In this Letter, the numerical simulation of three-dimensional hydrodynamic relativistic jet propagation from an active galactic nuclei has been performed by solving relativistic hydrodynamic equations in the computer code PLUTO [A. Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] using higher-order finite volume method. Furthermore, the invariants (P, Q, and R) of velocity gradient tensor ( ) have been analyzed using numerical simulation data in order to identify the local flow topology [M. S. Chong et al., “A general classification of three-dimensional flow fields,” Phys. Fluids A: Fluid Dyn. 2, 765–777 (1990); S. Suman and S. S. Girimaji, “Velocity gradient invariants and local flow-field topology in compressible turbulence,” J. Turbul. 11, N2 (2010); P. 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 (p.d.f) of obtained from numerical data depicts the presence of turbulent sheet-like structures during the propagation of this relativistic jet.
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