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

TL;DR

This study investigates the minimal wind strength needed to reverse the natural flow in a stratified space, revealing how stratification affects vulnerability to wind-induced flow reversal and providing bounds for stability.

Contribution

It extends previous models by incorporating transient dynamics and energetics, offering new insights into flow stability under wind disturbances in stratified environments.

Findings

Stratified spaces are more resistant to wind reversal than uniform ones.

Analytical bounds closely match exact solutions for various wind strengths.

Transient energetics significantly buffer against flow reversal.

Abstract

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