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We perform two-dimensional relativistic magnetohydrodynamic simulations of amildly relativistic shock propagating through an inhomogeneous medium. We showthat the postshock region becomes turbulent owing to preshock densityinhomogeneity, and the magnetic field is strongly amplified due to thestretching and folding of field lines in the turbulent velocity field. Theamplified magnetic field evolves into a filamentary structure intwo-dimensional simulations. The magnetic energy spectrum is flatter than theKolmogorov spectrum and indicates that a so-called small-scale dynamo isoccurring in the postshock region. We also find that the amount ofmagnetic-field amplification depends on the direction of the mean preshockmagnetic field, and the time scale of magnetic-field growth depends on theshock strength.

Magnetic Field Amplification by Turbulence in A Relativistic Shock Propagating through An Inhomogeneous Medium