Theoretical Estimate of Turbulence Effects on Magnetic-Field Equations
For the estimate of the Reynolds stress R ij and the turbulent electromotive force E M, we start from a kinematic approach and then proceed to a magnetohydrodynamic (MHD) approach. The former consists of kinematic and counter-kinematic methods. In the kinematic method, the generation of magnetic fluctuation b ′ under given velocity fluctuation u ′ is examined through the magnetic induction equation, and R ij and E M are evaluated. In the counter-kinematic method, this evaluation is made under given b ′ on the basis of the Navier–Stokes equation. In the MHD method, the generation process of R ij and E M are examined through the simultaneous treatment of u ′ and b ′. These three approaches are summarized symbolically as follows: Kinematic method: u ′ ⇒ b ′ ⇒ R i j , E M ; Counter-kinematic method: b ′ ⇒ u ′ ⇒ R i j , E M ; MHD method: u ′ , b ′ ⇒ R i j , E M .