Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence

Hew, J. K. J. & Federrath, C., 2023

Monthly Notices of the Royal Astronomical Society, 520, 6268  [ ADS link ]  [ PDF ]


Small-scale fluctuating magnetic fields of order nG are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel 3D magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The configuration used here is currently being tested in the shock tunnel at the National Ignition Facility (NIF). In order to probe the statistical properties of the post-shock turbulent region, we use 384x512x384 tracers to track its evolution through the Lagrangian framework, thus providing a high-fidelity analysis of the shocked medium. Our simulations indicate that the growth of the magnetic field, which accompanies the near-Saffman kinetic energy decay (Ekin ~ t^-1.15) without turbulence driving, exhibits slightly different characteristics as compared to periodic box simulations. Seemingly no distinct phases exist in its evolution because the shock passage and time to observe the magnetic field amplification during the turbulence decay are very short (~0.3 of a turbulent turnover time). Yet, the growth rate is still consistent with those expected for compressive (curl-free) turbulence driving in subsonic, compressible turbulence. Phenomenological understanding of the dynamics of the magnetic and velocity fields are also elucidated via Lagrangian frequency spectra, which are consistent with the expected inertial range scalings in the Eulerian-Lagrangian bridge.

Shock tube with turbulent region tracked by tracer particles

This movie shows our simulation of the NIF shock tube, where the shock is passing through a foam medium from the bottom to the top, with the post-shock region developing turbulence. This turbulent region is tracked by Lagrangian tracer particles (shown in blue). This allows us to determine the amplification of the magnetic field due to the turbulent dynamo, expected in these experiments.


We thank Siyao Xu and Yue Hu for their valuable comments on the manuscript. We further thank Turlough Downes for helpful discussions. We also thank the anonymous referee for their constructive feedback on the manuscript. We acknowledge the NIF Discovery Science Program for allocating upcoming facility time on the NIF Laser to test aspects of the models and simulations discussed in this paper. J.K.J.H. acknowledges funding via the ANU Chancellor’s International Scholarship. C.F. acknowledges funding provided by the Australian Research Council (Future Fellowship FT180100495 and Discovery Projects DP230102280), and the Australia-Germany Joint Research Cooperation Scheme (UA-DAAD). We further acknowledge high-performance computing resources provided by the Leibniz Rechenzentrum and the Gauss Centre for Supercomputing (grants pr32lo, pr48pi and GCS Large-scale project 10391), the Australian National Computational Infrastructure (grant ek9) and the Pawsey Supercomputing Centre (grant pawsey0810) in the framework of the National Computational Merit Allocation Scheme and the ANU Merit Allocation Scheme. The simulation software FLASH was in part developed by the DOE-supported Flash Center for Computational Science at the University of Chicago.

© C. Federrath 2024