Quasi-steady states in natural displacement ventilation driven by periodic gusting of wind

We investigate the natural displacement ventilation of a space connected to a body of warm fluid through high-and low-level vents. The space is subject to discrete periodic gusts of wind entering at high level from a cold exterior. The cold exterior air entering the space produces buoyancy differences between the space and the body of warm fluid, driving a ventilation flow. Initially we examine the case of a series of identical gusts of wind modelled as turbulent buoyant thermals. New laboratory experiments show that an approximately two-layer stratification is established and the height of the interface is quasi-steady if the period between thermals is much less than the draining time of the space but longer than the fall time of individual thermals. Experiments also show that the interface height depends on the average buoyancy flux associated with the wind gusts, the time between thermals as well as the geometric properties of the vents. This contrasts with the case of a continuous source of buoyancy where the interface height depends only on the geometric properties of the vents and is independent of the buoyancy flux. We develop a quasi-steady two-layer model of the flow based on the classical theory of turbulent thermals and show that it is consistent with our new experimental data. We generalize the model to explore the sensitivity of the results to temporal variations in the size of thermals. We then extend the model to explore the effects of longer interval times between successive thermals and find a two-layer stratification still develops but that the interface height now varies cyclically in time. We then discuss the implications of these results for the ventilation of a shopping mall subject to gusts of wind.