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Stochastic versions of a classical model for natural ventilation are proposedand investigated to demonstrate the effect of random fluctuations on stabilityand predictability. In a stochastic context, the well-known deterministicresult that ventilation driven by the competing effects of buoyancy and windadmits multiple steady states can be misleading. With fluctuations in thebuoyancy exchanged with an external environment modelled as a Wiener process,such systems tend to reside in the vicinity of global minima of theirpotential, rather than states associated with metastable equilibria. For aheated space with a leeward low-level and windward high-level opening,sustained buoyancy-driven flow opposing the wind direction is unlikely for windstrengths exceeding a statistically critical value, which is slightly largerthan the critical value of the wind strength at which bifurcation in thedeterministic system occurs. When fluctuations in the applied wind strength aremodelled as an Ornstein-Uhlenbeck process, the topology of the system'spotential is effectively modified due to the nonlinear role that wind strengthhas in the equation for buoyancy conservation. Consequently, large fluctuationsin the wind of sufficient duration rule out the possibility of sustainedventilation opposing the wind direction at large base wind strengths.

Stochastic models of ventilation driven by opposing wind and buoyancy