  Relativistic astrophysical phenomena such as gamma-ray bursts (GRBs) and
active galactic nuclei often require long-lived strong magnetic field. Here, we
report on three-dimensional special-relativistic magnetohydrodynamic (MHD)
simulations to explore the amplification and decay of macroscopic turbulence
dynamo excited by the so-called Richtmyer-Meshkov instability (RMI; a
Rayleigh-Taylor type instability). This instability is an inevitable outcome of
interactions between shock and ambient density fluctuations. We find that the
magnetic energy grows exponentially in a few eddy turnover times, and then,
following the decay of kinetic turbulence, decays with a temporal power-law
exponent of -0.7. The magnetic-energy fraction can reach $epsilon_B \sim$ 0.1
but depends on the initial magnetic field strength. We find that the magnetic
energy grows by at least two orders of magnitude compared to the magnetic
energy immediately behind the shock. This minimum degree of the amplification
does not depend on the amplitude of the initial density fluctuations, while the
growth timescale and the maximum magnetic energy depend on the degree of
inhomogeneity in the density. The transition from Kolmogorov cascade to MHD
critical balance cascade occurs at $\sim$ 1/10th the initial inhomogeneity
scale, which limits the maximum synchrotron polarization to less than 2%. New
results include the avoidance of electron cooling with RMI turbulence, the
turbulent photosphere model via RMI, and the shallow decay of the early
afterglow from RMI. We also performed a simulation of freely decaying
turbulence with relativistic velocity dispersion. We find that relativistic
turbulence begins to decay much faster than one eddy-turnover time because of
fast shock dissipation, which does not support the relativistic turbulence
model by Narayan & Kumar.
