Statistical theory of magnetohydrodynamic turbulence: recent results

In this review article we will describe recent developments in statistical theory of magnetohydrodynamic (MHD) turbulence. Kraichnan and Iroshnikov first proposed a phenomenology of MHD turbulence where Alfvén time-scale dominates the dynamics, and the energy spectrum E ( k ) is proportional to k - 3 / 2 . In the last decade, many numerical simulations show that spectral index is closer to 5 3 , which is Kolmogorovʹs index for fluid turbulence. We review recent theoretical results based on anisotropy and Renormalization Groups which support Kolmogorovʹs scaling for MHD turbulence. transfer among Fourier modes, energy flux, and shell-to-shell energy transfers are important quantities in MHD turbulence. We report recent numerical and field-theoretic results in this area. Role of these quantities in magnetic field amplification (dynamo) are also discussed. There are new insights into the role of magnetic helicity in turbulence evolution. Recent interesting results in intermittency, large-eddy simulations, and shell models of magnetohydrodynamics are also covered.