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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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