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Gravitational convection from instantaneous sources on inclined boundaries

Published online by Cambridge University Press:  20 April 2006

P. Beghin ,
E. J. Hopfinger  and
R. E. Britter
P. Beghin
Affiliation:
Institut de Mécanique (Laboratoire Associé au CNRS), Université de Grenoble, France
E. J. Hopfinger
Affiliation:
Institut de Mécanique (Laboratoire Associé au CNRS), Université de Grenoble, France
R. E. Britter
Affiliation:
Engineering Department, University of Cambridge, Cambridge
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Abstract

Two-dimensional buoyant clouds moving along inclined boundaries under a gravitational force are investigated theoretically and experimentally. It is found that the ‘thermal theory’ gives a good description of the flow in the slope angle range 5° [lsim ] θ ≤ 90°. In this range the spatial growth rates of the cloud height and length are constant for a given slope angle and show a linear dependence on θ. For a cloud released with zero initial velocity the front velocity Uf first increases and then decreases, with the characteristic time of acceleration predicted by theory. In the decelerating state Uf/(g0′Q0/xf)½ is 2·6 ± 0·2 at θ ≃ 15°, and then reduces uniformly with increasing θ to a value of 1·5 ≃ 0·2 at 90° (where g0′Q0 is the released buoyancy and xf is the front position measured from a virtual origin). The shape of the cloud is well approximated by a half-ellipse. The variation of the ratio of the principal axes of the half-ellipse with slope angle is identical with that of the head of an inclined starting plume (Britter & Linden 1980). However, the cloud has a greater growth rate than the head of a starting plume.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 107 , June 1981 , pp. 407 - 422
Copyright
© 1981 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Britter, R. E. & Linden, P. F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99, 531–543.Google Scholar
Britter, R. E. & Simpson, J. E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88, 223–240.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 432–448.Google Scholar
Hopfinger, E. J. & Tochon-Danguy, J. C. 1977 A model study of powder-snow avalanches. J. Glaciology 19, 343–356.Google Scholar
Hoult, D. P. 1972 Oil spreading on the sea. Ann. Rev. Fluid Mech. 4, 341–368.Google Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23.Google Scholar
Simpson, J. E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53, 759–768.Google Scholar
Tochon-Danguy, J. C. & Hopfinger, E. J. 1975 Simulation of the dynamics of powder avalanches. Proc. Grindelwald Symp., IAHS Publ. no. 114, pp. 369–380.Google Scholar
Tsang, G. 1971 Laboratory study of line thermals. Atm. Env. 4, 445–471.Google Scholar
Turner, J. S. 1962 The ‘starting plume’ in neutral surroundings. J. Fluid Mech. 13, 356–368.Google Scholar