Reduced models of magnetohydrodynamic turbulence in the interstellar medium and the solar wind

Recent developments in the derivation of reduced models for weakly compressible magnetohydrodynamic (MHD) turbulence are discussed. A four-field system of equations has been derived from the compressible magnetohydrodynamic (MHD) equations to describe turbulence in the interstellar medium and the solar wind. These equations apply to a plasma permeated by a spatially varying mean magnetic field when the plasma beta is of the order unity or less. In the presence of spatial inhomogeneities, the four-held equations predict pressure fluctuations of the order of the Mach number of the turbulence, as observed by Helios 1 and 2. In the presence of a uniform background field and a spatially homogeneous plasma, the four-field system reduces to the so-called nearly incompressible system. In the weak-turbulence limit, dominated by three-wave interactions, the anisotropic energy spectrum is deduced by a combination of exact analytical results and numerical simulations.