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We determine the smallest instantaneous increase in the strength of anopposing wind that is necessary to permanently reverse the forward displacementflow that is driven by a two-layer thermal stratification. With aninterpretation in terms of the flow's energetics, the results clarify why theventilation of a confined space with a stably-stratified buoyancy field is lesssusceptible to being permanently reversed by the wind than the ventilation of aspace with a uniform buoyancy field. For large opposing wind strengths wederive analytical upper and lower bounds for the system's marginal stability,which exhibit a good agreement with the exact solution, even for modestopposing wind strengths. The work extends a previous formulation of the problem(Lishman & Woods, 2009, Building and Env. 44, pp. 666-673) by accounting forthe transient dynamics and energetics associated with the homogenisation of theinterior, which prove to play a significant role in buffering temporalvariations in the wind.

On the robustness of emptying filling boxes to sudden changes in the wind