Advection of passive magnetic field by the Gaussian velocity field with finite correlations in time and spatial parity v
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dvection of Passive Magnetic Field by the Gaussian Velocity Field with Finite Correlations in Time and Spatial Parity Violation1 ˆ
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E. Jur c išinová and M. Jur c išin Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia email: [email protected], [email protected] Abstract—Using the field theoretic renormalization group technique the model of passively advected weak magnetic field by an incompressible isotropic helical turbulent flow is investigated up to the second order of the perturbation theory (twoloop approximation) in the framework of an extended Kazantsev–Kraichnan model of kinematic magnetohydrodynamics. Statistical fluctuations of the velocity field are taken in the form of a Gaussian distribution with zero mean and defined noise with finite correlations in time. The twoloop analysis of all possible scaling regimes is done and the influence of helicity on the stability of scaling regimes is discussed and shown in the plane of exponents ε – η, where ε characterizes the energy spectrum of the velocity field in the inertial range E ∞ k1 – 2ε, and η is related to the correlation time at the wave number k which is scaled as k–2 + η. It is shown that in nonhelical case the scaling regimes of the present vector model are completely identical and have also the same properties as those obtained in the corresponding model of passively advected scalar field. Besides, it is also shown that when the turbulent environment under consid eration is helical then the properties of the scaling regimes in models of passively advected scalar and vector (magnetic) fields are essentially different. The results demonstrate the importance of the presence of a sym metry breaking in a given turbulent environment for investigation of the influence of an internal tensor struc ture of the advected field on the inertial range scaling properties of the model under consideration and will be used in the analysis of the influence of helicity on the anomalous scaling of correlation functions of passively advected magnetic field. DOI: 10.1134/S1063779613020184 1
1. INTRODUCTION
explained by the existence of strong developed fluctu ations of the dissipative rate (intermittency) [1–4].
The main conclusion of the phenomenological Kolmogorov–Obukhov (KO) theory [1, 2] is the state ment that the statistical properties of random fields deep inside in the inertial interval l r L of fully developed turbulent system are independent of the integral scale L (a typical scale on which the energy is pumping into the system) as well as the viscous scale l (a typical scale on which the energy starts to dissipate). This behavior was formulated in the form of the well known Kolmogorov hypotheses. The assumption of validity of these hypotheses together with simple dimensional analysis then leads to the scaling behavior of correlation functions with definite exponents. On the other hand, it is also wellknown that both experimental and theoretical studies show the exist ence of deviations from th
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