Introduction to Strong Alfv\'enic MHD Turbulence

Abstract

Many astrophysical fluids are magnetized and turbulent. Such fluids can be often described by magnetohydrodynamics (MHD). In this review, we mainly consider MHD turbulence with a strong mean magnetic field whose energy density is greater than or equal to the local kinetic energy density. In these fluids, the MHD waves, especially Alfv\'en waves, play a dominant dynamical role. Alfv\'en waves travel along magnetic field lines and collisions of opposite-traveling Alfv\'en wave packets are essential for turbulence cascade. We focus on strong turbulence regime, where nonlinear interaction during the collision is sufficiently strong and thus one collision is enough to complete turbulence cascade. We will cover the following types of turbulence. First, we review strong Alfv\'enic MHD turbulence. If the mean magnetic field is very strong, wave packets move very fast and duration of collision is too short to complete turbulence cascade. Even in this case we will show that strong turbulence regime emerges on a small scale. Second, we will consider small-scale MHD turbulence, where interaction of small-scale variants of Alfv\'en waves (i.e., whistler waves) is important. Third, we review scaling relations in strong relativistic force-free MHD turbulence, where interaction of relativistic Alfv\'en waves is important. Finally, we briefly discuss scaling relations in compressible MHD turbulence, where interaction of Alfv\'en waves is still important.