Temporal Properties of Compressible MHD Turbulence

We will discuss recent results on 4D FFT analysis (temporal plus 3D spatial) of compressible MHD turbulence. Most fluctuation power is found to have nearly zero or very low frequencies with finite wavenumbers. They do not follow the dispersion surfaces of linearized MHD waves, though a very small fraction of the power is observed to fall within the expected dispersion relations for Alfven, Slow, and Fast modes. We present our interpretation of how to understand the temporal behavior in MHD turbulence. The temporal response of any particular wavenumber is shown to be a Lorentzian in frequency. Its profile peaks at the eigenfrequency of a given wave mode (Alfven, Fast, and Slow) but has very broad wings extending to both low and high frequencies. We quantify how the Lorentzian profiles can be used to explain the turbulence simulation results. Implications for understanding space and astrophysical turbulence will be discussed as well.