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Abstract We develop a suite of 3D hydrodynamic models of supernova remnants (SNRs) expanding against the circumstellar medium (CSM). We study the Rayleigh–Taylor instability forming at the expansion interface by calculating an angular power spectrum for each of these models. The power spectra of young SNRs are seen to exhibit a dominant angular mode, which is a diagnostic of their ejecta density profile as found by previous studies. The steep scaling of power at smaller modes and the time evolution of the spectra are indicative of the absence of a turbulent cascade. Instead, as the time evolution of the spectra suggests, they may be governed by an angular mode-dependent net growth rate. We also study the impact of anisotropies in the ejecta and in the CSM on the power spectra of velocity and density. We confirm that perturbations in the density field (whether imposed on the ejecta or the CSM) do not influence the anisotropy of the remnant significantly unless they have a very large amplitude and form large-scale coherent structures. In any case, these clumps can only affect structures on large angular scales. The power spectrum on small angular scales is completely independent of the initial clumpiness and governed only by the growth and saturation of the Rayleigh–Taylor instability. 

Abstract Active galactic nuclei (AGN) show a range of morphologies and dynamical properties, which are determined not only by parameters intrinsic to the central engine but also their interaction with the surrounding environment. We investigate the connection of kiloparsec scale AGN jet properties to their intrinsic parameters and surroundings. This is done using a suite of 40 relativistic hydrodynamic simulations spanning a wide range of engine luminosities and opening angles. We explore AGN jet propagation with different ambient density profiles, including r −2 (self-similar solution) and r −1 , which is more relevant for AGN host environments. While confirmation awaits future 3D studies, the Fanaroff–Riley (FR) morphological dichotomy arises naturally in our 2D models. Jets with low energy density compared to the ambient medium produce a center-brightened emissivity distribution, while emissivity from relatively higher energy density jets is dominated by the jet head. We observe recollimation shocks in our simulations that can generate bright spots along the spine of the jet, providing a possible explanation for “knots” observed in AGN jets. We additionally find a scaling relation between the number of knots and the jet-head-to-surroundings energy density ratio. This scaling relation is generally consistent with the observations of the jets in M87 and Cygnus A. Our model also correctly predicts M87 as FRI and Cygnus A as FRII. Our model can be used to relate jet dynamical parameters such as jet head velocity, jet opening angle, and external pressure to jet power, and ambient density estimates.