A Comparative Study of Velocity Statistics of Hydrodynamic and Magnetohydrodynamic Turbulence

Turbulence in an incompressible fluid with and without a magnetic field as well as moderately compressible MHD turbulence are compared. The results of three numerical simulation models in three dimensions of resolution up to 512 are used for this purpose. The compatibility of the spectra of all three models with the Kolmogorov spectrum is confirmed. For the magnetohydrodynamic (MHD) models the probability distribution functions of the velocity components perpendicular to the external magnetic field are like the incompressible hydrodynamic (HD) model while those parallel to the field have a smaller range of velocities. The probability distribution functions of the transverse velocity increments for the MHD models decline slower than the incompressible HD model. The similarity of incompressible HD and both incompressible and compressible MHD turbulence persists over high order longitudinal structure function scaling exponents measured in the global reference frame as well as for motions perpendicular to the local mean field. In these two frames the longitudinal scaling exponents of both MHD models seem to follow theoretical incompressible HD dissipation structure predictions while the transverse scaling exponents of the incompressible MHD model seem to follow the predictions for incompressible MHD. In the local magnetic system the motions parallel to the local mean field for both MHD models are different from incompressible HD motions. The fields of the MHD simulations are decomposed into Alfvenic, fast, and slow modes. In the global reference frame and for motions perpendicular to the local mean field the Alfvenic mode is mostly responsible for the fact that the longitudinal components of both MHD models follow the incompressible HD model and the incompressible HD theoretical dissipation structure predictions. In the global reference frame for the incompressible MHD model both the Alfvenic and slow modes seem to contribute significantly to the fact that the transverse components follow the incompressible MHD theoretical predictions. For motions perpendicular to the magnetic field for the incompressible MHD model it appears that the slow mode contributes most to the fact that the transverse component seems to follow the incompressible MHD predictions. PACS 47.27.E· 52.30.Cv · 52.35.B · 95.30.Qd