Astron. Astrophys. 362, 333-341 (2000)

## 3. Magnetohydrodynamic turbulence

We introduce a uniform magnetic field into the initial configuration. A weak field, in which the Alfvén and sound speeds are equal, has little overall influence (Fig. 4). The shock distribution is roughly isotropic and the shock number is not significantly altered from the equivalent hydrodynamic simulation. The power law section is not so well defined for the shock distribution parallel to the field.

 Fig. 4. The distribution of shocks in driven MHD turbulence with a `weak' magnetic field. The shock numbers are shown here parallel and transverse to the field, at times t=0, t=0.5 (dot-dash), t=1.0 (dotted) to t=1.5 (dashed) and the time t=3.0 (solid), by which time a statistical steady state has been reached. The driving wavenumber is . The straight dashed line represents an inverse square root power law.

A strong field introduces a strong anisotropy (Fig. 5). With a field such that the Alfvén speed equals the initial rms speed, the waves transverse to the field dominate . There are times more waves in the transverse direction for a given jump speed in each direction. The inverse square root power-law rule is again closely obeyed. We call these waves, rather than shocks, since the high Alfvén speed implies that a high fraction may be fast magnetosonic waves. The average number of zones, however, measured for each jump is only 4.7 (parallel) and 7.4 (transverse). This compares to an average of 5.4 for the hydrodynamic flow (and 23.7 zones for the initial Gaussian with k=4). Note these refer to the complete shock, not just the 2-3 zones across which the jump is highly non-linear and across which numerical viscosity is strong; there usually exists one or two zones on each side of the main jump across which the velocity joins smoothly onto the surrounding flow without oscillations. Hence, the zone measurements favour the interpretation that the dissipation is being carried out in short-wavelength non-linear magnetosonic waves.

 Fig. 5. The distribution of shocks in driven MHD turbulence with a strong magnetic field. The shock numbers are shown here parallel and transverse to the field, at times t=0, t=0.5 (dot-dash), t=1.0 (dotted) to t=1.5 (dashed) and the time t=3.0 (solid), by which time a statistical steady state has been reached.

A very similar difference between parallel and transverse shock numbers is found in the case of decaying turbulence (Paper 1). It is clear that the magnetic pressure is not damping the shock waves. In contrast, the extra magnetic energy which becomes tied up in the waves also helps maintain them.

© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100