Stochastic models of ventilation driven by opposing wind and buoyancy

Abstract

Stochastic versions of a classical model for natural ventilation are proposed and investigated to demonstrate the effect of random fluctuations on stability and predictability. In a stochastic context, the well-known deterministic result that ventilation driven by the competing effects of buoyancy and wind admits multiple steady states can be misleading. With fluctuations in the buoyancy exchanged with an external environment modelled as a Wiener process, such systems tend to reside in the vicinity of global minima of their potential, rather than states associated with metastable equilibria. For a heated space with a leeward low-level and windward high-level opening, sustained buoyancy-driven flow opposing the wind direction is unlikely for wind strengths exceeding a statistically critical value, which is slightly larger than the critical value of the wind strength at which bifurcation in the deterministic system occurs. When fluctuations in the applied wind strength are modelled as an Ornstein–Uhlenbeck process, the topology of the system’s potential is effectively modified due to the nonlinear role that wind strength has in the equation for buoyancy conservation. Consequently, large fluctuations in the wind of sufficient duration rule out the possibility of sustained ventilation opposing the wind direction at large base wind strengths.