 Buoyancy exchange time of a cold-air enclosure

Cold air leaving an opened enclosure must displace warmer air, so its driving acceleration is set by reduced gravity, rather than by unrestricted fall through vacuum. The ideal gas law at approximately common pressure gives a fractional mass density contrast of order $\Delta T/T$. Balancing gravitational potential energy against kinetic energy gives exchange speed $U\sim \sqrt{g^{\prime }H}$ over height $H$, and time $H/U$. Geometry, entrainment and shelves change its coefficient and can lengthen the time for complete replacement. The estimate describes the initial buoyancy-driven exchange.