Distributions of the density and magnetic field (top), the logarithm of the Alfvén Mach number ℳ_A (middle), and the coefficient A₂₃ of Eq. (13)(bottom) in a slice (z = 256) of the MHD turbulence simulations used in Soler et al. (2013) for initially weak (β = 100, left) and strong (β = 0.1, right) magnetic field in a snapshot taken at one-third of the flow crossing time. The coefficient A₂₃ is the term dominating the change in the relative orientation between ∇ρ and B according to Eq. (13).