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Temporal variation of non-ideal plumes with sudden reductions in buoyancy flux

Published online by Cambridge University Press:  26 March 2008

M. M. SCASE ,
C. P. CAULFIELD  and
S. B. DALZIEL
M. M. SCASE*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
C. P. CAULFIELD
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
S. B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
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Abstract

We model the behaviour of isolated sources of finite radius and volume flux which experience a sudden drop in buoyancy flux, generalizing the previous theory presented in Scase et al. (J. Fluid Mech., vol. 563, 2006, p. 443). In particular, we consider the problem of the source of an established plume suddenly increasing in area to provide a much wider plume source. Our calculations predict that, while our model remains applicable, the plume never fully pinches off into individual rising thermals.

We report the results of a large number of experiments, which provide an ensemble to compare to theoretical predictions. We find that provided the source conditions are weakened in such a way that the well-known entrainment assumption remains valid, the established plume is not observed to pinch off into individual thermals. Further, not only is pinch-off not observed in the ensemble of experiments, it cannot be observed in any of the individual experiments. We consider both the temporal evolution of the plume profile and a concentration of passive tracer, and show that our model predictions compare well with our experimental observations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 600 , 10 April 2008 , pp. 181 - 199
Copyright
Copyright © Cambridge University Press 2008

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References

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