Energetics of mixing for the filling box and the emptying-filling box |
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Authors: | Davies Wykes Megan S Hogg Charlie Partridge Jamie Hughes Graham O |
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Institution: | 1.Department of Engineering, Trumpington Street, Cambridge, CB2 1PZ, UK ;2.DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK ;3.Department of Civil and Environmental Engineering, Imperial College London, London, SW7 2AZ, UK ; |
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Abstract: | The mixing efficiency of a plume in a filling box and an emptying-filling box is calculated for both transient and steady states. The mixing efficiency of a plume in a filling box in an asymptotic state is 1/2, independent of the details of this state or how the plume is modelled.
The mixing efficiency of a plume in an emptying-filling box in steady state is \(1 - \xi \), where \(\xi = h/H\), the depth of the ambient layer h normalised by the height of the box H.
A deeper mixed layer therefore corresponds to a higher mixing efficiency. These results shed light on the interpretation of mixing efficiencies of open and closed systems. |
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