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Dam-break reflection

Hogg, Andrew J; Skevington, Edward W G


Andrew J Hogg


The unsteady reflection of dam-break flow along a horizontal channel by a remote barrier is modelled using the nonlinear shallow water equations. The interaction generates an upstream moving bore that connects the collapsing reservoir of fluid to a rapidly deepening fluid layer adjacent to the barrier. These motions are modified when the fluid is released into a channel containing a pre-wetted layer, because the oncoming flow is itself headed by a bore that alters the initial reflection. Solutions for these flows are calculated using quasi-analytical techniques that utilise the method of characteristics and the hodograph transformation of the governing equations, and the results are validated by comparison with direct numerical integration of the shallow water equations. The analytical solutions enable the precise identification of dynamical features in the flow, including the onset and development of discontinuous solutions that are manifest as bores, as well as their long term behaviour, the rate at which energy is dissipated, and for flows generated from the release of a finite reservoir, the maximum depth of the fluid layer at the barrier.


Hogg, A. J., & Skevington, E. W. G. (2021). Dam-break reflection. Quarterly Journal of Mechanics and Applied Mathematics, 74(4), 441-465.

Journal Article Type Article
Acceptance Date Aug 3, 2021
Online Publication Date Sep 8, 2021
Publication Date 2021-11
Deposit Date Jan 19, 2022
Publicly Available Date Jan 19, 2022
Journal The Quarterly Journal of Mechanics and Applied Mathematics
Print ISSN 0033-5614
Electronic ISSN 1464-3855
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 74
Issue 4
Pages 441-465
Keywords Applied Mathematics; Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
Public URL


Published article (1.3 Mb)

Copyright Statement
© The Author, 2021. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(, which permits unrestricted reuse, distribution, and reproduction in
any medium, provided the original work is properly cited.

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