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

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Part of the Lecture Notes in Computer Science book series (LNTCS,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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© 2012 Springer-Verlag Berlin Heidelberg

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Antonov, N.V., Gulitskiy, N.M. (2012). Two-Loop Calculation of the Anomalous Exponents in the Kazantsev-Kraichnan Model of Magnetic Hydrodynamics. In: Adam, G., Buša, J., Hnatič, M. (eds) Mathematical Modeling and Computational Science. MMCP 2011. Lecture Notes in Computer Science, vol 7125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28212-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-28212-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28211-9

  • Online ISBN: 978-3-642-28212-6

  • eBook Packages: Computer ScienceComputer Science (R0)