Authors: K.H. Yuen (LANL), Z. Gan (NMC), X. Fu (NMC), S. Du (LANL), H. Yan (DESY)

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 propose a new interpretation on 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 eigen-frequency of a given wave mode but has very broad wings extending to both low and high frequencies. We quantify how this new approach can be used to explain the turbulence simulation results. Such a new theory also allows a new approach to obtain scaling relationships in wavenumber space for compressible turbulence. Implications for understanding the solar wind turbulence, particularly the density variations and particle transport in the low beta regime will be discussed as well.