Unsteady Boussinesq-type flow equations for gradually-eroded beds: application to dike breaches

Dike breach due to overtopping involves unsteady flow over a curved bed continuously deforming in time due to erosion. The curvatures and slopes on the water surface and the bed profiles indicate that the shallow-water-equations may be inappropriate for modelling purposes. The next degree of mathema...

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Bibliographic Details
Published in:Journal of hydraulic research 2013-04, Vol.51 (2), p.203-208
Main Authors: Castro-Orgaz, Oscar, Hager, Willi H.
Format: Article
Language:English
Subjects:
Boussinesq equation
Boussinesq equations
Curvature
Curved
curved bed
dike
Dikes
Earth sciences
Earth, ocean, space
erodible bed
Exact sciences and technology
Flow control
Flow velocity
hydraulics
Hydrology
Hydrology. Hydrogeology
Marine and continental quaternary
Mathematical analysis
Mathematical models
open channel flow
Studies
Surficial geology
Unsteady
Unsteady flow
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Summary:Dike breach due to overtopping involves unsteady flow over a curved bed continuously deforming in time due to erosion. The curvatures and slopes on the water surface and the bed profiles indicate that the shallow-water-equations may be inappropriate for modelling purposes. The next degree of mathematical approximation is given by the Boussinesq equations accounting for vertical inertia effects. Herein novel unsteady flow equations for a curved erodible bed are developed. Using a Boussinesq-type closure, expressions for the vertical velocity, the pressure distribution and the momentum function are presented. These depend on two parameters relating to the temporal and spatial derivatives of the flow depth, namely bottom elevation and average flow velocity. The model equations are compared with previous unsteady Boussinesq-type models, indicating that the novel formulation is a generalization for erodible beds. The Boussinesq coefficients are further investigated using selected experiments conducted at VAW, ETH.
ISSN:0022-1686
1814-2079
DOI:10.1080/00221686.2012.739579