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Axisymmetric gravity currents on a cone

Published online by Cambridge University Press:  28 September 2006

ANDREW N. ROSS ,
STUART B. DALZIEL  and
P. F. LINDEN
ANDREW N. ROSS
Affiliation:
Institute for Atmospheric Science, School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK aross@env.leeds.ac.uk
STUART B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
P. F. LINDEN
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
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Abstract

The previously unstudied problem of an axisymmetric gravity current released on a cone is investigated. A formulation of the problem based on the shallow-water equations, with and without entrainment and bottom drag, is given. Analytical asymptotic solutions are found and compared to numerical solutions of the equations. The inclusion of entrainment and drag is seen to play a significant role in limiting the propagation speed of the gravity current and also in altering the shape of the current. These theoretical predictions are compared to laboratory experiments and to two-dimensional numerical simulations. The shallow-water solutions including entrainment are found to provide a much better comparison with the experiments than the solutions without entrainment. In particular, the observed front speed and dilution of the head are in good agreement. Some applications to industrial and environmental problems such as dense gas dispersion are briefly discussed.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 565 , 25 October 2006 , pp. 227 - 253
Copyright
© 2006 Cambridge University Press

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