Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

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Abstract

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropicKraichnan’s model, where various correlation functions exhibit anomalous scaling behavior with infiniteтsets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L. The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagon
Original languageEnglish
Pages (from-to)013002_1-25
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number1
DOIs
StatePublished - 2015

Keywords

  • renormalization group
  • magnitohydrodinamical turbulence
  • operator product expansion
  • passive vector advection

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