Time-Dependent Ventilation Flows Driven by Opposing Wind and Buoyancy

We consider transient flow in a box containing an isolated buoyancy source, ventilated by a windward high-level opening and a leeward low-level opening, so that prevailing wind acts to oppose buoyancy-driven flow. Hunt & Linden (J. Fluid Mech., vol. 527, 2005, p. 27) demonstrated that two stable steady states can exist above a critical wind strength: buoyancy-driven displacement ventilation with a two-layer stratification and wind-driven mixing ventilation with the whole interior contaminated by buoyant fluid. We present two time-dependent models for this system: a nonlinear ordinary differential equation (ODE) model following Kaye & Hunt (J. Fluid Mech., vol. 520, 2004, p. 135), assuming ‘perfect’ vertical mixing of fluid within each layer, and a partial differential equation model assuming zero vertical mixing, following Germeles (J. Fluid Mech., vol. 71, 1975, p. 601)