Temporal Properties of the Compressible Magnetohydrodynamic Turbulence

The temporal property of the compressible magneto-hydrodynamic (MHD) turbulence remains a fundamental unsolved question. Recent studies based on the spatial-temporal analysis in the global frame of reference suggest that the majority of fluctuation power in turbulence does not follow any of the MHD wave dispersion relations but has very low temporal frequency with finite wavenumbers. Here, we demonstrate that the Lorentzian broadening of the dispersion relations of the three MHD modes where the nonlinear effects act like the damping of a harmonic oscillator can explain many salient features of frequency spectra for all MHD modes. The low frequency fluctuations are dominated by modes with the low parallel wavenumbers that have been broadened by the nonlinear processes. The Lorentzian broadening widths of the three MHD modes exhibit scaling relations to the global frame wavenumbers and are intrinsically related to energy cascade of each mode. Our results provide a new window to investigate the temporal properties of turbulence which offers insights for building a comprehensive understanding of the compressible MHD turbulence.