- We argue that bulk spiral flows are ubiquitous in the cool cores (CCs) of clusters and groups of galaxies. Such flows are gauged by spiral features in the thermal and chemical properties of the intracluster medium, by the multiphase properties of CCs, and by X-ray edges known as cold fronts. We analytically show that observations of piecewise-spiral fronts impose strong constraints on the CC, implying the presence of a cold, fast flow, which propagates below a hot, slow inflow, separated by a slowly rotating, trailing, quasi-spiral, tangential discontinuity surface. This leads to the nearly logarithmic spiral pattern, two-phase plasma, ρ ~ r –1 density (or T ~ r 0.4 temperature) radial profile, and ~100 kpc size, characteristic of CCs. By advecting heat and mixing the gas, such flows can eliminate the cooling problem, provided that a feedback mechanism regulates the flow. In particular, we present a quasi-steady-state model for an accretion-quenched, composite flow, in which the fast phase is an outflow, regulated by active galactic nucleus bubbles, reproducing the observed low star formation rates and explaining some features of bubbles such as their Rb∝r size. The simplest two-component model reproduces several key properties of CCs, so we propose that all such cores harbor a spiral flow. Our results can be tested directly in the next few years, for example by ASTRO-H.