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 meta-stable
equilibria. For a heated space with a leeward low-level and windward highlevel 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 sufficiently short
duration rule out the possibility of sustained ventilation opposing the wind
direction at large base wind strengths.