878–883 (1990) Google Scholar
  99. N. Kleeorin, M. Mond, I. Rogachevskii, Magnetohydrodynamic instabilities in developed small-scale turbulence. Phys. Fluids 5, 4128–4134 (1993) Google Scholar
  100. N. Kleeorin, M. Mond, I. Rogachevskii, Magnetohydrodynamic turbulence in the solar convective zone as a source of oscillations and sunspots formation. Astron. Astrophys. 307, 293–309 (1996) ADSGoogle Scholar
  101. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. CR Acad. Sci. USSR 30, 299–303 (1941) Google Scholar
  102. G. Kowal, A. Lazarian, A. Beresnyak, Density fluctuations in MHD turbulence: spectra, intermittency, and topology. Astrophys. J. 658, 423–445 (2007) ADSGoogle Scholar
  103. G. Kowal, A. Lazarian, Velocity field of compressible magnetohydrodynamic turbulence: wavelet decomposition and mode scalings. Astrophys. J. 720, 742–756 (2010) ADSGoogle Scholar
  104. R.H. Kraichnan, Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387 (1965) MathSciNetADSGoogle Scholar
  105. F. Krause, K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon Press, Oxford, 1980) MATHGoogle Scholar
  106. A.G. Kritsuk, M.L. Norman, P. Padoan, R. Wagner, The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416–431 (2007) ADSGoogle Scholar
  107. A.G. Kritsuk, Å. Nordlund, D. Collins, P. Padoan, M.L. Norman, T. Abel, R. Banerjee, C. Federrath, M. Flock, D. Lee, P.S. Li, W.-C. Müller, R. Teyssier, S.D. Ustyugov, C. Vogel, H. Xu, Comparing numerical methods for isothermal magnetized supersonic turbulence. Astrophys. J. 737, 13 (2011) ADSGoogle Scholar
  108. R.M. Kulsrud, A critical review of galactic dynamos. Annu. Rev. Astron. Astrophys. 37, 37–64 (1999) ADSGoogle Scholar
  109. A. Lazarian, Astrophysical implications of turbulent reconnection: from cosmic rays to star formation, in Magnetic Fields in the Universe, ed. by E. de Gouveia Dal Pino, G. Lugones, A. Lazarian. AIP, vol. 784, (2005), pp. 42–54 Google Scholar
  110. A. Lazarian, Enhancement and suppression of heat transfer by MHD turbulence. Astrophys. J. Lett. 645, L25–L28 (2006). L06 ADSGoogle Scholar
  111. A. Lazarian, Obtaining spectra of turbulent velocity from observations. Space Sci. Rev. 143, 357–385 (2009) ADSGoogle Scholar
  112. A. Lazarian, A. Esquivel, Statistics of velocity from spectral data: modified velocity centroids. Astrophys. J. 592, L37–L40 (2003) ADSGoogle Scholar
  113. A. Lazarian, A. Esquivel, Velocity centroids as tracers of the turbulent velocity statistics. Astrophys. J. 631, 320–350 (2005) ADSGoogle Scholar
  114. A. Lazarian, D. Pogosyan, Velocity modification of HI power spectrum. Astrophys. J. 537, 720–748 (2000). LP00 ADSGoogle Scholar
  115. A. Lazarian, D. Pogosyan, Velocity modification of the power spectrum from an absorbing medium. Astrophys. J. 616, 943–965 (2004) ADSGoogle Scholar
  116. A. Lazarian, D. Pogosyan, Statistics of fluctuations along velocity coordinate: effects of absorption. Astrophys. J. 652, 1348 (2006) ADSGoogle Scholar
  117. A. Lazarian, D. Pogosyan, Studying velocity turbulence from Doppler-broadened absorption lines: statistics of optical depth fluctuations. Astrophys. J. 686, 350–362 (2008) ADSGoogle Scholar
  118. A. Lazarian, E.T. Vishniac, Reconnection in a weakly stochastic field. Astrophys. J. 517, 700–718 (1999). LV99 ADSGoogle Scholar
  119. A. Lazarian, E.T. Vishniac, Model of reconnection of weakly stochastic magnetic field and its implications. Rev. Mex. Astron. Astrofís. Conf. Ser. 36, 81–88 (2009) ADSGoogle Scholar
  120. A. Lazarian, A. Esquivel, R. Crutcher, Magnetization of cloud cores and envelopes and other observational consequences of reconnection diffusion. Astrophys. J. 757, 154 (2012a) ADSGoogle Scholar
  121. A. Lazarian, L. Vlahos, G. Kowal, H. Yan, A. Beresnyak, E.M. de Gouveia Dal Pino, Turbulence, magnetic reconnection in turbulent fluids and energetic particle acceleration. Space Sci. Rev. 173, 557–622 (2012b) ADSGoogle Scholar
  122. M. Lesieur, Turbulence in Fluids (Nijhoff, Dordrecht, 1990) MATHGoogle Scholar
  123. Y. Lithwick, P. Goldreich, Imbalanced weak magnetohydrodynamic turbulence. Astrophys. J. 582, 1220–1240 (2003) ADSGoogle Scholar
  124. Y. Lithwick, P. Goldreich, S. Sridhar, Imbalanced strong MHD turbulence. Astrophys. J. 655, 269–274 (2007) ADSGoogle Scholar
  125. J. Maron, P. Goldreich, Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 1175–1196 (2001) ADSGoogle Scholar
  126. W.H. Matthaeus, M.L. Goldstein, C. Smith, Evaluation of magnetic helicity in homogeneous turbulence. Phys. Rev. Lett. 48, 1256–1259 (1982) ADSGoogle Scholar
  127. D.B. Melrose, The emission and absorption of waves by charged particles in magnetized plasmas. Astrophys. Space Sci. 2, 171–235 (1968) MathSciNetADSGoogle Scholar
  128. M. Meneguzzi, U. Frisch, A. Pouquet, Helical and nonhelical turbulent dynamos. Phys. Rev. Lett. 47, 1060–1064 (1981) ADSGoogle Scholar
  129. M. Meneguzzi, A. Pouquet, Turbulent dynamos driven by convection. J. Fluid Mech. 205, 297–312 (1989) ADSGoogle Scholar
  130. M.S. Miesch, J. Toomre, Turbulence, magnetism, and shear in stellar interiors. Ann. Rev. Fluid Dyn. 41, 317–345 (2009) ADSGoogle Scholar
  131. M.S. Miesch, J. Scalo, J. Bally, Velocity field statistics in star-forming regions. I. Centroid velocity observations. Astrophys. J. 524, 895–922 (1999) ADSGoogle Scholar
  132. D. Mitra, P.J. Käpylä, R. Tavakol, A. Brandenburg, Alpha effect and diffusivity in helical turbulence with shear. Astron. Astrophys. 495, 1–8 (2009) ADSMATHGoogle Scholar
  133. D. Mitra, S. Candelaresi, P. Chatterjee, R. Tavakol, A. Brandenburg, Equatorial magnetic helicity flux in simulations with different gauges. Astron. Nachr. 331, 130–135 (2010) ADSMATHGoogle Scholar
  134. M.-A. Miville-Deschênes, G. Joncas, E. Falgarone, F. Boulanger, High resolution 21 cm mapping of the Ursa Major Galactic cirrus: power spectra of the high-latitude H I gas. Astron. Astrophys. 411, 109–121 (2003) ADSGoogle Scholar
  135. H.K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge Univ. Press, Cambridge, 1978) Google Scholar
  136. G. Münch, Internal motions in the Orion nebula. Rev. Mod. Phys. 30, 1035–1041 (1958) ADSGoogle Scholar
  137. R. Narayan, M.V. Medvedev, Thermal conduction in clusters of galaxies. Astrophys. J. 562, L129–L132 (2001) ADSGoogle Scholar
  138. C.S. Ng, A. Bhattacharjee, Interaction of shear-Alfvén wave packets: implication for weak magnetohydrodynamic turbulence in astrophysical plasmas. Astrophys. J. 465, 845–854 (1996) ADSGoogle Scholar
  139. Å. Nordlund, A. Brandenburg, R.L. Jennings, M. Rieutord, J. Ruokolainen, R.F. Stein, I. Tuominen, Dynamo action in stratified convection with overshoot. Astrophys. J. 392, 647–652 (1992) ADSGoogle Scholar
  140. C.R. O’dell, H.O. Castaneda, Evidence for turbulence in H II regions. Astrophys. J. 317, 686–692 (1987) ADSGoogle Scholar
  141. P. Padoan, M. Juvela, A. Kritsuk, M.L. Norman, The power spectrum of supersonic turbulence in Perseus. Astrophys. J. Lett. 653, 125–128 (2006) ADSGoogle Scholar
  142. P. Padoan, M. Juvela, A. Kritsuk, M.L. Norman, The power spectrum of turbulence in NGC 1333: outflows or large-scale driving? Astrophys. J. Lett. 707, L153–L157 (2009) ADSGoogle Scholar
  143. E.N. Parker, Cosmical Magnetic Fields (Clarendon, Oxford, 1979) Google Scholar
  144. J.C. Perez, S. Boldyrev, Role of cross-helicity in magnetohydrodynamic turbulence. Phys. Rev. Lett. 102, 025003 (2009) ADSGoogle Scholar
  145. V. Petrosian, H. Yan, A. Lazarian, Damping of magnetohydrodynamic turbulence in solar flares. Astrophys. J. 644, 603–612 (2006) ADSGoogle Scholar
  146. V.V. Pipin, The mean electro-motive force and current helicity under the influence of rotation, magnetic field and shear. Geophys. Astrophys. Fluid Dyn. 102, 21–49 (2008) MathSciNetADSGoogle Scholar
  147. J.J. Podesta, D.A. Roberts, M.L. Goldstein, Spectral exponents of kinetic and magnetic energy spectra in solar wind turbulence. Astrophys. J. 664, 543–548 (2007) ADSGoogle Scholar
  148. J.J. Podesta, S.P. Gary, Magnetic helicity spectrum of solar wind fluctuations as a function of the angle with respect to the local mean magnetic field. Astrophys. J. 734, 15 (2011) ADSGoogle Scholar
  149. É. Racine, P. Charbonneau, M. Ghizaru, A. Bouchat, P.K. Smolarkiewicz, On the mode of dynamo action in a global large-eddy simulation of solar convection. Astrophys. J. 735, 46 (2011) ADSGoogle Scholar
  150. K.-H. Rädler, On some electromagnetic phenomena in electrically conducting turbulently moving matter, especially in the presence of Coriolis forces. Geod. Geophys. Veröff., Reihe 2 13, 131–135 (1969) ADSGoogle Scholar
  151. K.-H. Rädler, On the influence of a large-scale magnetic field on turbulent motions in an electrically conducting medium. Astron. Nachr. 295, 265–273 (1974) MATHGoogle Scholar
  152. K.-H. Rädler, A. Brandenburg, F. Del Sordo, M. Rheinhardt, Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows. Phys. Rev. E 84, 4 (2011) Google Scholar
  153. A.B. Rechester, M.N. Rosenbluth, Electron heat transport in a Tokamak with destroyed magnetic surfaces. Phys. Rev. Lett. 40, 38–41 (1978) ADSGoogle Scholar
  154. M. Rheinhardt, A. Brandenburg, Test-field method for mean-field coefficients with MHD background. Astron. Astrophys. 520, A28 (2010) ADSGoogle Scholar
  155. M. Rheinhardt, A. Brandenburg, Modeling spatio-temporal nonlocality in mean-field dynamos. Astron. Nachr. 333, 71–77 (2012) ADSGoogle Scholar
  156. I. Rogachevskii, N. Kleeorin, Intermittency and anomalous scaling for magnetic fluctuations. Phys. Rev. E 56, 417–426 (1997) ADSGoogle Scholar
  157. I. Rogachevskii, N. Kleeorin, Magnetic fluctuations and formation of large-scale inhomogeneous magnetic structures in a turbulent convection. Phys. Rev. E 76, 056307 (2007) MathSciNetADSGoogle Scholar
  158. I. Rogachevskii, N. Kleeorin, A. Brandenburg, D. Eichler, Cosmic ray current-driven turbulence and mean-field dynamo effect. Astrophys. J. 753, 6 (2012) ADSGoogle Scholar
  159. G. Rüdiger, On the Reynolds stresses in mean-field hydrodynamics III. two-dimensional turbulence and the problem of differential rotation. Astron. Nachr. 295, 229–252 (1974) ADSMATHGoogle Scholar
  160. G. Rüdiger, L.L. Kitchatinov, A. Brandenburg, Cross helicity and turbulent magnetic diffusivity in the solar convection zone. Sol. Phys. 269, 3–12 (2011) ADSGoogle Scholar
  161. R. Santos-Lima, A. Lazarian, E.M. de Gouveia Dal Pino, J. Cho, Diffusion of magnetic field and removal of magnetic flux from clouds via turbulent reconnection. Astrophys. J. 714, 442–461 (2010) ADSGoogle Scholar
  162. R. Santos-Lima, E.M. de Gouveia Dal Pino, A. Lazarian, The role of turbulent magnetic reconnection in the formation of rotationally supported protostellar disks. Astrophys. J. 747, 21 (2012) ADSGoogle Scholar
  163. A.A. Schekochihin, J.L. Maron, S.C. Cowley, J.C. McWilliams, The small-scale structure of magnetohydrodynamic turbulence with large magnetic Prandtl numbers. Astrophys. J. 576, 806–813 (2002) ADSGoogle Scholar
  164. A.A. Schekochihin, S.C. Cowley, J.L. Maron, J.C. McWilliams, Critical magnetic Prandtl number for small-scale dynamo. Phys. Rev. Lett. 92, 054502 (2004a) ADSGoogle Scholar
  165. A.A. Schekochihin, S.C. Cowley, S.F. Taylor, J.L. Maron, J.C. McWilliams, Simulations of the small scale turbulent dynamo. Astrophys. J. 612, 276–307 (2004b) ADSGoogle Scholar
  166. A.A. Schekochihin, N.E.L. Haugen, A. Brandenburg, S.C. Cowley, J.L. Maron, J.C. McWilliams, Onset of small scale dynamo at small magnetic Prandtl numbers. Astrophys. J. 625, L115–L118 (2005) ADSGoogle Scholar
  167. R. Schlickeiser, Cosmic Ray Astrophysics. Astron. Astrophys. Lib. (Springer, Berlin, 2002) Google Scholar
  168. J.V. Shebalin, W.H. Matthaeus, D. Montgomery, Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525–547 (1983) ADSGoogle Scholar
  169. A. Skumanich, Time scales for CA II emission decay, rotational braking, and lithium depletion. Astrophys. J. 171, 565–567 (1972) ADSGoogle Scholar
  170. C.W. Smith, J.W. Bieber, Detection of steady magnetic helicity in low-frequency IMF turbulence, in 23rd International Cosmic Ray Conference, vol. 3, ed. by D.A. Leahy, R.B. Hicks, D. Venkatesan (World Scientific, Singapore, 1993), pp. 493–496 Google Scholar
  171. S. Spangler, C. Gwinn, Evidence for an inner scale to the density turbulence in the interstellar medium. Astrophys. J. 353, L29–L32 (1990) ADSGoogle Scholar
  172. S. Stanimirovic, L. Staveley-Smith, J.M. Dickey, R.J. Sault, S.L. Snowden, The large-scale HI structure of the Small Magellanic Cloud. Mon. Not. R. Astron. Soc. 302, 417–436 (1999) ADSGoogle Scholar
  173. L.G. Stenholm, Molecular cloud fluctuations. II. Methods of analysis of cloud maps. Astron. Astrophys. 232, 495–509 (1990) ADSGoogle Scholar
  174. K. Subramanian, Can the turbulent galactic dynamo generate large-scale magnetic fields? Mon. Not. R. Astron. Soc. 294, 718–728 (1998) ADSGoogle Scholar
  175. S. Sur, A. Brandenburg, K. Subramanian, Kinematic alpha effect in isotropic turbulence simulations. Mon. Not. R. Astron. Soc. 385, L15–L19 (2008) ADSGoogle Scholar
  176. H. Tennekes, J.L. Lumley, First Course in Turbulence (MIT Press, Cambridge, 1972) Google Scholar
  177. A.G. Tevzadze, L. Kisslinger, A. Brandenburg, T. Kahniashvili, Magnetic fields from QCD phase transitions. Astrophys. J. 759, 54 (2012) ADSGoogle Scholar
  178. H. Yan, A. Lazarian, Scattering of cosmic rays by magnetohydrodynamic turbulence. Phys. Rev. Lett. 89, 281102 (2002) ADSGoogle Scholar
  179. H. Yan, A. Lazarian, Cosmic-ray scattering and streaming in compressible magnetohydrodynamic turbulence. Astrophys. J. 614, 757–769 (2004) ADSGoogle Scholar
  180. H. Yan, A. Lazarian, Cosmic-ray propagation: nonlinear diffusion parallel and perpendicular to mean magnetic field. Astrophys. J. 673, 942–953 (2008) ADSGoogle Scholar
  181. S.I. Vainshtein, Ya.B. Zeldovich, Origin of magnetic fields in astrophysics. Sov. Phys. Usp. 15, 159–172 (1972) ADSGoogle Scholar
  182. J. Warnecke, P.J. Käpylä, M.J. Mantere, A. Brandenburg, Solar-like differential rotation in a convective dynamo with a coronal envelope. Astrophys. J. (2013, submitted). arXiv:1301.2248

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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Nordita, KTH Royal Institute of TechnologyStockholm UniversityStockholmSweden
  2. 2.Department of AstronomyStockholm UniversityStockholmSweden
  3. 3.Department of AstronomyUniversity of Wisconsin-MadisonMadisonUSA

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