Can Meandering Flows in Shallow Rectangular Reservoirs Be Modeled with the 2D Shallow Water Equations?
Publication: Journal of Hydraulic Engineering
Volume 141, Issue 6
Abstract
This paper discusses the ability of the two-dimensional (2D) shallow water equations to model meandering flows in shallow rectangular reservoirs. Four meandering flows of various shallowness were modeled using an academic flow model that includes a depth-averaged model accounting for the horizontal and vertical turbulent length-scales. Different roughness heights were considered for modeling the bottom friction. A proper orthogonal decomposition (POD) was applied to the simulation results to extract the behavior of the main structures responsible for the meandering flow. The same POD analysis was also performed for the reference experimental flow fields, obtained by large-scale particle image velocimetry. The first two POD modes obtained from the numerical simulations assuming a smooth bottom are in good agreement with the experimental modes in terms of energy, as well as temporal and spatial variations, whatever the shallowness. In contrast, the remaining simulated modes are not well rendered. The effect of an increased roughness height in the simulations is finally discussed. It leads to an improved reproduction of the first two modes and of the following modes, except when significant viscous effects govern in the flow.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research was funded by the University of Liège (Grant SFRD-12/27). The authors are grateful for the assistance provided by the research technicians during the experiments.
References
Aloui, F., and Souhar, M. (2000). “Experimental study of turbulent asymmetric flow in a flat duct symmetric sudden expansion.” J. Fluid. Eng., 122(1), 174–177.
Babarutsi, S., and Chu, V. H. (1998). “Modeling transverse mixing layer in shallow open-channel flows.” J. Hydraul. Eng., 718–727.
Babarutsi, S., Nassiri, M., and Chu, V. H. (1996). “Computation of shallow recirculating flow dominated by friction.” J. Hydraul. Eng., 367–372.
Berkooz, G., Holmes, P., and Lumley, J. L. (1993). “The proper orthogonal decomposition in the analysis of turbulent flows.” Annu. Rev. Fluid Mech., 25(1), 539–575.
Brevis, W., and García-Villalba, M. (2011). “Shallow-flow visualization analysis by proper orthogonal decomposition.” J. Hydraul. Res., 49(5), 586–594.
Camnasio, E., Erpicum, S., Orsi, E., Pirotton, M., Schleiss, A. J., and Dewals, B. (2013). “Coupling between flow and sediment deposition in rectangular shallow reservoirs.” J. Hydraul. Res, 51, 535–547.
Camnasio, E., Orsi, E., and Schleiss, A. J. (2011). “Experimental study of velocity fields in rectangular shallow reservoirs.” J. Hydraul. Res., 49(3), 352–358.
Camnasio, E., Pirotton, M., Erpicum, S., and Dewals, B. (2012). “Experimental and numerical investigation of a meandering jet in shallow rectangular reservoirs under different hydraulic conditions.” Proc., 3rd Int. Symp. on Shallow Flows, College of Engineering, Univ. of Iowa, Iowa, IA.
Canbazoglu, S., and Bozkir, O. (2004). “Analysis of pressure distribution of turbulent asymmetric flow in a flat duct symmetric sudden expansion with small aspect ratio.” Fluid Dyn. Res., 35(5), 341–355.
Cavar, D., and Meyer, K. E. (2012). “LES of turbulent jet in cross flow: Part 2—POD analysis and identification of coherent structures.” Int. J. Heat Fluid Flow, 36, 35–46.
Chen, D., and Jirka, G. H. (1999). “LIF study of plane jet bounded in shallow water layer.” J. Hydraul. Eng., 817–826.
Chu, V. H., and Babarutsi, S. (1988). “Confinement and bed-friction effects in shallow turbulent mixing layers.” J. Hydraul. Eng., 1257–1274.
Chu, V. H., Khayat, R. E., and Wu, J. H. (1983). “Stability of turbulent shear flows in shallow channel.” Proc., 20th IAHR Congress, International Association for Hydraulic Research (IAHR), Delft, Netherlands, 128–133.
Chu, V. H., Liu, F., and Altai, W. (2004). “Friction and confinement effects on a shallow recirculating flow.” J. Environ. Eng. Sci., 3(5), 463–475.
Couplet, M., Sagaut, P., and Basdevant, C. (2003). “Intermodal energy transfers in a proper orthogonal decomposition—Galerkin representation of a turbulent separated flow.” J. Fluid Mech., 491, 275–284.
Dewals, B., Kantoush, S. A., Erpicum, S., Pirotton, M., and Schleiss, A. J. (2008). “Experimental and numerical analysis of flow instabilities in rectangular shallow basins.” Environ. Fluid Mech., 8(1), 31–54.
Dufresne, M., Dewals, B., Erpicum, S., Archambeau, P., and Pirotton, M. (2012). “Flow patterns and sediment deposition in rectangular shallow reservoirs.” Water Environ. J., 26(4), 504–510.
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., and Pirotton, M. (2010a). “Classification of flow patterns in rectangular shallow reservoirs.” J. Hydraul. Res., 48(2), 197–204.
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., and Pirotton, M. (2010b). “Experimental investigation of flow pattern and sediment deposition in rectangular shallow reservoirs.” Int. J. Sediment Res., 25(3), 258–270.
Dufresne, M., Dewals, B. J., Erpicum, S., Archambeau, P., and Pirotton, M. (2011). “Numerical investigation of flow patterns in rectangular shallow reservoirs.” Eng. Appl. Comput. Fluid Mech., 5(2), 247–258.
Erpicum, S., Dewals, B. J., Archambeau, P., and Pirotton, M. (2010). “Dam break flow computation based on an efficient flux vector splitting.” J. Comput. Appl. Math., 234(7), 2143–2151.
Erpicum, S., Meile, T., Dewals, B. J., Pirotton, M., and Schleiss, A. J. (2009). “2D numerical flow modeling in a macro-rough channel.” Int. J. Numer. Method. Fluids, 61(11), 1227–1246.
Foss, J. F., and Jones, J. B. (1968). “Secondary flow effects in a bounded rectangular jet.” J. Basic Eng., 90(2), 241–248.
Hauet, A., et al. (2008). “Experimental system for real-time discharge estimation using an image-based method.” J. Hydrol. Eng., 105–110.
Hauet, A. (2009). “Discharge estimate and velocity measurement in river using large-scale particle image velocimetry.” La Houille Blanche, 1(1), 80–85.
Holdeman, J. D., and Foss, J. F. (1975). “The initiation, development, and decay of the secondary flow in a bounded jet.” J. Fluid. Eng., 97(3), 342–352.
Holmes, P., Lumley, J. L., Berkooz, G., and Rowley, C. W. (2012). Turbulence, coherent structures, dynamical systems and symmetry, 2nd Ed., Cambridge Univ., Cambridge. U.K.
Kantoush, S. A. (2008). “Experimental study on the influence of the geometry of shallow reservoirs on flow patterns and sedimentation by suspended sediments.” Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
Kantoush, S. A., De Cesare, G., Boillat, J. L., and Schleiss, A. J. (2008). “Flow field investigation in a rectangular shallow reservoir using UVP, LSPIV and numerical modelling.” Flow Meas. Instrum., 19(3–4), 139–144.
Khan, S., Melville, B. W., Shamseldin, A. Y., and Fischer, C. (2013). “Investigation of flow patterns in storm water retention ponds using CFD.” J. Environ. Eng., 61–69.
Le Coz, J., Hauet, A., Pierrefeu, G., Dramais, G., and Camenen, B. (2010). “Performance of image-based velocimetry (LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers.” J. Hydrol., 394(1–2), 42–52.
Mariotti, G., Falcini, F., Geleynse, N., Guala, M., Sun, T., and Fagherazzi, S. (2013). “Sediment eddy diffusivity in meandering turbulent jets: Implications for levee formation at river mouths.” J. Geophys. Res. Earth Surf., 118(3), 1908–1920.
MATLAB [Computer software]. Natick, MA, MathWorks.
Mullin, T., Shipton, S., and Tavener, S. J. (2003). “Flow in a symmetric channel with an expanded section.” Fluid Dyn. Res., 33(5–6), 433–452.
Oca, J., and Masaló, I. (2007). “Design criteria for rotating flow cells in rectangular aquaculture tanks.” Aquacult. Eng., 36(1), 36–44.
Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M., and Dewals, B. (2013). “Experimental and numerical investigation of meandering jets in shallow reservoir: Potential impacts on deposit patterns.” Two-phase modelling for sediment dynamics in geophysical flows, K. D. Nguyen, M. Benoit, S. Guillou, N. Sheibani, J. G. Philipps, and D. Pham Van Bang, eds., SHF-EDF R&D, Chatou, France.
Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M., and Dewals, B. (2014a). “Experimental investigation of meandering jets in shallow reservoir.” Environ. Fluid Mech., 14(3), 699–710.
Peltier, Y., Erpicum, S., Archambeau, P., Pirotton, M., and Dewals, B. (2014b). “Meandering jets in shallow rectangular reservoirs: POD analysis and identification of coherent structures.” Exp. Fluids, 55(6), 1–16.
Peng, Y., Zhou, J. G., and Burrows, R. (2011). “Modeling free-surface flow in rectangular shallow basins by using lattice Boltzmann method.” J. Hydraul. Eng., 1680–1685.
Perrin, R., et al. (2007). “Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD.” Exp. Fluids, 43(2–3), 341–355.
Rempfer, D., and Fasel, H. F. (1994). “Evolution of three-dimensional coherent structures in a flat-plate boundary layer.” J. Fluid Mech., 260, 351–375.
Roache, P. J. (1994). “Perspective: A method for uniform reporting of grid refinement studies.” J. Fluids Eng., 116(3), 405–413.
Rowland, J. C., Stacey, M. T., and Dietrich, W. E. (2009). “Turbulent characteristics of a shallow wall-bounded plane jet: Experimental implications for river mouth hydrodynamics.” J. Fluid Mech., 627, 423–449.
Sirovich, L. (1987). “Turbulence and the dynamics of coherent structures. Part I: coherent structures.” Q. Appl. Math., 45(3), 561–571.
Stovin, V. R., and Saul, A. J. (2000). “Computational fluid dynamics and the design of sewage storage chambers.” J. Chartered Inst. Water Environ. Manage., 14(2), 103–110.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 141 • Issue 6 • June 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 20, 2014
Accepted: Jan 9, 2015
Published online: Feb 17, 2015
Published in print: Jun 1, 2015
Discussion open until: Jul 17, 2015
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.