Applicability of Kinematic, Diffusion, and Quasi-Steady Dynamic Wave Models to Shallow Mud Flows
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 5
Abstract
Unsteady shallow-layer flows may be described through full dynamic models or using simplified momentum equations, based on kinematic, diffusion, and quasi-steady approximations, which guarantee a reduction of the computational effort. This paper aims to investigate through linear analysis the applicability range of simplified shallow-wave models with special concern to unsteady flows of mud. Considering a three-equation depth-integrated Herschel-Bulkley model, the applicability of the approximated wave models is discussed comparing the propagation characteristics of a small perturbation of an initial steady uniform flow as predicted by the simplified models with those of the full dynamic model. Based on this comparison, applicability criteria for the different wave approximations for mud flows of Herschel-Bulkley fluids, which account for the effects of the rheological parameters, are derived. The results show that accounting for the fluid rheology is mandatory for the choice of an appropriate simplified model.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ancey, C., Andreini, N., and Epely-Chauvin, G. (2012). “Viscoplastic dambreak waves: Review of simple computational approaches and comparison with experiments.” Adv. Water Resour., 48, 79–91.
Arattano, M., and Savage, W. Z. (1994). “Modelling debris flow as kinematic waves.” Bull. Int. Assoc. Eng. Geol., 49(1), 3–13.
Coussot, P. (1994). “Steady, laminar, flow of concentrated mud suspensions in open channel.” J. Hydraul. Res., 32(4), 535–559.
Coussot, P. (1997). Mudflow rheology and dynamics. Balkema, Leiden, The Netherlands.
Dent, J. D., and Lang, T. E. (1983). “A biviscous modified Bingham model of snow avalanche motion.” Ann. Glaciol., 4, 42–46.
Di Cristo, C., Iervolino, M., and Vacca, A. (2012a). “Discussion of ‘Analysis of dynamic wave model for unsteady flow in an open channel.’” J. Hydraul. Eng., 915–917.
Di Cristo, C., Iervolino, M., and Vacca, A. (2012b). “Green’s function of the linearized Saint–Venant equations in laminar and turbulent flows.” Acta Geophys., 60(1), 173–190.
Di Cristo, C., Iervolino, M., and Vacca, A. (2013a). “Boundary conditions effect on linearized mud-flow shallow model.” Acta Geophys., 61(3), 649–667.
Di Cristo, C., Iervolino, M., and Vacca, A. (2013b). “Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane.” Appl. Math. Sci., 7(33), 1623–1641.
Di Cristo, C., Iervolino, M., and Vacca, A. (2013c). “On the applicability of minimum channel length criterion for roll-waves in mud-flows.” J. Hydrol. Hydromech., 61(4), 286–292.
Di Cristo, C., Iervolino, M., and Vacca, A. (2013d). “Waves dynamics in a linearized mud-flow shallow model.” Appl. Math. Sci., 7(8), 377–393.
Di Cristo, C., Iervolino, M., Vacca, A., and Zanuttigh, B. (2008). “Minimum channel length for roll-wave generation.” J. Hydraul. Res., 46(1), 73–79.
Di Cristo, C., Iervolino, M., Vacca, A., and Zanuttigh, B. (2010). “Influence of relative roughness and Reynolds number on the roll-waves spatial evolution.” J. Hydraul. Eng., 24–33.
Di Cristo, C., and Vacca, A. (2005). “On the convective nature of roll waves instability.” J. Appl. Math., 2005(3), 259–271.
Dooge, J. C. I., and Napiorkowski, J. J. (1987). “Applicability of diffusion analogy in flood routing.” Acta Geophys. Pol., 35(1), 65–75.
Ferrick, M. G. (1985). “Analysis of river wave types.” Water Resour. Res., 21(2), 209–220.
Fread, D. L. (1983). “Applicability criteria for kinematic and diffusion routing models.” HRL 183, Hydrologic Research Laboratory, National Weather Service, National Oceanic and Atmospheric Administration, Silver Spring, MD.
Greco, M., Iervolino, M., Leopardi, A., and Vacca, A. (2012). “A two-phase model for fast geomorphic shallow flows.” Int. J. Sediment Res., 27(4), 409–425.
Huang, X., and Garcia, M. H. (1997). “A perturbation solution for Bingham-plastic mudflows.” J. Hydraul. Eng., 986–994.
Huang, X., and Garcia, M. H. (1998). “A Herschel-Bulkley model for mud flow down a slope.” J. Fluid Mech., 374, 305–333.
Iverson, R. M. (1997). “The physics of debris flows.” Rev. Geophys., 35(3), 245–296.
Julien, P. Y., and Hartley, D. M. (1986). “Formation of roll waves in laminar sheet flow.” J. Hydraul. Res., 24(1), 5–17.
Lamberti, P., and Pilati, S. (1996). “Flood propagation models for real-time forecasting.” J. Hydrol., 175(1–4), 239–265.
Litrico, X., and Fromion, V. (2004). “Simplified modeling of irrigation canals for controller design.” J. Irrig. Drain. Eng., 373–383.
Liu, K. F., and Mei, C. C. (1989). “Slow spreading of a sheet of Bingham fluid on an inclined plane.” J. Fluid Mech., 207, 505–529.
Menéndez, A. N., and Norscini, R. (1982). “Spectrum of shallow water waves.” J. Hydr. Div., 108(1), 75–94.
Montuori, C. (1963). “Discussion of ‘Stability aspects of flow in open channels.’” J. Hydr. Div., 89(HY4), 264–273.
Moramarco, T., Pandolfo, C., and Singh, V. P. (2008). “Accuracy of kinematic wave and diffusion wave approximations for flood routing. I: Steady analysis.” J. Hydrol. Eng., 1078–1088.
Moramarco, T., and Singh, V. P. (2000). “A practical method for analysis or river waves and for kinematic wave routing in natural channel networks.” Hydrol. Process., 14(1), 51–62.
Moramarco, T., and Singh, V. P. (2002). “Accuracy of kinematic wave and diffusion wave for spatial-varying rainfall excess over a plane.” Hydrol. Process., 16(17), 3419–3435.
Moussa, R., and Bocquillon, C. (1996). “Criteria for the choice of flood routing methods in natural channels.” J. Hydrol., 186(1–4), 1–30.
O’Brien, J. S., Julien, P. Y., and Fullerton, W. T. (1993). “Two-dimensional water flood and mudflow simulation.” J. Hydrol. Eng., 244–261.
Pascal, J. P. (1999). “Linear stability of fluid flow down a porous inclined plane.” J. Phys. D, 32(4), 417–422.
Pitman, E. B., and Le, L. (2005). “A two-fluid model for avalanche and debris flows.” Phil. Trans. R. Soc. A, 363(1832), 1573–1601.
Ponce, V. M., Li, R. M., and Simons, D. B. (1978). “Applicability of kinematic and diffusion models.” J. Hydr. Div., 104(HY3), 353–360.
Ponce, V. M., and Simons, D. B. (1977). “Shallow water propagation in open channel flow.” J. Hydr. Div., 103(HY12), 1461–1476.
Ridolfi, L., Porporato, A., and Revelli, R. (2006). “Green’s function of the linearized de Saint-Venant equations.” J. Eng. Mech., 125–132.
Singh, V. P. (1994). “Accuracy of kinematic-wave and diffusion-wave approximations for space-independent flows.” Hydrol. Process., 8(1), 45–62.
Singh, V. P. (1996). Kinematic wave modeling in water resource-surface water hydrology. Wiley, New York.
Singh, V. P., and Aravamuthan, Y. (1995). “Errors of kinematic-wave and diffusion-wave approximations for time-independent flows.” Water Resour. Manage., 9(3), 175–202.
Tsai, C. W.-S. (2003). “Applicability of kinematic, noninertia, and quasi-steady dynamic wave models to unsteady flow routing.” J. Hydrol. Eng., 613–626.
Venutelli, M. (2011). “Analysis of dynamic wave model for unsteady flow in an open channel.” J. Hydrol. Eng., 1072–1078.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 20, 2013
Accepted: Jul 10, 2013
Published online: Jul 12, 2013
Discussion open until: Dec 12, 2013
Published in print: May 1, 2014
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.