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Who Needs Turbulence?

A Review of Turbulence Effects in the Heliosphere and on the Fundamental Process of Reconnection

Abstract

The significant influences of turbulence in neutral fluid hydrodynamics are well accepted but the potential for analogous effects in space and astrophysical plasmas is less widely recognized. This situation sometimes gives rise to the question posed in the title; “Who need turbulence?” After a brief overview of turbulence effects in hydrodynamics, some likely effects of turbulence in solar and heliospheric plasma physics are reviewed here, with the goal of providing at least a partial answer to the posed question.

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References

  1. S.D. Bale, P.J. Kellogg, F.S. Mozer, T.S. Horbury, H. Reme, Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 94, 215002 (2005). doi:10.1103/PhysRevLett.94.215002. http://link.aps.org/abstract/PRL/v94/e215002

  2. G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978)

  3. B. Bavassano, M. Dobrowolny, F. Mariani, N.F. Ness, Radial evolution of power spectra of interplanetary Alfvénic turbulence. J. Geophys. Res. 87, 3617 (1982a)

  4. B. Bavassano, M. Dobrowolny, G. Fanfoni, F. Mariani, N.F. Ness, Statistical properties of MHD fluctuations associated with high-speed streams from Helios-2 observations. Sol. Phys. 78, 373–384 (1982b)

  5. A. Bhattacharjee, Y. Huang, H. Yang, B. Rogers, Fast reconnection in high-Lundquist-number plasmas due to the plasmoid instability. Phys. Plasmas 16(11), 112102 (2009). doi:10.1063/1.3264103

  6. J.W. Bieber, W. Wanner, W.H. Matthaeus, Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport. J. Geophys. Res. 101, 2511–2522 (1996)

  7. G. Birkhoff, Hydrodynamics (Princeton University Press, Princeton, 1960)

  8. D. Biskamp, Magnetic reconnection via current sheets. Phys. Fluids 29, 1520 (1986)

  9. J.E. Borovsky, Flux tube texture of the solar wind: strands of the magnetic carpet at 1 AU? J. Geophys. Res. 113, 8110 (2008). doi:10.1029/2007JA012684

  10. J.E. Borovsky, H.O. Funsten, MHD turbulence in the earth’s plasma sheet: dynamics, dissipation, and driving. J. Geophys. Res. 108, 1284 (2003). doi:10.1029/2002JA009625

  11. J.E. Borovsky, R.C. Elphic, H.O. Funsten, M.F. Thomsen, The Earth’s plasma sheet as a laboratory for flow turbulence in high-β MHD. J. Plasma Phys. 57, 1–34 (1997)

  12. A. Brandenburg, The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824 (2001)

  13. B. Breech, W.H. Matthaeus, L.J. Milano, C.W. Smith, Probability distributions of the induced electric field of the solar wind. J. Geophys. Res. 108, 1153 (2003). doi:1029/2002JA009529

  14. B. Breech, W.H. Matthaeus, J. Minnie, S. Oughton, S. Parhi, J.W. Bieber, B. Bavassano, Radial evolution of cross helicity in high-latitude solar wind. Geophys. Res. Lett. 32, 06103 (2005). doi:10.1029/2004GL022321

  15. B. Breech, W.H. Matthaeus, J. Minnie, J.W. Bieber, S. Oughton, C.W. Smith, P.A. Isenberg, Turbulence transport throughout the heliosphere. J. Geophys. Res. (2008). doi:10.1029/2007JA012711

  16. L.F. Burlaga, N.F. Ness, Macro- and micro-structure of the interplanetary magnetic field. Can. J. Phys. 46, 962 (1968)

  17. L.F. Burlaga, N.F. Ness, Tangential discontinuities in the solar wind. Sol. Phys. 9, 467–477 (1969). doi:10.1007/BF02391672

  18. P.A. Cassak, M.A. Shay, J.F. Drake, Scaling of Sweet–Parker reconnection with secondary islands. Phys. Plasmas 16(12), 120702 (2009). doi:10.1063/1.3274462. http://link.aip.org/link/?PHP/16/120702/1

  19. B.D.G. Chandran, P. Pongkitiwanichakul, P.A. Isenberg, M.A. Lee, S.A. Markovskii, J.V. Hollweg, B.J. Vasquez, Resonant interactions between protons and oblique Alfvén/ion-cyclotron waves in the solar corona and solar flares. Astrophys. J. 722, 710–720 (2010). doi:10.1088/0004-637X/722/1/710. http://stacks.iop.org/0004-637X/722/i=1/a=710

  20. C.H.K. Chen, R.T. Wicks, T.S. Horbury, A.A. Schekochihin, Interpreting power anisotropy measurements in plasma turbulence. Astrophys. J. 711, 79–83 (2010). doi:10.1088/2041-8205/711/2/L79

  21. P.J. Coleman, Hydromagnetic waves in the interplanetary plasma. Phys. Rev. Lett. 17, 207–211 (1966)

  22. P.J. Coleman, Turbulence, viscosity, and dissipation in the solar wind plasma. Astrophys. J. 153, 371–388 (1968)

  23. S.R. Cranmer, Self-consistent models of the solar wind. Space Sci. Rev. (2010). doi:10.1007/s11214-010-9674-7

  24. S.R. Cranmer, A.A. van Ballegooijen, R. Edgar, Self-consistent coronal heating and solar wind acceleration from anisotropic magnetohydrodynamic turbulence. Astrophys. J. Suppl. Ser. 171, 520–551 (2007). doi:10.1086/518001

  25. S. Dasso, L.J. Milano, W.H. Matthaeus, C.W. Smith, Anisotropy in fast and slow solar wind fluctuations. Astrophys. J. 635, 181–184 (2005)

  26. T. de Kármán, L. Howarth, On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 164, 192–215 (1938)

  27. B. De Pontieu, S.W. McIntosh, M. Carlsson, V.H. Hansteen, T.D. Tarbell, C.J. Schrijver, A.M. Title, R.A. Shine, S. Tsuneta, Y. Katsukawa, K. Ichimoto, Y. Suematsu, T. Shimizu, S. Nagata, Chromospheric Alfvénic waves strong enough to power the solar wind. Science 318, 1574–1577 (2007). doi:10.1126/science.1151747

  28. B. De Pontieu, S.W. McIntosh, V.H. Hansteen, C.J. Schrijver, Observing the roots of solar coronal heating—in the chromosphere. Astrophys. J. 701, 1–6 (2009). doi:10.1088/0004-637X/701/1/L1. http://stacks.iop.org/1538-4357/701/L1

  29. P. Dmitruk, D.O. Gómez, Astrophys. J. 484, L83 (1997)

  30. P. Dmitruk, D.O. Gómez, W.H. Matthaeus, Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics. Phys. Plasmas 10, 3584–3591 (2003). doi:10.1063/1.1602698

  31. C.F. Driscoll, K.S. Fine, Experiments on vortex dynamics in pure electron plasmas. Phys. Fluids, B Plasma Phys. 2, 1359–1366 (1990). doi:10.1063/1.859556

  32. G. Einaudi, M. Velli, Nanoflares and current sheet dissipation. Space Sci. Rev. 68, 97 (1994)

  33. G. Einaudi, M. Velli, H. Politano, A. Pouquet, Energy release in a turbulent corona. Astrophys. J. 457, 113 (1996)

  34. U. Frisch, Turbulence (CUP, Cambridge, 1995)

  35. M. Georgoulis, M. Velli, G. Einaudi, Statistical properties of magnetic activity in the solar corona. Astrophys. J. 497, 957 (1998)

  36. M.L. Goldstein, D.A. Roberts, A.E. Deane, S. Ghosh, H.K. Wong, Numerical simulation of Alfvénic turbulence in the solar wind. J. Geophys. Res. 104, 14 (1999). doi:10.1029/1998JA900128

  37. A. Greco, P. Chuychai, W.H. Matthaeus, S. Servidio, P. Dmitruk, Intermittent MHD structures and classical discontinuities. Geophys. Res. Lett. (2008). doi:10.1029/2008GL035454

  38. A. Greco, W.H. Matthaeus, S. Servidio, P. Chuychai, P. Dmitruk, Statistical analysis of discontinuities in solar wind ACE data and comparison with intermittent MHD turbulence. Astrophys. J. 691, 111–114 (2009). doi:10.1088/0004-637X/691/2/L111

  39. K. Hamilton, C.W. Smith, B.J. Vasquez, R.J. Leamon, Anisotropies and helicities in the solar wind inertial and dissipation ranges at 1 AU. J. Geophys. Res. (2008). doi:10.1029/2007JA012559

  40. T. Hartlep, W.H. Matthaeus, N.S. Padhye, C.W. Smith, Magnetic field strength distribution in interplanetary turbulence. J. Geophys. Res. 105, 5135–5139 (2000)

  41. J. Heyvaerts, E.R. Priest, A self-consistent turbulent model for solar coronal heating. Astrophys. J. 390, 297 (1992)

  42. J.V. Hollweg, On wkb expansions for Alfvén waves in the solar-wind. J. Geophys. Res. 95, 14873 (1990)

  43. J.V. Hollweg, Comment on “Gravitational damping of Alfvén waves in stellar atmospheres and winds”. Astrophys. J. 488, 895 (1997)

  44. T. Horbury, A. Balogh, R.J. Forsyth, E.J. Smith, Observations of evolving turbulence in the polar solar wind. Geophys. Res. Lett. 22, 3401–3404 (1995)

  45. A. Ishizawa, R. Horiuchi, H. Ohtani, Two-scale structure of the current layer controlled by meandering motion during steady-state collisionless driven reconnection. Phys. Plasmas 11, 3579 (2004)

  46. J.R. Jokipii, Turbulence and scintillations in the interplanetary plasma. Annu. Rev. Astron. Astrophys. 11, 1 (1973)

  47. E.J. Kim, P.H. Diamond, On turbulent reconnection. Astrophys. J. 556, 1052–1065 (2001a)

  48. E.J. Kim, P.H. Diamond, Towards a self-consistent theory of turbulent reconnection. Phys. Lett. A 291, 407 (2001b)

  49. J.L. Kohl, et al., UVCS/SOHO empirical determination of anisotropic velocity distributions in the solar corona. Astrophys. J. 501, 127 (1998)

  50. A.N. Kolmogorov, Local structure of turbulence in an incompressible viscous fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305 (1941a). [Reprinted in Proc. R. Soc. London, Ser. A 434, 9–13 (1991)]

  51. A.N. Kolmogorov, On degeneration of isotropic turbulence in an incompressible viscous liquid. C. R. Acad. Sci. U.R.S.S. 31, 538–540 (1941b)

  52. A.N. Kolmogorov, 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 (1962)

  53. G. Kowal, A. Lazarian, E.T. Vishniac, K. Otmianowska-Mazur, Numerical tests of fast reconnection in weakly stochastic magnetic fields. Astrophys. J. 700, 63–85 (2009). doi:10.1088/0004-637X/700/1/63

  54. R.H. Kraichnan, Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385–1387 (1965)

  55. G. Lapenta, Self-feeding turbulent magnetic reconnection on macroscopic scales. Phys. Rev. Lett. 100(23), 235001 (2008). doi:10.1103/PhysRevLett.100.235001

  56. A. Lazarian, E.T. Vishniac, Reconnection in a weakly stochastic field. Astrophys. J. 517, 700–718 (1999)

  57. R.J. Leamon, W.H. Matthaeus, C.W. Smith, H.K. Wong, Contribution of cyclotron-resonant damping to kinetic dissipation of interplanetary turbulence. Astrophys. J. 507, 181–184 (1998a)

  58. R.J. Leamon, C.W. Smith, N.F. Ness, W.H. Matthaeus, H.K. Wong, Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103, 4775 (1998b)

  59. R.J. Leamon, W.H. Matthaeus, C.W. Smith, G.P. Zank, D.J. Mullan, S. Oughton, MHD-driven kinetic dissipation in the solar wind and corona. Astrophys. J. 537, 1054–1062 (2000). doi:10.1086/309059

  60. E. Lee, M.E. Brachet, A. Pouquet, P.D. Mininni, D. Rosenberg, Lack of universality in decaying magnetohydrodynamic turbulence. Phys. Rev. E (2010). doi:10.1103/PhysRevE.81.016318

  61. X. Li, S. Habbal, J.V. Hollweg, R. Esser, Heating and cooling of protons by turbulence-driven ion cyclotron waves in the fast solar wind. J. Geophys. Res. 104, 2521 (1999)

  62. N.F. Loureiro, D.A. Uzdensky, A.A. Schekochihin, S.C. Cowley, T.A. Yousef, Turbulent magnetic reconnection in two dimensions. Mon. Not. R. Astron. Soc. (2009). doi:10.1111/j.1745-3933.2009.00742.x

  63. B.T. MacBride, C.W. Smith, M.A. Forman, The turbulent cascade at 1 AU: Energy transfer and the third-order scaling for MHD. Astrophys. J. 679, 1644–1660 (2008). doi:10.1086/529575. http://www.journals.uchicago.edu/doi/abs/10.1086/529575

  64. B.T. MacBride, C.W. Smith, B.J. Vasquez, Inertial-range anisotropies in the solar wind from 0.3 to 1 au: Helios 1 observations. J. Geophys. Res. (2010). doi:10.1029/2009JA014939

  65. F. Malara, M. Velli, Parametric instability of a large-amplitude nonmonochromatic Alfvén wave. Phys. Plasmas 3, 4427–4433 (1996)

  66. F. Malara, L. Primavera, P. Veltri, Dissipation of Alfvén waves in compressible inhomogeneous media. Nuovo Cimento Soc. Ital. Fis., C Geophys. Space Phys. 20, 903–909 (1997)

  67. W.H. Matthaeus, Magnetic reconnection in two dimensions: localization of current and vorticity near magnetic X-points. Geophys. Res. Lett. 9, 660 (1982)

  68. W.H. Matthaeus, M.L. Goldstein, Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res. 87, 6011–6028 (1982)

  69. W.H. Matthaeus, S.L. Lamkin, Rapid magnetic reconnection caused by finite amplitude fluctuations. Phys. Fluids 28, 303–307 (1985)

  70. W.H. Matthaeus, S.L. Lamkin, Turbulent magnetic reconnection. Phys. Fluids 29, 2513–2534 (1986)

  71. W.H. Matthaeus, D. Montgomery, Selective decay hypothesis at high mechanical and magnetic Reynolds numbers. Ann. N.Y. Acad. Sci. 357, 203–222 (1980)

  72. W.H. Matthaeus, M.L. Goldstein, D.A. Roberts, Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind. J. Geophys. Res. 95, 20 (1990)

  73. W.H. Matthaeus, G.P. Zank, S. Oughton, D.J. Mullan, P. Dmitruk, Coronal heating by MHD turbulence driven by reflected low-frequency waves. Astrophys. J. 523, 93–96 (1999)

  74. J.F. McKenzie, M. Banaszkiewicz, W.I. Axford, Acceleration of the high speed solar wind. Astron. Astrophys. 303, 45 (1995)

  75. Z. Mikić, D.D. Schnack, G. Van Hoven, Creation of current filaments in the solar corona. Astrophys. J. 338, 1148 (1989)

  76. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, vol. 1 (MIT Press, Cambridge, 1971)

  77. A.S. Monin, A.M. Yaglom, Statistical Fluid Mechanics, vol. 2 (MIT Press, Cambridge, 1975)

  78. W.C. Müller, D. Biskamp, Scaling properties of three-dimensional magnetohydrodynamc turbulence. Phys. Rev. Lett. 84, 475 (2000)

  79. Y. Narita, K.H. Glassmeier, R.A. Treumann, Wave-number spectra and intermittency in the terrestrial foreshock region. Phys. Rev. Lett. 97, 191101 (2006). doi:10.1103/PhysRevLett.97.191101. http://link.aps.org/abstract/PRL/v97/e191101

  80. A.M. Obukhov, On the energy distribution in the spectrum of a turbulent flow. Dokl. Akad. Nauk SSSR 32, 22–24 (1941a). [C.R. (Dokl.) Acad. Sci. URSS 32, 19 (1963)]

  81. A.M. Obukhov, Spectral energy distribution in a turbulent flow. Izv. Acad. Nauk. SSSR. Ser. Georg. Geofiz. 5, 453 (1941b)

  82. A.M. Obukhov, Some specific features of atmospheric turbulence. J. Fluid Mech. 13, 77–81 (1962a)

  83. A.M. Obukhov, Some specific features of atmospheric turbulence. J. Geophys. Res. 67, 3011–3014 (1962b)

  84. S.A. Orszag, Lectures on the statistical theory of turbulence, in Fluid Dynamics, ed. by R. Balian, J.L. Peube (Gordon and Breach, New York, 1977), p. 235. Les Houches Summer School, 1973

  85. S.A. Orszag, L.C. Kells, Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159 (1980)

  86. K.T. Osman, T.S. Horbury, Multispacecraft measurement of anisotropic correlation functions in solar wind turbulence. Astrophys. J. 654, 103–106 (2007)

  87. K.T. Osman, T.S. Horbury, Quantitative estimates of the slab and 2-d power in solar wind turbulence using multispacecraft data. J. Geophys. Res. (2009). doi:10.1029/2008JA014036

  88. K.T. Osman, W.H. Matthaeus, A. Greco, S. Servidio, Evidence for inhomogeneous heating in the solar wind. Astrophys. J. 727, 11 (2011). doi:10.1088/2041-8205/727/1/L11

  89. S. Oughton, E.R. Priest, W.H. Matthaeus, The influence of a mean magnetic field on three-dimensional MHD turbulence. J. Fluid Mech. 280, 95–117 (1994). doi:10.1017/S0022112094002867

  90. E.N. Parker, Sweet’s mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res. 62, 509 (1957)

  91. E. Parker, Astrophys. J. 174, 499 (1972)

  92. E.N. Parker, Cosmical Magnetic Fields: Their Origin and Activity (OUP, Oxford, 1979)

  93. E.N. Parker Astrophys. J. 372, 719 (1991)

  94. H.E. Petschek, Magnetic field annihilation, in Physics of Solar Flares, ed. by W.N. Hess. NASA SP-50 (NASA, Washington, 1964), pp. 425–439

  95. M.S. Plesset, Am. J. Phys. 19, 471 (1951)

  96. J.J. Podesta, Laws for third-order moments in homogeneous anisotropic incompressible magnetohydrodynamic turbulence. J. Fluid Mech. 609, 171–194 (2008). doi:10.1017/S0022112008002280

  97. J.J. Podesta, M.A. Forman, C.W. Smith, Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence. Phys. Plasmas 14(9), 092305 (2007). doi:10.1063/1.2783224. http://link.aip.org/link/?PHP/14/092305/1

  98. H. Politano, A. Pouquet, Dynamical length scales for turbulent magnetized flows. Geophys. Res. Lett. 25, 273–276 (1998a). doi:10.1029/97GL03642

  99. H. Politano, A. Pouquet, von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57, 21 (1998b)

  100. Y. Ponty, P.D. Mininni, D.C. Montgomery, J.F. Pinton, H. Politano, A. Pouquet, Numerical study of dynamo action at low magnetic Prandtl numbers. Phys. Rev. Lett. 94, 164502 (2005). doi:10.1103/PhysRevLett.94.164502. http://link.aps.org/abstract/PRL/v94/e164502

  101. A.F. Rappazzo, M. Velli, G. Einaudi, R.B. Dahlburg, Nonlinear dynamics of the Parker scenario for coronal heating. Astrophys. J. 677, 1348–1366 (2008). doi:10.1086/528786

  102. A.F. Rappazzo, M. Velli, G. Einaudi, Shear photospheric forcing and the origin of turbulence in coronal loops. Astrophys. J. 722, 65–78 (2010a). doi:10.1088/0004-637X/722/1/65. http://stacks.iop.org/0004-637X/722/i=1/a=65

  103. A. Retinó, D. Sundkvist, A. Vaivads, F. Mozer, M. André, C.J. Owen: In situ evidence of magnetic reconnection in turbulent plasma. Nat. Phys. 3, 236 (2007)

  104. J.D. Richardson, K.I. Paularena, A.J. Lazarus, J.W. Belcher, Radial evolution of the solar wind from IMP 8 to Voyager 2. Geophys. Res. Lett. 22, 325 (1995)

  105. A. Richter, E. Naudascher, Fluctuating forces on a rigid circular cylinder in confined flow. J. Fluid Mech. 78, 561–576 (1976). doi:10.1017/S0022112076002607

  106. D.A. Roberts, Interplanetary observational constraints on Alfvén wave acceleration of the solar wind. J. Geophys. Res. 94, 6899–6905 (1989)

  107. D.A. Roberts, Demonstrations that the solar wind is not accelerated by waves or turbulence. Astrophys. J. 711(2), 1044–1050 (2010). doi:10.1088/0004-637X/711/2/1044. http://stacks.iop.org/0004-637X/711/1044

  108. D.A. Roberts, L.W. Klein, M.L. Goldstein, W.H. Matthaeus, The nature and evolution of magnetohydrodynamic fluctuations in the solar wind: Voyager observations. J. Geophys. Res. 92, 11 (1987a)

  109. D.A. Roberts, M.L. Goldstein, L.W. Klein, W.H. Matthaeus, Origin and evolution of fluctuations in the solar wind: Helios observations and Helios-Voyager comparisons. J. Geophys. Res. 92, 12 (1987b)

  110. D.A. Roberts, S. Ghosh, M.L. Goldstein, W.H. Matthaeus, Magnetohydrodynamic simulation of the radial evolution and stream structure of solar wind turbulence. Phys. Rev. Lett. 67, 3741 (1992a)

  111. D.A. Roberts, M.L. Goldstein, W.H. Matthaeus, S. Ghosh, Velocity shear generation of solar wind turbulence. J. Geophys. Res. 97, 17 (1992b)

  112. D.C. Robinson, M.G. Rusbridge, Structure of turbulence in the zeta plasma. Phys. Fluids 14, 2499–2511 (1971). doi:10.1063/1.1693359

  113. M.E. Ruiz, S. Dasso, W.H. Matthaeus, E. Marsch, J.M. Weygand, Anisotropy of the magnetic correlation function in the inner heliosphere, in Twelfth International Solar Wind Conference, vol. 1216 (2010), pp. 160–163. doi:10.1063/1.3395826

  114. F. Sahraoui, M.L. Goldstein, G. Belmont, P. Canu, L. Rezeau, Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys. Rev. Lett. 105(13), 131101 (2010). doi:10.1103/PhysRevLett.105.131101

  115. J. Sakai, T. Tajima, F. Brunel, Forced reconnection by nonlinear magnetohydrodynamic waves. Sol. Phys. 91, 103–113 (1984). doi:10.1007/BF00213617

  116. T. Sato, T. Hayashi, Externally driven magnetic reconnection and a powerful energy converter. Phys. Fluids 22, 1189 (1979)

  117. C.J. Schrijver, A.M. Title, The topology of a mixed-polarity potential field, and inferences for the heating of the quiet solar corona. Sol. Phys. 207, 223–240 (2002)

  118. C.J. Schrijver, M.L. De Rosa, A.M. Title, T.R. Metcalf, The nonpotentiality of active-region coronae and the dynamics of the photospheric magnetic field. Astrophys. J. 628, 501–513 (2005). doi:10.1086/430733

  119. S. Servidio, W.H. Matthaeus, M.A. Shay, P.A. Cassak, P. Dmitruk, Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 102, 115003 (2009). doi:10.1103/PhysRevLett.102.115003. http://link.aps.org/abstract/PRL/v102/e115003

  120. S. Servidio, W.H. Matthaeus, M.A. Shay, P. Dmitruk, P.A. Cassak, M. Wan, Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 17(3), 032315 (2010). doi:10.1063/1.3368798. http://link.aip.org/link/?PHP/17/032315/1

  121. Z. She, E. Lévêque, Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336 (1994)

  122. 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)

  123. L. Sorriso-Valvo, R. Marino, V. Carbone, A. Noullez, F. Lepreti, P. Veltri, R. Bruno, B. Bavassano, E. Pietropaolo, Observation of inertial energy cascade in interplanetary space plasma. Phys. Rev. Lett. 99, 115001 (2007). doi:10.1103/PhysRevLett.99.115001. http://link.aps.org/abstract/PRL/v99/e115001

  124. T.K. Suzuki, S. Inutsuka, Solar winds driven by nonlinear low-frequency Alfvén waves from the photosphere: parametric study for fast/slow winds and disappearance of solar winds. J. Geophys. Res. 111, 06101 (2006). doi:10.1029/2005JA011502

  125. P.A. Sweet, The production of high-energy particles in solar flares. Suppl. Nuovo Cim. 8, 188 (1958)

  126. D. Telloni, E. Antonucci, M.A. Dodero, O VI kinetic temperature and outflow velocity in solar corona beyond 3R????, in SOHO-17. 10 Years of SOHO and Beyond, vol. 617 (ESA Special Publication, 2006)

  127. J.A. Tessein, C.W. Smith, B.T. MacBride, W.H. Matthaeus, M.A. Forman, J.E. Borovsky, Spectral indices for multi-dimensional interplanetary turbulence at 1 au. Astrophys. J. 692, 684–693 (2009). doi:10.1088/0004-637X/692/1/684

  128. B.T. Tsurutani, E.J. Smith, Interplanetary discontinuities—Temporal variations and the radial gradient from 1 to 8.5 AU. J. Geophys. Res. 84, 2773–2787 (1979)

  129. C.Y. Tu, E. Marsch, A model of solar wind fluctuations with two components: Alfvén waves and convective structures. J. Geophys. Res. 98, 1257 (1993)

  130. C.Y. Tu, E. Marsch, MHD structures, waves and turbulence in the solar wind. Space Sci. Rev. 73, 1–210 (1995)

  131. A.A. Van Ballegooijen, Cascade of magnetic energy as a mechanism of coronal heating. Astrophys. J. 311, 1001–1014 (1986)

  132. M. van Dyke, An Album of Fluid Motion (The Parabolic Press, Palo Alto, 1982)

  133. B.J. Vasquez, V.I. Abramenko, D.K. Haggerty, C.W. Smith, Numerous small magnetic field discontinuities of Bartels rotation 2286 and the potential role of Alfvénic turbulence. J. Geophys. Res. 112, 11102 (2007a). doi:10.1029/2007JA012504

  134. B.J. Vasquez, C.W. Smith, K. Hamilton, B.T. MacBride, R.J. Leamon, Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU. J. Geophys. Res. (2007b). doi:10.1029/2007JA012305

  135. M. Velli, S.R. Habbal, R. Esser, Coronal plumes and fine-scale structured in high-speed solar-wind streams. Space Sci. Rev. 70, 391 (1994)

  136. A. Verdini, M. Velli, Alfvén waves and turbulence in the solar atmosphere and solar wind. Astrophys. J. 662, 669–676 (2007). doi:10.1086/510710

  137. A. Verdini, M. Velli, W.H. Matthaeus, S. Oughton, P. Dmitruk, A turbulence-driven model for heating and acceleration of the fast wind in coronal holes. Astrophys. J. 708, 116–120 (2010). doi:10.1088/2041-8205/708/2/L116

  138. M.K. Verma, D.A. Roberts, M.L. Goldstein, Turbulent heating and temperature evolution in the solar wind plasma. J. Geophys. Res. 100, 19–839 (1995)

  139. M. Wan, S. Oughton, S. Servidio, W.H. Matthaeus, Generation of non-Gaussian statistics and coherent structures in ideal magnetohydrodynamics. Phys. Plasmas 16(8), 080703 (2009a). doi:10.1063/1.3206949

  140. M. Wan, S. Servidio, S. Oughton, W.H. Matthaeus, The third-order law for increments in magnetohydrodynamic turbulence with constant shear. Phys. Plasmas 16, 090703 (2009b). doi:10.1063/1.3240333. http://link.aip.org/link/?PHP/16/090703/1

  141. M. Wan, S. Oughton, S. Servidio, W.H. Matthaeus, On the accuracy of simulations of turbulence. Phys. Plasmas 17, 082308 (2010). doi:10.1063/1.3474957. http://link.aip.org/link/?PHP/17/082308/1

  142. J.M. Weygand, W.H. Matthaeus, S. Dasso, M.G. Kivelson, L.M. Kistler, C. Mouikis, Anisotropy of the Taylor scale and the correlation scale in plasma sheet and solar wind magnetic field fluctuations. J. Geophys. Res. (2009). doi:10.1029/2008JA013766

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Correspondence to W. H. Matthaeus.

Additional information

We are indebted to S. Fuselier, J. Gosling, and S. Antiochos for posing the title question at the Yosemite meeting and elsewhere.

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Matthaeus, W.H., Velli, M. Who Needs Turbulence?. Space Sci Rev 160, 145 (2011). https://doi.org/10.1007/s11214-011-9793-9

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Keywords

  • Magnetic reconnection
  • Turbulence
  • Solar wind
  • Corona