A hierarchical modeling approach is undertaken to understand some basic dynamics of this problem. First, an effective diffusivity diagnostic tool is applied to unforced barotropic vorticity ring breakdowns in order to identify and characterize basic flow regimes during PV mixing events. While this tool shows many chaotic mixing regions, in particular we seek to determine the existence and magnitude of partial barrier regions where flow trajectories are integrable. Understanding the transient location and magnitudes of both these regions clarifies how a passive tracer, such as water vapor, is asymmetrically mixed between the eye and eyewall during PV hollow tower breakdowns. Secondly, this mixing process is examined in a dry quasi-static primitive equation model using unforced hurricane-like PV hollow towers. The preferred isentropic layers for mixing are examined and wave-mean flow diagnostics are presented to understand how these events change the mean vortex intensity.