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Local implications for self-similar turbulent plume models

Published online by Cambridge University Press:  07 March 2007

M. M. SCASE ,
C. P. CAULFIELD ,
P. F. LINDEN  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
P. F. LINDEN
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
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

The local implications of the well-known flux conservation equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p.1) for plumes and jets are considered. Given the vertical velocity distributions of a model plume or jet, the divergence-free radial velocity distributions are calculated. It is shown that in general the velocity of the plume boundary is not described by the local total fluid velocity in this way. A two-fluid model tracking the evolution of both ‘plume’ and ‘ambient’ fluid is proposed which resolves this apparent inconsistency and also provides a way of explicitly describing the mixing process within a model plume. The plume boundary acts as a phase boundary across which ambient fluid is entrained, and the plume boundary moves at the velocity of the plume fluid. The difference between the plume-fluid radial velocity and the total fluid velocity quantifies in a natural way the purely horizontal entrainment flux of ambient fluid into the plume across the phase boundary at the plume edge.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 257 - 265
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. (Eds.) 1965 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, S 6.1. Dover.Google Scholar
Caulfield, C. P. 1991 Stratification and buoyancy in geophysical flows. PhD Thesis, University of Cambridge, UK.Google Scholar
Caulfield, C. P. & Woods, A. W. 1995 Plumes with non-monotonic mixing behaviour. Geophys. Astrophys. Fluid Dyn. 79, 173–199.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. B. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.CrossRefGoogle Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.CrossRefGoogle 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, 1–32.Google Scholar
Scase, M. M., Caulfield, C. P. & Dalziel, S. B. 2006 Boussinesq plumes with decreasing source strengths in stratified environments. J. Fluid Mech. 563, 463–472.CrossRefGoogle Scholar
Scase, M. M., Caulfield, C. P., Dalziel, S. B. & Hunt, J. C. R. 2006 Time-dependent plumes and jets with decreasing source strengths. J. Fluid Mech. 563, 443–461.CrossRefGoogle Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–472.CrossRefGoogle Scholar
Zeldovich, Y. B. 1937 The asymptotic laws of freely-ascending convective flows. Zhur. Eksper. Teor. Fiz. 7, 1463–1465 (in Russian). English transl. in Selected Works of Yakov Borisovich Zeldovich, Vol. 1 1992 (ed. Ostriker, J. P.), pp. 82–85. Princeton University Press.Google Scholar