Wind fluctuations affect the mean behaviour of naturally ventilated systems

Stochastic models of ventilation driven by opposing wind and buoyancy

“…Here, however, it will be assumed that (2.8) models the system’s evolution for durations over which W and σ can be treated as being independent of time. As demonstrated in §5, as an extension of the more tractable model considered in this section, finite time correlations of fluctuations in the wind can be incorporated by modelling W in (2.4) as an Ornstein–Uhlenbeck process with an autocorrelation that decays exponentially in time [18,48,49].…”

“…In general, such an equation could be adapted to produce a specific wind speed distribution from a given set of environmental conditions [22]. One particular, if somewhat idealized, approach is to represent fluctuations in the wind velocity that affect the bulk pressure difference (normalΔpfalse^ in §2a) as an Ornstein–Uhlenbeck process [18], which can account for temporal correlations. If the stochastic buoyancy flux from §2a is retained, the governing equations become dBt=afalse(Bt,Ut;Wfalse) dt+σfalse(Bt;Wfalse)∘ dξtand dUt=−γUt dt+ν dζt,where, following [18], Ut corresponds to dimensionless fluctuations in the wind velocity, which is proportional to the square root of the resulting pressure difference: afalse(Bt,Ut;Wfalse):=1−cfalsefalse|Bt−false(1+Utfalse)2W|1/2 …”

“…One particular, if somewhat idealized, approach is to represent fluctuations in the wind velocity that affect the bulk pressure difference (normalΔpfalse^ in §2a) as an Ornstein–Uhlenbeck process [18], which can account for temporal correlations. If the stochastic buoyancy flux from §2a is retained, the governing equations become dBt=afalse(Bt,Ut;Wfalse) dt+σfalse(Bt;Wfalse)∘ dξtand dUt=−γUt dt+ν dζt,where, following [18], Ut corresponds to dimensionless fluctuations in the wind velocity, which is proportional to the square root of the resulting pressure difference: afalse(Bt,Ut;Wfalse):=1−cfalsefalse|Bt−false(1+Utfalse)2W|1/2 Bt.The parameter …”

“…In contrast to the deterministic models described in the previous paragraph, there is growing recognition that probabilistic methods are useful, if not essential, in analysing and predicting the performance of buildings [18,19]. For modelling occupancy [20], passive tracers [21] and wind speeds [11,22], such methods are already used.…”

“…However, the problem was not formulated as a stochastic differential equation and analytical information that can be obtained from the associated Fokker–Planck equation was not used. More recently, stochastic fluctuations have been applied to the wind opposing the displacement ventilation driven by a point source of buoyancy [18]. Owing to the nonlinear dependence of the ventilation on the opposing wind strength, the incorporation of fluctuations in the wind modifies the interface height associated with the resulting two-layer stratification.…”