BlackHoleWeather -- Jet-regulated chaotic cold accretion across the meso scale: Variability and kinematics

Chaotic cold accretion (CCA) predicts that supermassive black holes are fed by multiphase clouds condensing from turbulent hot atmospheres. In jet-regulated systems cold gas must also remain dynamically connected to the central accretion region. We investigate how a self-regulated kinetic jet modifies the kinematics, radial transport, and variability of CCA across the meso-scale of a typical galaxy-group atmosphere. The runs differ only in turbulent driving strength. We measure accretion histories, Eddington ratios, power spectra, phase-separated mass fluxes, projected k-plots, and cooling-to-eddy-time (C-ratio) profiles. Both runs become CCA-fed once precipitation begins, with accretion rising from Bondi-like to strongly super-Bondi values while remaining mostly low-Eddington and mechanically dominated. The strongly stirred run develops an early stormy phase with extended condensation, bursty feeding, and strong inflow/outflow variability, but later enters a cloudy phase in which cold and warm gas persist at meso- and inner macro-scales while sink coupling weakens. The calmer run maintains a compact rainy state with a longer-lived central reservoir. Accretion-rate spectra show flicker-like low-frequency slopes and red-noise tails; in the cloudy phase, the normalization drops and the low-frequency slope flattens. Phase-separated fluxes show fountain-like recycling in the strongly stirred run, but inner-kpc recycling in the calmer run. The jet excavates a hot channel where sustained condensation is suppressed, while C~1 is reached mostly outside the cone and near the jet-ambient interface. Jet-regulated CCA is controlled by meso-scale transport, not only by cold-gas production. Within the BlackHoleWeather framework, combined k-plot and C-ratio diagnostics are crucial to distinguish cold gas that is merely present from cold gas dynamically linked to SMBH feeding.