Shallow Flows over Curved Beds: Application of the Serre–Green–Naghdi Theory to Weir Flow
Publication: Journal of Hydraulic Engineering
Volume 148, Issue 1
Abstract
The Serre–Green–Naghdi (SGN) theory is used widely in maritime hydraulics for the computation of water waves from shallow to intermediate water depths. However, it has been largely ignored in problems of open-channel hydraulics. This research applies the SGN theory to compute shallow flows over curved beds, focusing on round-crested control structures. A systematic and complete analysis is presented, including the solution of both the unsteady and steady versions of the SGN theory. A new steady SGN solver is presented, allowing for automatic computation of the rating curves of the structures, thereby avoiding tedious trial and error iterations. The SGN theory is applied to a wide portfolio of obstacle shapes used in practice, resulting in agreement with experimental evidence within the shallowness limit determined. A higher-order approach is discussed, pointing to a possible path to increase the validity of SGN-type solvers in high overflow problems.
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Data Availability Statement
The computational codes developed for this research are available from the corresponding author upon reasonable request.
Acknowledgments
The first author expresses his deep gratitude to Prof. Takashi Hosoda, Kyoto University, for the long discussions of Boussinesq modeling in open-channel hydraulics, and especially for instructing him on the pioneering Japanese contributions to the topic. The work of the first author was supported by the Spanish project PID2020-114688RB-I00 and Grant María de Maeztu for Centers and Units of Excellence in R&D (Ref. CEX2019-000968-M).
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Journal of Hydraulic Engineering
Volume 148 • Issue 1 • January 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 12, 2021
Accepted: Aug 18, 2021
Published online: Oct 27, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 27, 2022
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