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In the second test we compare three-dimensional models of strongly magnetized supersonic turbulence in both cases: classical MHD with isotropic pressure, and kinetic MHD with anisotropic pressure.The Alfven and sonic Mach numbers for these models are $ 1$ and $ 7$, respectively. In Figure 2 we show density and column density structures developed in magnetized supersonic turbulence when the pressure is isotropic (MHD formulation) and anisotropic (CGL-MHD formulation). The density structures evolve in a very different way in both models. While the MHD turbulence produces dominating small-scale structure, the CGL-MHD model gives structures at larger scales. At the same times, the contrast of density in models with anisotropic pressure is reduces. The different type of structure generated during the turbulence evolution is visible in the maps of column densities, as well.

In Figure 3 we present the structure of magnetic field for MHD and CGL-MHD models. The magnetic field topology do not show much deviation in the case of anisotropic pressure as compared to classical MHD models of turbulence. It is justified by two facts. Firstly, the anisotropic pressure contributes directly to the motions of the fluid through the motions equations. Secondly, the strong magnetic field is less sensitive to the changes due to the magnetic tension.

Figure 2: Images of the logarithm of density for magnetized supersonic turbulence for MHD and CGL-MHD plasma (the top left and right plots, respectively). Two right images show corresponding column densities for these models (bottom left and right plots MHD and CGL-MHD, respectively).
Figure 3: Texture maps of the magnetic lines in the direction parallel (top) and perpendicular (bottom) to the mean magnetic field. The left column shows magnetic field structure for MHD turbulence. The right column shows corresponding plots for CGL-MHD models.
Finally, we compare power spectra for density and velocity for both MHD and CGL-MHD formulations in Figure 4. Clearly, the anisotropy of pressure introduces substantial changes in the evolution of turbulence. The structures of velocity at the small-scales are dominant in the case of turbulence with the anisotropic pressure.
Figure 4: The comparison of density (top) and velocity (bottom) power spectra for MHD and CGL-MHD turbulence. Sonic and Alfven Mach numbers are ${\cal M}_s \sim 7$ and ${\cal M}_A \sim 0.7$, respectively.
density spectrum
velocity spectrum

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Next: Bibliography Up: Test Problems Previous: Firehose and Mirror Instabilities