Anisotropic Turbulent Advection of a Passive Vector Field: Effects of the Finite Correlation Time

• Published in: EPJ Web of Conferences Vol. 108; p. 2008
• Main Authors: Antonov, N. V., Gulitskiy, N. M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2016
• Subjects: Advection; Anisotropy; Asymptotic properties; Computational fluid dynamics; Correlation analysis; Dependence; Energy spectra; Exponents; Logarithms; Operators (mathematics); Scaling; Turbulence; Turbulent flow; Velocity distribution
• ISSN: 2100-014X; 2101-6275; 2100-014X
• DOI: 10.1051/epjconf/201610802008

The turbulent passive advection under the environment (velocity) field with finite correlation time is studied. Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is investigated by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and prescribed pair correlation function. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to nontrivial fixed points of the RG equations and depend on the relation between the exponents in the energy energy spectrum ε ∝ k⊥1-ξ and the dispersion law ω ∝ k⊥2-η. The corresponding anomalous exponents are associated with the critical dimensions of tensor composite operators built solely of the passive vector field itself. In contrast to the well-known isotropic Kraichnan 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. Due to the presence of the anisotropy in the model, all multiloop diagrams are equal to zero, thus this result is exact.