Analysis of the Friction Term in the One-Dimensional Shallow-Water Model
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 9
Abstract
The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The flow velocity data measured by the Statistics and Gauging Service of the Ebro River Basin Water Authority (Confederación Hidrográfica del Ebro) have been very useful to validate the friction models analyzed in this work and are acknowledged. This work has been partially funded by the Spanish Ministry of Science and Education under Research Project No. CGL2005-07059-C02-02.
References
Bathurst, J. C., Simons, D. B., and Li, R. M. (1981). “Resistance equations for large-scale roughness.” J. Hydr. Div., 107(12), 1593–1613.
Bettess, R., and White, W. R. (1987). “Extremal hypotheses applied to river regime.” Sediment transport in gravel bed rivers, C. R. Thorne, J. C. Bathurst, and R. D. Hey, eds., Wiley, Chichester, 767–789.
Burguete, J., and García-Navarro, P. (2001). “Efficient construction of high-resolution TVD conservative schemes for equations with source terms: Application to shallow-water flows.” Int. J. Numer. Methods Fluids, 37(2), 209–248.
Burguete, J., and García-Navarro, P. (2004a). “Implicit schemes with large time step for nonlinear equations: Application to river flow hydraulics.” Int. J. Numer. Methods Fluids, 46(6), 607–636.
Burguete, J., and García-Navarro, P. (2004b). “Improving simple explicit methods for unsteady open channel and river flow.” Int. J. Numer. Methods Fluids, 45(2), 125–156.
Cao, Z., Meng, J., Pender, G., and Wallis, S. (2006). “Flow resistance and momentum flux in compound open channels.” J. Hydraul. Eng., 132(12), 1272–1282.
Chanson, H. (1999). The hydraulics of open channel flow, Arnold, London.
Chow, V. T. (1959). Open channel hydraulics, McGraw-Hill, New York.
Courant, R., Friedrichs, K. O., and Lewy, H. (1928). “Über die partiellen differenzengleichungen der mathematischen physik.” Math. Ann., 100(1), 32–74.
Cunge, J. A., Holly, F. M., Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics, Pitman, London.
Darcy, H. P. G. (1858). Recherches expérimentales relatives aux mouvements de l’eau dans les tuyaux, Mémoires Présentées à l’Académie des Sciences, Paris.
de Saint-Venant, A. J. C. B. (1871). Théorie de mouvement non-permanent des eaux avec application aux crues de rivières et á l’introduction des marées dans leur lit, Comptes Rendues de l’Académie des Sciences, Paris.
García-Navarro, P., Playán, E., and Zapata, N. (2000). “Solute transport modeling in overland flow applied to fertigation.” Irrig. Drain., 126(1), 33–40.
Gauckler, P. G. (1867). Études théoriques et pratiques sur l’écoulement et le mouvement des eaux, Comptes Rendues de l’Académie des Sciences, Paris.
Jarrett, R. D. (1984). “Hydraulics of high-gradient streams.” J. Hydraul. Eng., 110(11), 1519–1539.
Kellerhals, R. (1967). “Stable channels with gravel-paved beds.” J. Wtrwy. and Harb. Div., 93(1), 63–84.
Knight, D. W. (2004). “FCF Series.” Flow Database at the Univ. of Birmingham, ⟨www.flowdata.bham.ac.uk⟩ (Jan. 22, 2007).
Knight, D. W. (2006). “River flood-hydraulics: Validation issues in one-dimensional flood routing models.” River basin modelling for flood risk mitigation, D. W. Knight and A. Y. Shamesildin, eds., Taylor & Francis, London.
Liggett, J. A., and Cunge, J. A. (1977). “Numerical methods of solution of the unsteady flow equations.” Unsteady flow in open channels, K. Mahmood and V. Yevjevich, eds., Water Resources, Fort Collins, Colo.
MacGahey, C., Samuels, P. G., and Knight, D. W. (2006). “A practical approach to estimating the flow capacity of rivers—Application and analysis.” Proc., River Flow 2006, Taylor & Francis, Lisboa.
Manning, R. (1890). “On the flow of water in open channels and pipes.” Trans. Inst. Civil Engineers, 20, 161–207.
Shiono, K., Muto, Y., Knight, D. W., and Hyde, A. F. L. (1999). “Energy losses due to secondary flow and turbulence in meandering channels with overbank flow.” J. Hydraul. Res., 37(5), 641–664.
Smart, G. M. (1999). “Turbulent velocity profiles and boundary shear in gravel-bed rivers.” J. Hydraul. Eng., 125(2), 106–116.
Smart, G. M., Duncan, M. J., and Walsh, J. M. (2002). “Relatively rough flow resistance equations.” J. Hydraul. Eng., 128(6), 568–578.
Strickler, A. (1923). Beiträge zur Frage der Geschwindigkeitsformel und der Rauhligkeitszahlen für Ströme, Kanäle und Geschlossene Leitungen, Mitt. des Eidgenössischen Amtes für Wasser-wirtschaft, Bern, Vol. 16.
White, F. M. (1991). Viscous fluid flow, McGraw-Hill, New York.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 133 • Issue 9 • September 2007
Pages: 1048 - 1063
Copyright
© 2007 ASCE.
History
Received: Aug 12, 2005
Accepted: Mar 20, 2007
Published online: Sep 1, 2007
Published in print: Sep 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.