Turbulent Magnetic Field Amplification by the Interaction of Shock Wave and Inhomogeneous Medium

Magnetic fields on the order of 100 $\mu$G observed in young supernova remnants cannot be amplified by shock compression alone. To investigate the amplification caused by turbulent dynamo, we perform three-dimensional MHD simulations of the interaction between shock wave and inhomogeneous density distribution with a shallow spectrum in the preshock medium. The postshock turbulence is mainly driven by the strongest preshock density contrast and follows the Kolmogorov scaling. The resulting turbulence amplifies the postshock magnetic field. The time evolution of the magnetic fields agrees with the prediction of the nonlinear turbulent dynamo theory in Xu & Lazarian (2016). When the initial weak magnetic field is perpendicular to the shock normal, the maximum amplification of the field's strength achieves a factor of $\approx200$, which is twice larger than that for a parallel shock. We find that the perpendicular shock exhibits a smaller turbulent Alfv\'en Mach number in the vicinity of the shock front than the parallel shock. However, the strongest magnetic field has a low volume filling factor and is limited by the turbulent energy due to the reconnection diffusion taking place in a turbulent and magnetized fluid. The magnetic field strength averaged along the $z$-axis is reduced by a factor $\gtrsim10$. We decompose the turbulent velocity and magnetic field into solenoidal and compressive modes. The solenoidal mode is dominant and evolves to follow the Kolmogorov scaling, even though the preshock density distribution has a shallow spectrum. When the preshock density distribution has a Kolmogorov spectrum, the turbulent velocity's compressive component increases.