Serre Equations in Channels and Rivers of Arbitrary Cross Section
Publication: Journal of Hydraulic Engineering
Volume 149, Issue 7
Abstract
A variational approach was used to derive a set of Serre equations for fully nonlinear, dispersive waves in channels of arbitrary cross section. A family of travelling waves was found, as well as the relation between amplitude and celerity of solitary waves. An upper bound is proposed for the solitary wave amplitude as a function of the Froude number in trapezoidal cross-sectional canals, and it showed good agreement with existing theory. For waves of moderate amplitude, cnoidal waves result with a soliton limit; these waves and their properties (celerity and wave number) are written as functions of the channel bank slope and channel bank curvature. The theoretical findings are in agreement with well-established results in the literature, in particular with more-recent Boussinesq-type theories. A validation is proposed against existing experimental data.
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Data Availability Statement
No data, models, or code were generated or used during the study.
Acknowledgments
This work was funded by Électricité de France (EDF). The author is grateful to Prof. Oscar Castro-Orgaz (Universidad de Córdoba, Spain) for inviting him to contribute to this special issue. The author also thanks Prof. Willi Hager (ETH Zurich, Switzerland) for his fruitful comments that helped improve this work. The author also is indebted to an anonymous reviewer for providing useful comments and advice on the original manuscript. All formulas and figures were checked with Scientific WorkPlace 5.5.
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Journal of Hydraulic Engineering
Volume 149 • Issue 7 • July 2023
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© 2023 American Society of Civil Engineers.
History
Received: Jul 18, 2022
Accepted: Mar 1, 2023
Published online: Apr 26, 2023
Published in print: Jul 1, 2023
Discussion open until: Sep 26, 2023
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