Sub-sonic compressible magnetohydrodynamic turbulence I. Alfv'enic and fast-magnetosonic injection, amplitude dependence, and compressibility effects

We investigate how sub-sonic compressible magnetohydrodynamic (MHD) turbulence properties that are relevant for cosmic-ray (CR) transport in the Galaxy are affected by the nature and amplitude of initial fluctuations, and by the plasma compressibility beta. We perform 3D simulations of decaying compressible ideal-MHD turbulence at 1024 cubed resolution with the PLUTO code. The level of density fluctuations in fully developed turbulence is insensitive to whether this state is reached starting from Alfv'enic or fast-magnetosonic perturbations. Fast-magnetosonic injection is characterized by an early phase of rapid shock dissipation, followed by a turbulence-dominated decay with a rate comparable to that of the Alfv'enic case. The contribution of fast-magnetosonic fluctuations in fully developed turbulence remains relevant only when the initial injection consists exclusively of fast modes. Large-amplitude turbulence (delta B/B 0>1) is characterized by a nearly isotropic Kolmogorov or Iroshnikov-Kraichnan spectrum for Alfv'enic or fast-magnetosonic injection, respectively. At low amplitudes (delta B/B 0 1), both initial Alfv'enic and mixed-wave perturbations lead to strongly anisotropic turbulence with spectra proportional to k-5/3 and proportional to k z-2 (becoming steeper at beta 1), whereas fast-magnetosonic perturbations produce a turbulent state populated by shocks with a nearly isotropic k-2 spectrum. Magnetic-field curvature and mirror structures are strongly sensitive to fluctuation amplitude and plasma beta. The predicted-2.5 power-law scaling emerges only in the large-amplitude regime at high beta. This work highlights that features of sub-sonic compressible MHD turbulence that may affect CR transport are sensitive to large-scale conditions and to the plasma beta. Their effect on CR diffusion and field-line random walk is the object of Paper II.