We study the growth rate and saturation level of the turbulent dynamo in magnetohydrodynamical simulations of turbulence, driven with solenoidal (divergence-free) or compressive (curl-free) forcing. For models with Mach numbers ranging from 0.02 to 20, we find significantly different magnetic field geometries, amplification rates, and saturation levels, decreasing strongly at the transition from subsonic to supersonic flows, due to the development of shocks. Both extreme types of turbulent forcing drive the dynamo, but solenoidal forcing is more efficient, because it produces more vorticity.
The movie shows the turbulent magnetic field structure in four computer models representing vastly different physical conditions. The Sun for example, is only weakly compressible and characterised by subsonic flows (top left), while the plasma in the early Universe was likely dominated by strong compressions and highly supersonic turbulence (bottom right).
Stimulating discussions with A. Brandenburg, E. Dormy, P. Girichidis, P. Hennebelle, P. Lesaffre, W. Schmidt, and S. Sur, and useful comments by the anonymous referees are gratefully acknowledged. C.F., G.C., and D.R.G.S. thank for funding under the European Community's FP7/2007–2013 Grant Agreement No. 247060 and 229517. RB acknowledges funding from the DFG grant BA 3706. C.F., R.B., and R.S.K. acknowledge subsidies from the Baden-Württemberg-Stiftung (grant P-LS-SPII/18) and from the German BMBF (grant 05A09VHA). The simulations were run at the LRZ (grant pr32lo) and the JSC (grants hhd14, hhd17, hhd20). The FLASH code was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago.