Skip to main content
SpringerLink
Log in

Magnetohydrodynamic Turbulence

  • Chapter
  • First Online:
Interdisciplinary Aspects of Turbulence

Part of the book series: Lecture Notes in Physics ((LNP,volume 756))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Batchelor, G.K.: Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. II 12(3), 233–239 (1969)

    MATH  Google Scholar 

  2. Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  3. Baumjohann, W., Treumann, R.A.: Basic Space Plasma Physics. Imperial College Press, London (2004)

    MATH  Google Scholar 

  4. Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., Succi, S.: Extended self-similarity in turbulent flows. Phys. Rev. E 48(1), R29–R32 (1993)

    Article  ADS  Google Scholar 

  5. Bershadskii A.: Three-dimensional isotropic magnetohydrodynamic turbulence and thermal velocity of the solar wind ions. Phys. Plasmas. 10(12), 4613–4615 (2003)

    Article  ADS  Google Scholar 

  6. Birkhoff G.D.: Proof of the ergodic theorem. Proc. Natl. Acad. Sci. USA 17, 656–660, (1931)

    Article  ADS  MATH  Google Scholar 

  7. Biskamp D.: Nonlinear Magnetohydrodynamics. Cambridge University Press, Cambridge (1993)

    Book  Google Scholar 

  8. Biskamp D.: Scaling properties in MHD turbulence. Chaos, Solitons & Fractals, 5(10), 1779–1793 (1995)

    Article  ADS  Google Scholar 

  9. Biskamp D.: Magnetic Reconnection in Plasmas. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  10. Biskamp D.: Magnetohydrodynamic Turbulence. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  11. Biskamp, D., Müller W.-C.: Decay laws for three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 83(11), 2195–2198 (1999)

    Article  ADS  Google Scholar 

  12. Biskamp, D., Müller W.-C.: Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence. Phys. Plasmas 7(12), 4889–4900 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  13. Biskamp, D., Schwarz E.: On two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 8(7), 3282–3292 (2001)

    Article  ADS  Google Scholar 

  14. Biskamp, D., Welter H.: Dynamics of decaying two-dimensional magnetohydrodynamic turbulence. Phys. Fluids B 1(10), 1964–1979 (1989)

    Article  ADS  Google Scholar 

  15. Boldyrev S.: On the spectrum of magnetohydrodynamic turbulence. Astrophys. J. 626, L37–L40 (2005)

    Article  ADS  Google Scholar 

  16. Boldyrev, S., Nordlund, Å., Padoan P.: Scaling relations of supersonic turbulence in star-forming molecular clouds. Astrophys. J. 573, 678–684 (2002)

    Article  ADS  Google Scholar 

  17. Brandenburg, A., Subramanian K.: Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  18. Burlaga L.F.: Intermittent turbulence in the solar wind. J. Geophy. Res. 96(A4), 5847–5851 (1991)

    Article  ADS  Google Scholar 

  19. Busse F.H.: Homogeneous dynamos in planetary cores and in the laboratory. Annu Rev. Fluid Mech. 32, 383–408 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Carbone, V., Veltri P.: A shell model for anisotropic magnetohydrodynamic turbulence. Geophy. Astrophys. Fluid Dyn. 52, 153–181 (1990)

    Article  ADS  Google Scholar 

  21. Cho, J., Lazarian, A., Vishniac E.T.: Simulations of magnetohydrodynamic turbulence in a strongly magnetized medium. Astrophys. J. 564, 291–301 (2002)

    Article  ADS  Google Scholar 

  22. Cho, J., Vishniac E.T.: The anisotropy of magnetohydrodynamic Alfvénic turbulence. Astrophys. J. 539, 273–282 (2000)

    Article  ADS  Google Scholar 

  23. Comte-Bellot, G., Corrsin S.: The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25(4), 657–682 (1966)

    Article  ADS  Google Scholar 

  24. Dobrowolny, M., Mangeney, A., Veltri P.: Fully developed anisotropic hydromagnetic turbulence in interplanetary space. Phys. Rev. Lett. 45(2), 144–147 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  25. Dubrulle B.: Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance. Phys. Rev. Lett. 73(7), 959–962 (1994)

    Article  ADS  Google Scholar 

  26. Edwards S.F.: The statistical dynamics of homogeneous turbulence. J. Fluid Mech. 18, 239–273 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  27. Elsässer W.M.: The hydromagnetic equations. Phys. Rev. 79, 183 (1950)

    Article  ADS  MATH  Google Scholar 

  28. Falkovich G.: Bottleneck phenomenon in developed turbulence. Phys. Fluids 6(4), 1411–1414 (1994)

    Article  ADS  MATH  Google Scholar 

  29. Frisch U.: Turbulence. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  30. Frisch, U., Lesieur, M., Brissaud A.: A Markovian random coupling model for turbulence. J. Fluid Mech. 65(1), 145–152 (1974)

    Article  ADS  MATH  Google Scholar 

  31. Frisch U., Pouquet, A., Léorat, J., Mazure A.: Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. J. Fluid Mech. 68(4), 789–778 (1975)

    Article  ADS  MATH  Google Scholar 

  32. Galtier, S., Nazarenko, S.V., Newell, A.C., Pouquet A.: A weak turbulence theory for incompressible magnetohydrodynamics. J. Plasma Phys. 63(5), 447–488 (2000)

    Article  ADS  MATH  Google Scholar 

  33. Galtier, S., Politano, H., Pouquet A.: Self-similar energy decay in magnetohydrodynamic turbulence. Phys. Rev. Lett. 79(15), 2807–2810 (1997)

    Article  ADS  Google Scholar 

  34. Galtier, S., Pouquet, A., Mangeney A.: On spectral scaling laws for incompressible anisotropic MHD. J. Plasma Phys. 12, 092310 (2005)

    Article  Google Scholar 

  35. Goldreich, P., Sridhar S.: Toward a theory of interstellar turbulence. II. Strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995)

    Article  ADS  Google Scholar 

  36. Goldreich, P., Sridhar S.: Magnetohydrodynamic turbulence revisited. Astrophys. J. 485, 680–688 (1997)

    Article  ADS  Google Scholar 

  37. Grappin R.: Onset and decay of two-dimensional magnetohydrodynamic turbulence with velocity-magnetic field correlation. Phys. Fluids 29(8), 2433–2443 (1986)

    Article  ADS  MATH  Google Scholar 

  38. Grappin, R., Pouquet, A., Léorat J.: Dependence of MHD turbulence spectra on the velocity field-magnetic field correlation. Astron. Astrophys. 126, 51–58 (1983)

    ADS  Google Scholar 

  39. Grappin, R., Frisch, U., Léorat, J., Pouquet A.: Alfvénic fluctuations as asymptotic states of MHD turbulence. Astron. Astrophys. 105, 6–14 (1982)

    ADS  MATH  Google Scholar 

  40. Grauer, R., Krug, J., Marliani C.: Scaling of high-order structure functions in magnetohydrodynamic turbulence. Phys. Lett. A 195, 335–338 (1994)

    Article  ADS  Google Scholar 

  41. Hatori T.: Kolmogorov-style argument for the decaying homogeneous MHD turbulence. J. Phys. Soc. Japan 53(8), 2539–2545 (1984)

    Article  ADS  Google Scholar 

  42. Haugen, N.E.L., Brandenburg, A., Dobler W.: Is nonhelical hydromagnetic turbulence peaked at small scales? Astrophys. J. 597, L141–L144 (2003)

    Article  ADS  Google Scholar 

  43. Herring J.R.: Self-consistent-field approach to turbulence theory. Phys. Fluids 8(12), 2219–2225 (1965)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Hinze J.O.: Turbulence. McGraw-Hill, New York (1987)

    Google Scholar 

  45. Horbury, T.S., Balogh A.: Structure function measurements of the intermittent MHD turbulent cascade. Nonlinear Processes in Geophys. 4, 185–199 (1997)

    Article  ADS  Google Scholar 

  46. Iroshnikov P.S.: Turbulence of a conducting fluid in a strong magnetic field. Soviet Astron. 7, 566–571 (1964) [Astron. Zh., 40, 742, 1963]

    ADS  MathSciNet  Google Scholar 

  47. Kolmogorov A.N.: On the degeneration of isotropic turbulence in an incompressible viscous liquid. Doklady Akademiia Nauk SSSR 31, 538–540 (1941)

    MathSciNet  Google Scholar 

  48. Kolmogorov A.N.: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Kolmogorov A.N.: Dissipation of energy in the locally isotropic turbulence. Proc. Roy. Soc. A 434, 15–17 (1991) [Dokl. Akad. Nauk SSSR, 32(1), 1941]

    Google Scholar 

  50. Kolmogorov A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc. Roy. Soc. A 434, 9–13 (1991) [Dokl. Akad. Nauk SSSR, 30(4), 1941]

    Google Scholar 

  51. Kraichnan R.H.: The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543 (1959)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Kraichnan R.H.: Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8(7), 1385–1387 (1965)

    Article  ADS  Google Scholar 

  53. Kraichnan R.H.: Lagrangian-history closure approximation for turbulence. Phys. Fluids 8(4), 575–598 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  54. Kraichnan R.H.: An almost Galilean-invariant turbulence model. J. Fluid Mech. 47(3), 513–524 (1971)

    Article  ADS  MATH  Google Scholar 

  55. Leamon, R.J. Smith, C.W., Ness, N.F., Matthaeus, W.H., Wong H.K.: Observational constraints on the dynamics of the interplanetary magnetic field dissipation range. J. Geophys. Res. 103(A3), 4775–4787 (1998)

    Article  ADS  Google Scholar 

  56. Lesieur M.: Turbulence in Fluids. Kluwer Academic Publishers, Dordrecht (1997)

    Book  MATH  Google Scholar 

  57. Lesieur, M., Schertzer D.: Amortissement autosimilaire d’une turbulence à grand nombre de Reynolds. Journal de Mécanique 17(4), 609–646 (1978)

    ADS  MathSciNet  MATH  Google Scholar 

  58. Leslie D.C.: Developments in the Theory of Turbulence. Clarendon Press, Oxford (1983)

    MATH  Google Scholar 

  59. Lohse, D., Müller-Groeling A.: Bottleneck effects in turbulence: Scaling phenomena in r versus p space. Phys. Rev. Lett. 74(10), 1747–1750 (1995)

    Article  ADS  Google Scholar 

  60. Mac Low, M.-M., Klessen, R.S., Burkert, A. Smith M.D.: Kinetic energy decay rates of supersonic and super-alfvénic turbulence in star-forming clouds. Phys. Rev. Lett. 80(13), 2754–2757 (1998)

    Article  ADS  Google Scholar 

  61. Maron, J., Goldreich P.: Simulations of incompressible magnetohydrodynamic turbulence. Astrophys. J. 554, 1175–1196 (2001)

    Article  ADS  Google Scholar 

  62. Matthaeus, W.H., Ghosh, S., Oughton, S., Roberts D.: Anisotropic three-dimensional MHD turbulence. J. Geophys. Res. 101(A4), 7619–7629 (1996)

    Article  ADS  Google Scholar 

  63. Milano, L.J., Matthaeus, W.H., Dmitruk, P., Montgomery D.C.: Local anisotropy in incompressible magnetohydrodynamic turbulence. Phys. Plasmas 8(6), 2673–2681 (2001)

    Article  ADS  Google Scholar 

  64. Moffatt H.K.: The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35(1), 117–129 (1969)

    Article  ADS  MATH  Google Scholar 

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

    Google Scholar 

  66. Monin, A.S., Yaglom A.M.: Statistical Fluid Mechanics, vol. 2. MIT Press, Cambridge, Massachusetts (1981)

    Google Scholar 

  67. Müller, W.-C., Biskamp D.: Scaling properties of three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 84(3), 475–478 (2000)

    Article  ADS  Google Scholar 

  68. Müller, W.-C., Biskamp, D., Grappin R.: Statistical anisotropy of magnetohydrodynamic turbulence. Phys. Rev. E 67, 066302–1–066302–4 (2003)

    MathSciNet  Google Scholar 

  69. Müller W.-C., Grappin R.: Energy dynamics in magnetohydrodynamic turbulence. Phys. Rev. Lett. 95, 114502–1–114502–4 (2005)

    Article  Google Scholar 

  70. Orszag S.A.: Analytical theories of turbulence. J. Fluid Mech. 41(2), 363–386 (1970)

    Article  ADS  MATH  Google Scholar 

  71. Ortolani, S., Schnack D.D.: Magnetohydrodynamics of Plasma Relaxation. World Scientific, Singapore (1993)

    Book  Google Scholar 

  72. Padoan, P., Jimenez, R., Nordlund, Å., Boldyrev S.: Structure function scaling in compressible super-Alfvénic MHD turbulence. Phys. Rev. Lett. 92(19), 191102–1–191102–4 (2004)

    Article  Google Scholar 

  73. Parker E.N.: Cosmical Magnetic Fields. Clarendon Press, Oxford (1979)

    Google Scholar 

  74. Politano, H., Pouquet A.: Model of intermittency in magnetohydrodynamic turbulence. Phys. Rev. E 52(1), 636–641 (1995)

    Article  ADS  Google Scholar 

  75. Politano, H., Pouquet A.: Dynamical length scales for turbulent magnetized flows. Geophys. Res. Lett. 25(3), 273–276 (1998)

    Article  ADS  Google Scholar 

  76. Politano, H., Pouquet A.: Von Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57(1), R21–R24 (1998)

    Article  ADS  Google Scholar 

  77. Politano, H., Pouquet, A., Carbone V.: Determination of anomalous exponents of structure functions in two-dimensional magnetohydrodynamic turbulence. Europhys. Lett. 43(5), 516–521 (1998)

    Article  ADS  Google Scholar 

  78. Politano, H., Pouquet, A., Sulem P.L.: Inertial ranges and resistive instabilities in two-dimensional magnetohydrodynamic turbulence. Phys. Fluids B 1(12), 2330–2339 (1989)

    Article  ADS  Google Scholar 

  79. Pope S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  80. Pouquet, A., Frisch, U., Léorat J.: Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77(2), 321–354 (1976)

    Article  ADS  MATH  Google Scholar 

  81. Richardson L.F.: Weather Prediction by Numerical Process. Cambridge University Press, Cambridge (1922)

    MATH  Google Scholar 

  82. Rose, H.A., Sulem P.L.: Fully developed turbulence and statistical mechanics. Journal de Physique 39(5), 441–483 (1978)

    Article  MathSciNet  Google Scholar 

  83. She, Z.-S., Lévêque E.: Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72(3), 336–339 (1994)

    Article  ADS  Google Scholar 

  84. She, Z.-S., Waymire E.C.: Quantized energy cascade and log-Poisson statistics in fully developed turbulence. Phys. Rev. Lett. 74(2), 262–265 (1995)

    Article  ADS  Google Scholar 

  85. Shebalin, J.V., Matthaeus, W.H., Montgomery D.: Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29(3), 525–547 (1983)

    Article  ADS  Google Scholar 

  86. Smith, M.R., Donnelly, R.J., Goldenfeld, N., Vinen W.F.: Decay of vorticity in homogeneous turbulence. Phys. Rev. Lett. 71(16), 2583–2586 (1993)

    Article  ADS  Google Scholar 

  87. Soward, A.M., Jones, C.A., Hughes, D.W., Weiss, N.O. (Eds.): Fluid Dynamics and Dynamos in Astrophysics and Geophysics. CRC Press, Boca Raton, Florida (2005)

    MATH  Google Scholar 

  88. Sreenivasan, K.R., Antonia R.A.: The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  89. Sridhar, S., Goldreich P.: Toward a theory of interstellar turbulence. I. Weak Alfvénic turbulence. Astrophys. J. 432, 612–621 (1994)

    Article  ADS  Google Scholar 

  90. Stone, J.M., Ostriker, E.C., Gammie C.F.: Dissipation in compressible magnetohydrodynamic turbulence. Astrophys. J. 508, L99–L102 (1998)

    Article  ADS  Google Scholar 

  91. Ting, A.C., Matthaeus, W.H., Montgomery D.: Turbulent relaxation processes in magnetohydrodynamics. Phys. Fluids 29(10), 3261–3274 (1986)

    Article  ADS  Google Scholar 

  92. Tritton D.J.: Physical Fluid Dynamics. Clarendon Press, Oxford (1998)

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  94. Wesson J.: Tokamaks. Clarendon Press, Oxford (1997)

    MATH  Google Scholar 

  95. Yoshizawa, A., Itoh, S.-I., Itoh K.: Plasma and Fluid Turbulence. Institute of Physics Publishing, Bristol (2003)

    Book  MATH  Google Scholar 

  96. Zeldovich, Ya.B., Ruzmaikin, A.A., Sokoloff D.D.: Magnetic Fields In Astrophysics. Gordon and Breach Science Publishers, New York (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institut für Plasmaphysik, 85748, Garching, Germany

    W.-C. Müller

Authors
  1. W.-C. Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. MPI für Astrophysik, 85741, Garching, Germany

    Wolfgang Hillebrandt  & Friedrich Kupka  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Müller, WC. (2008). Magnetohydrodynamic Turbulence. In: Hillebrandt, W., Kupka, F. (eds) Interdisciplinary Aspects of Turbulence. Lecture Notes in Physics, vol 756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78961-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78961-1_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78960-4

  • Online ISBN: 978-3-540-78961-1

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation