Title: Self-similar solutions of the axisymmetric shallow-water equations governing converging inviscid gravity currents
Abstract: A phase-plane approach is used to determine similarity solutions of the axisymmetric shallow-water equations which represent inwardly propagating, inviscid gravity currents. A Froude number condition characterizes the movement of the front. The unique similarity exponent is found numerically as a function of the frontal Froude number and the height and velocity profiles are presented for three different Froude numbers. The fluid speed and height are seen to increase monotonically towards the front except very close to the front where the height decreases. The maxima in both height and speed increase as the Froude number increases, reflecting the change in ambient resistance.For the Froude number that has been obtained experimentally for lock-exchange Boussinesq flows (. This similarity solution describes the formation of a shock, as well as its initial propagation.
Publication Year: 2004
Publication Date: 2004-04-30
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 15
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