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Unsteady draining of reservoirs over weirs and through constrictions

Skevington, Edward W. G.; Hogg, Andrew J.


Andrew J. Hogg


The gravitationally driven flow of fluid from a reservoir following the partial collapse of its confining dam, or the partial opening of its confining lock, is modelled using the nonlinear shallow water equations, coupled to outflow conditions, in which the drainage is modelled as flow over a constricted, broad-crested weir. The resulting unsteady motion reveals systematic draining, on which strong and relatively rapid oscillations are imposed. The oscillations propagate between the outflow and the impermeable back wall of the reservoir. This dynamics is investigated utilising three methods: hodograph techniques to yield quasi-analytical solutions, asymptotic analysis at relatively late times after initiation and numerical integration of the governing equations. The hodograph transformation is used to find exact solutions at early times, revealing that from initially quiescent conditions the fluid drains and yet repeatedly generates intervals during which there are regions of constant depth and velocity adjacent to the boundaries. A novel modified multiscale asymptotic analysis designed for late times is employed to determine the limiting rate of draining and wave structure. It is shown that the excess height drains as


Skevington, E. W. G., & Hogg, A. J. (2020). Unsteady draining of reservoirs over weirs and through constrictions. Journal of Fluid Mechanics, 882,

Journal Article Type Article
Acceptance Date Oct 1, 2019
Online Publication Date Nov 6, 2019
Publication Date Jan 10, 2020
Deposit Date Jan 19, 2022
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 882
Article Number A9
Keywords Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
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