Jets launched by the supermassive black holes in the centers of cool-core clusters are the most likely heat source to solve the cooling flow problem. One way for this heating to occur is through generation of a turbulent cascade by jet-inflated bubbles. Measurements of the X-ray intensity power spectra show evidence of this cascade in different regions of the cluster, constraining the role of driving mechanisms. We analyze feedback simulations of the Perseus cluster to constrain the effect of the jet activity on the intensity fluctuations and kinematics of the cluster atmosphere. We find that, within the inner 60 kiloparsecs, the power spectra of the predicted surface brightness fluctuations are broadly consistent with those measured by Chandra and that even a single episode of jet activity can generate a long-lasting imprint on the intensity fluctuations in the innermost region of the cluster. AGN-driven motions within the same region approach the values reported by Hitomi during and right after the AGN episode. However, the line-of-sight velocity dispersion excited by the jet in simulations underpredicts the Hitomi measurement. This indicates that driving a volume-filling sustained level of turbulence requires several episodes of jet activity, and/or additional processes drive turbulence outside the 60-kpc sphere. This also suggests that sharp edges of the bubbles in the innermost region of the cluster contribute substantially to the intensity of fluctuations, consistent with the Perseus observations in the inner 30-kpc region. We discuss new diagnostics to decompose annular power spectra to constrain past episodes of jet activity.
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