Abstract This paper describes the fluid mechanics of natural ventilation by the combined effects of buoyancy and wind. Attention is restricted to transient draining flows in a space containing buoyant fluid, when the wind and buoyancy forces reinforce one another. The flows have been studied theoretically and the results compared with small-scale laboratory experiments. Connections between the enclosure and the surrounding fluid are with high-level and low-level openings on both windward and leeward faces. Dense fluid enters through windward openings at low levels and displaces the lighter fluid within the enclosure through high-level, leeward openings. A strong, stable stratification develops in this case and a displacement flow is maintained for a range of Froude numbers. The rate at which the enclosure drains increases as the wind-induced pressure drop between the inlet and outlet is increased and as the density difference between the exterior and interior environment is increased. A major result of this work is the identification of the form of the nonlinear relationship between the buoyancy and wind effects. It is shown that there is a Pythagorean relationship between the combined buoyancy and wind-driven velocity and the velocities which are produced by buoyancy and wind forces acting in isolation. This study has particular relevance to understanding and predicting the air flow in a building which is night cooled by natural ventilation, and to the flushing of gas from a building after a leak.