title: Logarithmic violation of scaling in strongly anisotropic turbulent  transfer of a passive vector field
metadata.name: dc.contributor.author
metadata.value: N. V. Antonov
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: N. M. Gulitskiy
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-07T19:52:00Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-07T19:52:00Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2014-06-15
metadata.lang: -
metadata.name: dc.identifier
metadata.value: 10.1103/PhysRevE.91.013002
metadata.lang: -
metadata.name: dc.identifier.issn
metadata.value: 10.1103/PhysRevE.91.013002
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1953
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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 advecting velocity field is Gaussian, not correlated in time,
  with the pair correlation function of the form $\propto \delta(t-t') /
  k_{\bot}^{d-1+\xi}$, where $k_{\bot}=|{\bf k}_{\bot}|$ and ${\bf k}_{\bot}$ is
  the component of the wave vector, perpendicular to the distinguished direction
  (`direction of the flow') -- the $d$-dimensional generalization of the ensemble
  introduced by Avellaneda and Majda [{\it Commun. Math. Phys.} {\bf 131}: 381
  (1990)]. 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 isotropic Kraichnan's model, where
  various correlation functions exhibit anomalous scaling behavior with infinite
  sets of anomalous exponents, here the dependence on the integral turbulence
  scale $L$ has a logarithmic behavior: instead of power-like 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 diagonalized. The detailed proof of
  this fact is given for correlation functions of arbitrary order.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Saint Petersburg
  State University within research Grant No. 11.38.185.2014 and
  by the Russian Foundation for Basic Research within Project
  No. 12-02-00874-a. N.M.G. was also supported by the Dmitry
  Zimin’s Dynasty foundation.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: American Physical Society
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Physics - Statistical Mechanics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Physics - Statistical Mechanics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Nonlinear Sciences - Chaotic Dynamics
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Logarithmic violation of scaling in strongly anisotropic turbulent  transfer of a passive vector field
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: PhysRevE_91_013002.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1953/1/PhysRevE_91_013002.pdf
resources.format: Adobe PDF
resources.size: 1,14 MB