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.