Some theoretical and observational studies suggest that the plasma around relativistic shock waves, such as gamma-ray bursts or jetted active galactic nuclei, can be turbulent. This turbulence is important for the acceleration of charged particles by relativistic shock waves. We performed the three-dimensional special relativistic simulations in order to understand the downstream turbulence generated by interactions between a relativistic shock wave and density clumps The solenoidal and compressive mode decomposition shows that both modes are comparable, and that their power spectra follow a -5/3 slope which is consistent with the Kolmogorov turbulence. The shock-like structures are generated by the interactions, and these can affect the particle acceleration by the relativistic shock waves.
Kanji Morikawa (Tue,) studied this question.