A comparative study of four-field and fully compressible magnetohydrodynamic turbulence in the solar wind

A four-field system of equations has been recently derived from the compressible magnetohydrodynamic (MHD) equations to describe turbulence in 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-field equations predict pressure fluctuations of the order of the Mach number of the turbulence, as observed by Helios 1 and 2. It is shown that inhomogeneities that occur only in the form of pressure-balanced structures cannot account for density fluctuations as large as the Mach number of the turbulence. Numerical predictions from the four-field and compressible MHD equations are compared using the same initial condition. The comparison shows that the predictions of the four-field model are qualitatively consistent with the predictions of the compressible MHD model and suggests that the four-field model is a viable model of compressible turbulence in the solar wind.