TY - JOUR

T1 - Passive advection of a vector field: Anisotropy, finite correlation time, exact solution, and logarithmic corrections to ordinary scaling

AU - Antonov, N. V.

AU - Gulitskiy, N. M.

PY - 2015

Y1 - 2015

N2 - In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015)] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n, all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E∝k1−ξ⊥ and the dispersion law ω∝k2−η⊥. In contrast to the we

AB - In this work we study the generalization of the problem considered in [Phys. Rev. E 91, 013002 (2015)] to the case of finite correlation time of the environment (velocity) field. The model describes a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow. Inertial-range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and preassigned pair correlation function. Due to the presence of distinguished direction n, all the multiloop diagrams in this model vanish, so that the results obtained are exact. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to the two nontrivial fixed points of the RG equations. Their stability depends on the relation between the exponents in the energy spectrum E∝k1−ξ⊥ and the dispersion law ω∝k2−η⊥. In contrast to the we

KW - anomalous scaling

KW - kinematic dynamo

KW - renormalization group

KW - operator product expansion

U2 - 10.1103/PhysRevE.92.043018

DO - 10.1103/PhysRevE.92.043018

M3 - Article

VL - 92

SP - 043018

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 4

ER -