Waves and non-propagating modes in stratified MHD turbulence subject to a weak mean magnetic field

In this study we consider a freely decaying, stably stratified homogeneous magnetohydrodynamic turbulent plasma with a weak vertical background magnetic field (B-0 = B0z<^>), aligned with the density gradient of strength NN (i.e. Brunt-Vaisala frequency). Both linear theory and direct numerical simulations (DNS) are used to analyse the flow dynamics for a Boussinesq fluid with unitary magnetic and thermal Prandtl numbers. We implemented a normal mode decomposition emphasizing different types of motions depending on whether both the Froude F-r and Alfven-Mach MM numbers are small or only F-r is small but MM is finite. In the former case, there is a non-propagating (NP) mode and fast modes: Alfven waves with frequency omega a omega a and magnetogravity waves with frequency omega(.)(ag) In the latter case, there are fast gravity waves with frequency omega(g) and slow modes: NP mode and slow Alfven waves. The numerical simulations carried out are started from initial isotropic conditions with zero initial magnetic and density fluctuations, so that the initial energy of the NP mode is strictly zero, for 0 < B-0/(LiN) <= 0.12 and a weak mean magnetic field (B-0 = 0.2 or B-0= 0.4), where L-i denotes the isotropic integral length scale. The DNS results indicate a weak turbulence regime for which F-r is small and MM is finite. It is found that the vertical magnetic energy as well as the energy of the NP mode are drastically reduced as NN increases, while there is instead a forward cascade even for the magnetic field. The contribution coming from the energy of fast (gravity) waves does not exceed 50%,50%, while that coming from the energy of the NP mode does not exceed 10%.10%. Vertical motions are more affected by the effect of stratification than by the effect of the mean magnetic field, while it is the opposite for horizontal motions. We show that the spectrum of slow (Alfven) waves and fast (gravity) waves tends to follow the power law k(perpendicular to)(-3) for a wide range of time, 3 < t < 20. At high vertical (or horizontal) wave numbers, the main contribution to total energy comes from the energy of slow Alfven waves. At large and intermediate horizontal (or vertical) scales, the spectra of the energy of NP mode exhibit a flat shape.