Magnetohydrodynamic Turbulence: Generalized Energy Spectra

A general framework that incorporates the Iroshnikov-Kraichnan (IK) and Goldreich-Sridhar (GS) phenomenalogies of magnetohydrodynamic (MHD) turbulence is developed. This affords a clarification of the regimes of validity of IK and GS phenomenalogies and hence help resolve some controversies in this problem. Magnetohydrodynamic (MHD) flows that occur naturally (like astrophysical situations) and in modern technological systems (like fusion reactors) show turbulence. Early theoretical investigations of MHD turbulence considered the isotropic case. On the latter premise, Iroshnikov [1] and Kraichnan [2] (IK) made arguments á la Kolmogorov [3] and proposed that statistical properties of the small-scale components of the velocity and magnetic fields *are controlled by the shear Alfvén wave dynamics; *show, in the limit of large viscous and magnetic Reynolds numbers, some universality in the inertial range. and gave for the total energy spectral density E(k), the behavior E(k) ∼ k 3 2 . Montgomery et al. [4] and [5], Goldreich and Sridhar [6] [8] (GS) pointed out that the isotropy assumption in the IK theory is not a very sound one in the MHD case, thanks to the magnetic field of the large-scale eddies, and gave for the energy spectrum in the plane transverse to the magnetic field the behavior E(k⊥) ∼ k − 5 3 ⊥ [8]. However, DNS of MHD turbulence in a strong applied magnetic field (Maron and Goldreich [9], Muller et al. [10] and [11]) showed that the transverse energy spectrum is close