  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.

Fluid Dynamics