Invariants of velocity gradient tensor in three-dimensional relativistic astrophysical jet/spherical dense cloud interaction

In this Letter, the numerical simulation of three-dimensional hydrodynamic relativistic jet/spherical dense cloud interaction has been performed by solving relativistic hydrodynamic equations in the computer code PLUTO [Mignone et al., “PLUTO: A numerical code for computational astrophysics,” Astrophys. J. Suppl. Ser. 170, 228 (2007)] using the higher-order finite volume method. The invariants (P, Q, and R) of the velocity gradient tensor (∂ui∂xj) reveal the detailed turbulent structures [Chong et al., “A general classification of three-dimensional flow fields,” Phys. Fluids A 2, 765–777 (1990); C. Meneveau, “Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows,” Annu. Rev. Fluid Mech. 43, 219–245 (2011); Thaker et al., “Invariants of the velocity gradient tensor in a spatially developing compressible round jet,” J. Fluid Mech. 971, A18 (2023)] by identifying the local flow topology. The joint probability density distributions (j.p.d.f.) of Q–R obtained from numerical data, depicts the presence of turbulent sheet-like structures during this complex dynamical interaction. The j.p.d.f. of Q–R also reveals that the presence of turbulence producing sheets (unstable node/saddle/saddle) is more significant when a dense cloud lies in the trajectory of the relativistic jet than when it is absent.