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. Supernova remnants (SNRs) exhibit varying degrees of anisotropy, which have been extensively modeled using numerical methods. We implement a technique to measure anisotropies in SNRs by calculating power spectra from their high-resolution images. To test this technique, we develop 3D hydrodynamical models of SNRs and generate synthetic X-ray images from them. Power spectra extracted from both the 3D models and the synthetic images exhibit the same dominant angular scale, which separates large-scale features from small-scale features due to hydrodynamic instabilities. The angular power spectrum at small length scales during relatively early times is too steep to be consistent with Kolmogorov turbulence, but it transitions to Kolmogorov turbulence at late times. As an example of how this technique can be applied to observations, we extract a power spectrum from a Chandra observation of Tycho’s SNR and compare with our models. Our predicted power spectrum picks out the angular scale of Tycho’s fleecelike structures and also agrees with the small-scale power seen in Tycho. We use this to extract an estimate for the density of the circumstellar gas (n ∼ 0.28/cm^3), consistent with previous measurements of this density by other means. The power spectrum also provides an estimate of the density profile of the outermost ejecta. Moreover, we observe additional power at large scales, which may provide important clues about the explosion mechanism itself.
