Shock–turbulence interaction during relativistic astrophysical jet propagation inside a low radio-shift cluster

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.