We will consider two problems that both involve turbulent plumes in a confined space. The problems stem from models of buoyancy-driven building ventilation, in which the distribution of boundary heating and externally imposed pressure differences are crucial in determining the temperature structure within a space.
For the first problem we will zoom in and analyse the mixing that results from convection driven by point sources of buoyancy located on the bottom and top boundaries of a horizontally periodic box. We will compare results from direct numerical simulations at different aspect ratios with predictions for dissipation and diapycnal mixing derived from plume theory.
For the second problem we will zoom out and analyse the wind-opposed ventilation of a heated space with high- and low-level openings on the windward and leeward side of a space, respectively. We determine the minimal gust of wind that is required to reverse displacement ventilation, comprising a stable, two-layer stratification, to produce mixing ventilation in which the stratification is destroyed.