SIII 40Magnetic pressure and the density field in MHD turbulence with slab geometry

T. P. Passot , E. Vazquez-Semadeni 
The relation between magnetic pressure b² and the density 21#21 in fully turbulent MHD flows is investigated in ``1+2/3'' dimensions. Previous work [1] in the context of polytropic neutral flows suggests that the value of the polytropic exponent appears to play a major role in the dynamics, and in particular in the determination of the functional shape of the PDF. A lognormal density PDF appears in the isothermal (22#22) case, but a power-law tail at either large or densities appears for 23#23 and 24#24, respectively. In the magnetic isothermal case the relevant parameter is the field fluctuation amplitude. For field fluctuations (generally the case for large mean fields), an excess of low density events with respect to a lognormal PDF is observed, and the magnetic pressure is relatively constant over the range of density values. On the other hand, at large fluctuation amplitudes (weak mean fields), the density PDF is closer to lognormal and a strong scatter (decorrelation) is observed in the magnetic field fluctuations as a function of density. Some of these results can be interpreted using classical properties of simple nonlinear MHD waves. At fluctuation amplitudes, the density fluctuation production is dominated by the slow mode of the nonlinear MHD waves, for which the magnetic pressure is approximately constant in this limit. In this case, the constancy of the magnetic pressure implies a Burgers-like behavior, explaining the excess at low densities in the PDF [T. Passot and E. Vazquez-Semadeni, Phys. Rev. E, 58, 4501 (1998)]. At large fluctuation amplitudes, the density fluctuation production is controlled in relatively equal amounts by the slow and fast modes. However, for the fast mode the magnetic pressure scales roughly as 25#25, and therefore the value of b² associated with a particular density fluctuation depends on its particular time history, so that b² decorreates from rho. In this case, b² acts more as a random forcing than as a pressure, and the density PDF is determined by the (isothermal) behavior of the thermal pressure, roughly recovering a lognormal PDF. These results suggest that modeling magnetic pressure in terms a power-law function of the density may be inadequate in the fully turbulent regime.