We present a model for compressible sub-Alfvénic isothermal magnetohydrodynamic (MHD) turbulence in low- $\beta$ plasmas and numerically test it. We separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that production of slow and fast modes by Alfvénic turbulence is suppressed. As a result, Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.

• Received 1 March 2002

DOI:https://doi.org/10.1103/PhysRevLett.88.245001