Advertisement

Electron magnetohydrodynamic turbulence: universal features

  • Bhimsen K. ShivamoggiEmail author
Regular Article

Abstract

The energy cascade of electron magnetohydrodynamic (EMHD) turbulence is considered. Fractal and multi-fractal models for the energy dissipation field are used to determine the spatial intermittency corrections to the scaling behavior in the high-wavenumber (electron hydrodynamic limit) and low-wavenumber (magnetization limit) asymptotic regimes of the inertial range. Extrapolation of the multi-fractal scaling down to the dissipative microscales confirms in these asymptotic regimes a dissipative anomaly previously indicated by the numerical simulations of EMHD turbulence. Several basic features of the EMHD turbulent system are found to be universal which seem to transcend the existence of the characteristic length scale d e (which is the electron skin depth) in the EMHD problem: equipartition spectrum; Reynolds-number scaling of the dissipative microscales; scaling of the probability distribution function (PDF) of the electron-flow velocity (or magnetic field) gradient (even with intermittency corrections); dissipative anomaly; and critical exponent scaling.

Keywords

Plasma Physics 

References

  1. 1.
    M. Yamada, H. Ji, S. Hsu, T. Carter, R.M. Kulsrud, F. Trintchouk, Phys. Plasmas 7, 1781 (2000)CrossRefADSGoogle Scholar
  2. 2.
    O. Alexandrova, V. Carbone, P. Veltri, L. Sorriso-Valvo, ApJ 674, 1153 (2008)CrossRefADSGoogle Scholar
  3. 3.
    A.S. Kingsep, K.V. Chukbar, V.V. Yan’kov, Rev. Plasma Phys. 16, 243 (1990)Google Scholar
  4. 4.
    A.V. Gordeev, A.S. Kingsep, L.I. Rudakov, Phys. Rep. 243, 215 (1994)CrossRefADSGoogle Scholar
  5. 5.
    D. Biskamp, E. Schwarz, J.F. Drake, Phys. Rev. Lett. 76, 1264 (1996)CrossRefADSGoogle Scholar
  6. 6.
    D. Biskamp, E. Schwarz, A. Zeiler, A. Celani, J.F. Drake, Phys. Plasmas 6, 751 (1999)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    S. Dastgeer, A. Das, P. Kaw, P.H. Diamond, Phys. Plasmas 7, 571 (2000)CrossRefADSGoogle Scholar
  8. 8.
    A. Celani, R. Prandi, G. Boffetta, Europhys. Lett. 41, 13 (1997)CrossRefADSGoogle Scholar
  9. 9.
    G. Boffetta, A. Celani, A. Crisanti, R. Prandi, Phys. Rev. E 59, 3724 (1999)CrossRefADSGoogle Scholar
  10. 10.
    K. Germaschewski, R. Grauer, Phys. Plasmas 6, 3788 (1999)CrossRefADSGoogle Scholar
  11. 11.
    K.R. Sreenivasan, Phys. Fluids 27, 1048 (1984)CrossRefADSGoogle Scholar
  12. 12.
    K.R. Sreenivasan, Phys. Fluids 10, 528 (1998)CrossRefADSzbMATHMathSciNetGoogle Scholar
  13. 13.
    U. Frisch, P.L. Sulem, M. Nelkin, J. Fluid Mech. 87, 719 (1978)CrossRefADSzbMATHGoogle Scholar
  14. 14.
    U. Frisch, G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climatic Dynamics, edited by M. Ghil, R. Benzi, G. Parisi (North Holland, 1985), p. 84Google Scholar
  15. 15.
    K.H. Kiyani, S.C. Chapman, Yu.V. Khotyaintsev, M.W. Dunlop, F. Sahraoui, Phys. Rev. Lett. 103, 075006 (2009)CrossRefADSGoogle Scholar
  16. 16.
    N. Kukharin, S.A. Orszag, V. Yakhot, Phys. Rev. Lett. 75, 2486 (1995)CrossRefADSGoogle Scholar
  17. 17.
    B.K. Shivamoggi, Ann. Phys. 317, 1 (2005). Addendum: Ann. Phys. 322, 1247 (2007)CrossRefADSzbMATHMathSciNetGoogle Scholar
  18. 18.
    J.M. Burgers, Verh. K. Akad. Wet. Amsterdam 32, 643 (1929)Google Scholar
  19. 19.
    E. Hopf, J. Ration. Mech. Anal. 1, 87 (1952)zbMATHMathSciNetGoogle Scholar
  20. 20.
    T.D. Lee, Quart. Appl. Math. 10, 69 (1952)zbMATHMathSciNetGoogle Scholar
  21. 21.
    R.H. Kraichnan, J. Acoust. Soc. Am. 27, 438 (1955)CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    S.A. Orszag, G.S. Patterson, Phys. Rev. Lett. 28, 76 (1972)CrossRefADSGoogle Scholar
  23. 23.
    E.A. Novikov, Arch. Mech. 26, 741 (1974)zbMATHGoogle Scholar
  24. 24.
    B. Mandelbrot, in Turbulence and Navier-Stokes Equations, Lecture Notes in Mathematics, edited by R. Temam (Springer-Verlag, 1975), Vol. 565Google Scholar
  25. 25.
    T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Proccacia, B. I. Shraiman, Phys. Rev. A 33, 1141 (1986)CrossRefADSzbMATHMathSciNetGoogle Scholar
  26. 26.
    H.G.E. Hentschel, I. Procaccia, Physica D 8, 435 (1983)CrossRefADSzbMATHMathSciNetGoogle Scholar
  27. 27.
    C. Meneveau, K.R. Sreenivasan, J. Fluid Mech. 224, 429 (1991)CrossRefADSzbMATHGoogle Scholar
  28. 28.
    G. Paladin, A. Vulpiani, Phys. Rev. A 35, 1971 (1987)CrossRefADSGoogle Scholar
  29. 29.
    K.R. Sreenivasan, C. Meneveau, Phys. Rev. A 38, 6287 (1988)CrossRefADSGoogle Scholar
  30. 30.
    M. Nelkin, Phys. Rev. A 42, 7226 (1990)CrossRefADSGoogle Scholar
  31. 31.
    L.D. Landau, Fiz. Sowjetunion 11, 26 (1937)zbMATHGoogle Scholar
  32. 32.
    B.K. Shivamoggi, Chaos Solitons Fractals 32, 628 (2007)CrossRefADSzbMATHMathSciNetGoogle Scholar
  33. 33.
    M. Nelkin, Phys. Rev. A 9, 388 (1974)CrossRefADSGoogle Scholar
  34. 34.
    V. Yakhot, S.A. Orszag, Phys. Rev. Lett. 57, 1722 (1986)CrossRefADSGoogle Scholar
  35. 35.
    G. Eyink, N. Goldenfeld, Phys. Rev. E 50, 4679 (1994)CrossRefADSzbMATHMathSciNetGoogle Scholar
  36. 36.
    A. Esser, S. Grossmann, Eur. Phys. J. B 7, 467 (1999)CrossRefADSGoogle Scholar
  37. 37.
    B.K. Shivamoggi, Ann. Phys. 270, 263 (1998). Addendum: Ann. Phys. 312, 268 (2004)CrossRefADSzbMATHMathSciNetGoogle Scholar
  38. 38.
    B.K. Shivamoggi, Ann. Phys. 243, 177 (1995). Addendum: Ann. Phys. 318, 497 (2005)CrossRefADSzbMATHMathSciNetGoogle Scholar
  39. 39.
    B.K. Shivamoggi, Ann. Phys. 253, 239 (1997). Erratum: Ann. Phys. 312, 270 (2004)CrossRefADSzbMATHGoogle Scholar
  40. 40.
    H.A. Rose, P.L. Sulem, J. Phys. T 39, 441 (1978)CrossRefMathSciNetGoogle Scholar
  41. 41.
    P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)CrossRefADSGoogle Scholar
  42. 42.
    U. Frisch, Z.S. She, Fluid Dyn. Res. 8, 139 (1991)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Kavli Institute of Theoretical PhysicsUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations