Identification of vortical coherent modes during relativistic jet propagation from active galactic nuclei using data-driven techniques

In this article, two-dimensional numerical simulations of magnetized relativistic jets propagating through a uniform interstellar medium (ISM) were conducted by solving the relativistic magnetohydrodynamic (RMHD) equations using a high-order finite volume method in PLUTO solver Mignone et al. (2007). Vortical coherent structures generated by jet–ISM interactions were identified through the application of both standard Dynamic Mode Decomposition (DMD) and Hankel DMD. While dominant coherent modes were extracted using linear DMD, transient and nonlinear structures were more effectively captured by Hankel DMD due to its time-delay embedding formulation. A parametric study was performed to investigate the mechanisms governing energy dissipation, with variations introduced in jet Lorentz factor, magnetization strength, and the comparison between relativistic hydrodynamic (RHD) and magnetized (RMHD) configurations. Across all cases, eigenvalues were consistently located within the unit circle, signifying temporal decay of vortical modes due to strong dissipation imposed by the jet head shock. It was shown that dissipation was sustained with increasing Lorentz factor, that magnetization exerted control over the stability and coherence of vortical structures, and that RMHD jets followed distinct dissipation pathways relative to RHD jets. Overall, nonlinear coherent dynamics were more effectively revealed through Hankel DMD, and dissipation trends were elucidated via systematic parametric variation.