The blowdown (rapid release) of high pressure gas from a pressure vessel adiabatically cools the gas remaining in the vessel. The gas near the wall is warmed by conduction from the wall, producing radial temperature and density gradients that affect the flow, the mass efflux rate, and the thermodynamic states of both the outflowing and the contained gas. The resulting buoyancy-driven flow circulates the gas through the vessel and reduces, but does not eliminate, these gradients. The purpose of this technical brief is to estimate when blowdown cooling is rapid enough that the gas in the pressure vessel is neither isothermal nor isopycnic, though it remains isobaric. I define a dimensionless number, the buoyancy circulation number, that parametrizes these effects.