In this article, the numerical simulation of a three-dimensional hydrodynamic relativistic jet issuing from an active galactic nucleus and its propagation inside a low radio-shift cluster has been performed by solving relativistic hydrodynamic equations using the computer code PLUTO Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007), which is based on the higher-order finite volume method. The detailed flow physics associated with relativistic jet propagation inside both uniform medium and low radio-shift clusters has been discussed thoroughly. Furthermore, the invariants (P, Q, and R) of the velocity gradient tensor (∂ui∂xj) have been analyzed using numerical simulation data to identify the local flow topology Chong et al., “A general classification of three-dimensional flow fields,” Phys. Fluids A 2, 765–777 (1990); Suman and Girimaji, “Velocity gradient invariants and local flow-field topology in compressible turbulence,” J. Turbul. 11, N2 (2010); Thaker et al., “Invariants of the velocity gradient tensor in a spatially developing compressible round jet,” J. Fluid Mech. 971, A18 (2023) and thereby shock–turbulence interaction. The joint probability density function of Q–R obtained from numerical data, depicts the presence of turbulent sheet-like structures during the propagation of this relativistic jet through both uniform medium and low radio-shift cluster environments. Eventually, the study reveals that the occurrence of sheet-like structures is more dominant in the uniform medium due to strong shock–turbulence amplification inside the cocoon of the uniform medium over the low radio-shift cluster environment.
Pal et al. (Mon,) studied this question.