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

Published online by Cambridge University Press:  11 April 2019

John Craske Open the ORCID record for John Craske [Opens in a new window]  and
Graham O. Hughes Open the ORCID record for Graham O. Hughes [Opens in a new window]
John Craske*
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
Graham O. Hughes
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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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, Build. Environ., vol. 44 (4), 2009, 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.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Convection: Plumes/thermals Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 868 , 10 June 2019 , R3
Copyright
© 2019 Cambridge University Press 

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References

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