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

  • John Craske (a1) and Graham O. Hughes (a1)


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.


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Coomaraswamy, I. & Caulfield, C. 2011 Time-dependent ventilation flows driven by opposing wind and buoyancy. J. Fluid Mech. 672, 3359.
Gladstone, C. & Woods, A. W. 2001 On buoyancy-driven natural ventilation of a room with a heated floor. J. Fluid Mech. 441, 293314.
Hughes, G. O., Gayen, B. & Griffiths, R. W. 2013 Available potential energy in Rayleigh–Bérnard convection. J. Fluid Mech. 729, R3.
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Kaye, N. B. & Hunt, G. R. 2004 Time-dependent flows in an emptying filling box. J. Fluid Mech. 520, 135156.
Linden, P. F. 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31 (1), 201238.
Linden, P. F., Lane-Serff, G. F. & Smeed, D. A. 1990 Emptying filling boxes: the fluid mechanics of natural ventilation. J. Fluid Mech. 212, 309335.
Lishman, B. & Woods, A. W. 2009 On transitions in natural ventilation flow driven by changes in the wind. Build. Environ. 44 (4), 666673.
Yuan, J. & Glicksman, L. R. 2008 Multiple steady states in combined buoyancy and wind driven natural ventilation: the conditions for multiple solutions and the critical point for initial conditions. Build. Environ. 43 (1), 6269.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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