The intracluster medium of a galaxy cluster often shows an extended quasi-spiral structure, accentuated by tangential discontinuities known as cold fronts (CFs). These discontinuities are thought to isolate between low-entropy, high-metallicity gas inside (i.e., below) the CF that was lifted from the center of the cluster by some radial factor f i , and high-entropy, low-metallicity gas outside the CF that was pushed inward by a factor f o . We find broad support for such a picture, by comparing the entropy and metallicity discontinuities with the respective azimuthal averages, using newly deprojected thermal profiles in clusters A2029, A2142, A2204 and Centaurus, supplemented by deprojected CFs from the literature. In particular, the mean advection factors f K and f Z , inferred respectively from entropy and metallicity, strongly correlate (R = 0.7 +0.2 −0.3 ) with each other, consistent with large-scale advection. However, unlike sloshing simulations, in which the inside/outside phases are an inflow/outflow settling back to equilibrium after a violent perturbation, our results are more consistent with an outflow/inflow, with the fast, Mach M i ∼ 0.8 gas inside the CF being a rapidly heated or mixed outflow, probably originating from the cD galaxy, and gas outside the CF being a M o ∼ 0.03, slowly-cooling inflow. In particular, entropy indicates an outside advection factor f Ko ≃ 1.33 ± 0.04 that is approximately constant in all CFs, gauging the distance traversed by inflowing gas within a cooling time. In contrast, 1.1 f Ki 2.5 and 1 f Z 17 vary considerably among clusters, and strongly correlate (3.1σ-4.2σ) with the virial mass, f Ki ∝ M 0.14±0.07 200 and f Z ∝ M 1.4±0.4 200 , suggesting that each cluster sustains a quasi-steady spiral flow.