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Merging of two or more plumes arranged around a circle

Published online by Cambridge University Press:  11 May 2016

G. G. Rooney
G. G. Rooney*
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
*
†Email address for correspondence: gabriel.rooney@metoffice.gov.uk
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Abstract

A model is presented of merging turbulent plumes from sources evenly spaced around a horizontal circle in a quiescent, unstratified background. This follows the previously developed method of (i) identifying the boundaries of interacting plumes with velocity-potential contours of line sinks and (ii) closing the generalised plume equations with an entrainment assumption based on the integrated flux across the plume boundaries. It includes the simplest case of two merging plumes, as well as being applicable to plume flows in restricted corner configurations. The model is shown to display the expected limiting behaviour for the source plumes and the merged plume. Consideration of the plume fluxes in the merging region leads to a revision of the entrainment assumption. The resulting revised model compares satisfactorily with previous estimates of volume flux in two merging plumes.

JFM classification

Convection: Convection Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 796 , 10 June 2016 , pp. 712 - 731
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Copyright
© Crown Copyright. Published by Cambridge University Press 2016 

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References

Alessandrini, S., Ferrero, E. & Anfossi, D. 2013 A new Lagrangian method for modelling the buoyant plume rise. Atmos. Environ. 77, 239–249.Google Scholar
Babrauskas, V. 1980 Flame lengths under ceilings. Fire Mater. 4 (3), 119–126.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Campbell, I. H. & Turner, J. S. 1985 Turbulent mixing between fluids with different viscosities. Nature 313, 39–42.CrossRefGoogle Scholar
Cenedese, C. & Linden, P. F. 2014 Entrainment in two coalescing axisymmetric turbulent plumes. J. Fluid Mech. 752, R2.Google Scholar
Cetegen, B. M., Zukoski, E. E. & Kubota, T. 1984 Entrainment in the near and far field of fire plumes. Combust. Sci. Technol. 39, 305–331.Google Scholar
Davidson, M. J., Papps, D. A. & Wood, I. R. 1994 The behaviour of merging buoyant jets. In Recent Research Advances in the Fluid Mechanics of Turbulent Jets and Plumes (ed. Davies, P. A. & Neves, M. J. V.), NATO ASI Series, vol. 255, pp. 465–478. Springer.CrossRefGoogle Scholar
Ezzamel, A., Salizzoni, P. & Hunt, G. R. 2015 Dynamical variability of axisymmetric buoyant plumes. J. Fluid Mech. 765, 576–611.Google Scholar
Hunt, G. R. & Kaye, N. B. 2005 Lazy plumes. J. Fluid Mech. 533, 329–338.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.Google Scholar
Kaye, N. B. & Linden, P. F. 2004 Coalescing axisymmetric turbulent plumes. J. Fluid Mech. 502, 41–63.Google Scholar
Kimura, S., Holland, P. R., Jenkins, A. & Piggott, M. 2014 The effect of meltwater plumes on the melting of a vertical glacier face. J. Phys. Oceanogr. 44, 3099–3117.Google Scholar
Lai, A. C. H. & Lee, J. H. W. 2012 Dynamic interaction of multiple buoyant jets. J. Fluid Mech. 708, 539–575.Google Scholar
Linden, P. F., Lane-Serff, G. F. & Smeed, D. A. 1990 Emptying filling boxes: the fluid mechanics of natural ventilation. J. Fluid Mech. 212, 309–335.Google Scholar
Mokhtarzadeh-Dehghan, M. R., König, C. S. & Robins, A. G. 2006 Numerical study of single and two interacting turbulent plumes in atmospheric cross flow. Atmos. Environ. 40 (21), 3909–3923.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
van Reeuwijk, M. & Craske, J. 2015 Energy-consistent entrainment relations for jets and plumes. J. Fluid Mech. 782, 333–355.Google Scholar
Rooney, G. G. 2015 Merging of a row of plumes or jets with an application to plume rise in a channel. J. Fluid Mech. 771, R1.Google Scholar
Rooney, G. G. & Linden, P. F. 1996 Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318, 237–250.Google Scholar
Taylor, G. I. 1958 Flow induced by jets. J. Aero. Sci. 25, 464–465.Google Scholar
Turner, J. S. 1969 Buoyant plumes and thermals. Annu. Rev. Fluid Mech. 1, 29–44.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Wang, H. & Law, A. W.-K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397–428.Google Scholar
Yannopoulos, P. 2010 Advanced integral model for groups of interacting round turbulent buoyant jets. Environ. Fluid Mech. 10 (4), 415–450.CrossRefGoogle Scholar