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Two-Loop Calculation of the Anomalous Exponents in the Kazantsev-Kraichnan Model of Magnetic Hydrodynamics

  • Nikolay V. Antonov
  • Nikolay M. Gulitskiy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)

Abstract

The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. Field theoretic renormalization group methods are applied to the Kazantsev–Kraichnan model of a passive vector advected by the Gaussian velocity field with zero mean and correlation function ∝ δ(t − t′)/k d + ε . Inertial-range anomalous scaling for the tensor pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain “dangerous” composite operators, whose negative critical dimensions determine the anomalous exponents. The main technical result is the calculation of the anomalous exponents in the order ε 2 of the ε expansion (two-loop approximation).

Keywords

Turbulence Renormalization Group Operator Product Expansion Anomalous Scaling Kraichnan’s Rapid-Change Model 

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References

  1. 1.
    Adzhemyan, L.T., Antonov, N.V.: Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow. Phys. Rev. E 58, 7381 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adzhemyan, L.T., Antonov, N.V., Barinov, V.A., Kabrits, Y.S., Vasil’ev, A.N.: Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ε 3. Phys. Rev. E 64, 056306 (2001)CrossRefGoogle Scholar
  3. 3.
    Adzhemyan, L.T., Antonov, N.V., Honkonen, J., Kim, T.L.: Anomalous scaling of a passive scalar advected by the Navier-Stokes velocity field: Two-loop approximation. Phys. Rev. E 71, 016303 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Adzhemyan, L.T., Antonov, N.V., Vasil’ev, A.N.: Renormalization group, operator product expansion, and anomalous scaling in a model of advected passive scalar. Phys. Rev. E 58, 1823 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Antonov, N.V., Lanotte, A., Mazzino, A.: Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence. Phys. Rev. E 61, 6586 (2000)CrossRefGoogle Scholar
  6. 6.
    Hnatich, M., Honkonen, J., Jurcisin, M., Mazzino, A., Sprinc, S.: Anomalous scaling of passively advected magnetic field in the presense of strong anisotropy. Phys. Rev. E 71, 066312 (2005)CrossRefGoogle Scholar
  7. 7.
    Kraichnan, R.H.: Small-Scale Structure of a Scalar Field Convected by Turbulence. Phys. Fluids 11, 945 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lanotte, A., Mazzino, A.: Anisotropic non-perturbative zero modes for passively advected magnetic fields. Phys. Rev. 60, R3483 (1996)Google Scholar
  9. 9.
    Obukhov, A.M.: Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk. SSSR, Ser. Georg. Geofiz. 13, 58 (1949)MathSciNetGoogle Scholar
  10. 10.
    Salem, C., Mangeney, A., Bale, S.D., Veltri, P.: Solar wind MHD turbulence: anomalous scaling and role of intermittency. Astrophys. J. 702, 537 (2009)CrossRefGoogle Scholar
  11. 11.
    Vasiliev, A.N.: The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics. St. Petersburg Institute of Nuclear Physics, St. Petersburg (1998). English translation: Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  12. 12.
    Zeldovich, Y.B., Ruzmaikin, A.A., Sokoloff, D.D.: Magnetic Fields in Astrophysics. Gordon and Breach, New York (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Nikolay V. Antonov
    • 1
  • Nikolay M. Gulitskiy
    • 2
  1. 1.Department of PhysicsSt. Petersburg State UniversitySt. PetersburgRussian Federation
  2. 2.D.I. Mendeleyev Institute for MetrologySt.PetersburgRussian Federation

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