We investigate the mixing of a stratified fluid of finite volume by a turbulent buoyant plume. We develop a model to describe the mixing and apply this to both the cases of a two-layer stratification and a continuous stratification. With a two-layer stratification, the plume intrudes at the interface where it supplies an intermediate layer of fluid. This new layer gradually deepens, primarily mixing the original near-source layer of fluid through entrainment. Eventually, this intermediate layer becomes sufficiently buoyant that the plume penetrates into the more distal layer, leaving a partially mixed region between the original layers of fluid. Analysis of new experiments shows that the growth of the intermediate layer depends primarily on the ratio λ of (i) the filling box time, during which the plume entrains a volume of fluid equal to that in the near-source layer, and (ii) the time for the buoyancy of the near-source layer to increase to that of the more distal layer. For small values of λ, the near-source layer becomes approximately well mixed, and the penetration time of the plume scales with the buoyancy evolution time of the near-source layer. In the limit λ ∼ O(1), however, the plume penetrates through into the distal layer long before the nearsource layer becomes well mixed; instead, at the time of penetration, the plume leaves an intermediate partially mixed zone between the two original layers. We develop a new phenomenological model to account for the mixing in this intermediate layer based on the effective turbulent diffusion associated with the kinetic energy in the plume and compare this with the model for penetrative entrainment proposed by Kumagai (J. Fluid Mech., vol. 147, 1984, p. 105). In comparison with the experimental data, the models provide a reasonably accurate prediction of the plume penetration time, while the diffusive mixing model provides a somewhat more accurate description of the evolution of the density profile for a range 0 < λ < 1. The diffusive mixing model also leads to predictions which are consistent with some new experimental data for the case in which a plume mixes a continuously stratified layer. In particular, the model is able to predict the initial transient mixing of the region between the source and the height at which the plume intrudes laterally in the ambient fluid, thereby providing an advance on the late-time mixing model of Cardoso and Woods (J. Fluid Mech., vol. 250, 1993, p. 277). We consider the implications of these results on the turbulent penetrative entrainment associated with buoyant plumes.https:/www.cambridge.org/core/terms. https://doi.

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We investigate the mixing of a warm enclosed space by a series of discrete gusts of cold air from a high-level opening. Initially we examine the case of a series of gusts of identical size each modelled as a turbulent buoyant thermal. We develop a model of the filling box-like flow which develops in the space and identify the key parameter in the system as the ratio between the initial gust size and the product of the height of the room and the entrainment coefficient. We find an approximate analytic solution for the evolution of the density profile within the space which is in good agreement with a full numerical solution of the governing equations. We successfully test the predictions of the model with a series of new laboratory experiments. The experiments combined with the model also provide a new independent estimate for the entrainment coefficient of a thermal, = 0.37 ± 0.02, based on the propagation speed of a filling box front. We then examine the mixing produced by a series of thermals of non-identical size which we characterize in terms of a mean size and coefficient of variation. We find that as the coefficient of variation increases, the density profile becomes progressively more stratified owing to the asymmetry of dilution through entrainment of large and small thermals. We discuss the implications of these results for the ventilation of a building subject to gusts 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.