Recent developments in the theory of magnetohydrodynamic turbulence

Recent results based on high‐resolution direct numerical simulations of incompressible magnetohydrodynamic (MHD) turbulence are summarized. With regard to the nonlinear dynamics of turbulent energy a yet unexplained scaling behavior is found in systems permeated by a strong mean magnetic field which contradicts the phenomenological Goldreich‐Sridhar picture. For macroscopically isotropic and anisotropic MHD turbulence EDQNM closure analysis leads to a simple relation between the spectra of total $(EkK + EkM)$ and residual $(|EkK − EkM|)$ energy. The relation is based on a clear physical picture and is well confirmed by numerical simulations. In addition, the Lagrangian approach is presented as a straightforward diagnostic for the investigation of turbulent diffusion and pair‐dispersion. Some results from a comparative study of pair‐dispersion in Navier‐Stokes and MHD turbulence are briefly outlined. It is shown that the presence of magnetic fluctuations significantly reduces turbulent dispersion due to the alignment of velocity fluctuations with the local mean magnetic field.