Extended Theory of Hydraulic Hysteresis in Open-Channel Flow
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 9
Abstract
The occurrence of hysteresis in a supercritical, open-channel flow approaching an obstacle has been recognized and investigated both experimentally and theoretically over the last few decades. However, the available theory and experimental investigations in the literature do not include the case when subcritical flow, controlled from downstream, can establish across the obstacle. The present work fills this gap by proposing a new theory that includes this occurrence and shows that two different steady flow states can establish for the same obstacle geometry and flow conditions—one with supercritical to subcritical transition far downstream from the obstacle, and the other with supercritical to subcritical transition far upstream from the obstacle. The proposed, more general theory includes the existing theory as a special case. Finally, two specific examples are illustrated and discussed, i.e., the case of flow over a raised bed hump, and the case of flow through a channel contraction.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abecasis, F. M., and Quintela, A. C. (1964). “Hysteresis in steady free-surface flow.” Water Power, 4, 147–151.
Akers, B., and Bokhove, O. (2008). “Hydraulic flow through a channel contraction: Multiple steady states.” Phys. Fluids, 20(5), 056601.
Austria, P. (1987). “Catastrophe model for the forced hydraulic jump.” J. Hydraul. Res., 25(3), 269–280.
Baines, P. (1984). “A unified description of two-layer flow over topography.” J. Fluid Mech., 146, 127–167.
Baines, P., and Whitehead, J. A. (2003). “On multiple states in single-layer flows.” Phys. Fluids, 15(2), 298–307.
Castro-Orgaz, O., and Hager, W. (2009). “Classical hydraulic jump: Basic flow features.” J. Hydraul. Res., 47(6), 744–754.
Catella, M., and Bechi, G. (2006). “Conservative schemes for flow numerical modeling of submerged bridges.” RiverFlow2006: Proc., Int. Conf. on Fluvial Hydraulics, Vol. 1, R. Ferreira, E. Alves, J. Leal, and A. Cardoso, eds., Taylor & Francis, London, 747–755.
Cozzolino, L., Cimorelli, L., Covelli, C., Della Morte, R., and Pianese, D. (2015). “The analytic solution of the shallow-water equations with partially open sluice-gates: The dam-break problem.” Adv. Water Resour., 80, 90–102.
Defina, A., and Susin, F. M. (2003). “Hysteretic behavior of the flow under a vertical sluice gate.” Phys. Fluids, 15(9), 2541–2548.
Defina, A., and Susin, F. M. (2006). “Multiple states in open channel flow.” Vorticity and turbulence effects in fluid structures interactions—Advances in fluid mechanics, M. Brocchini and F. Trivellato, eds., Wessex Insitute of Technology Press, Southampton, U.K., 105–130.
Defina, A., Susin, F. M., and Viero, D. P. (2008). “Bed friction effects on the stability of a stationary hydraulic jump in a rectangular upward sloping channel.” Phys. Fluids, 20(3), 036601.
Defina, A., and Viero, D. P. (2010). “Open channel flow through a linear contraction.” Phys. Fluids, 22(3), 036602.
Henderson, F. M. (1966). Open-channel flow, MacMillan, New York.
Jaafar, H., and Merkley, G. (2010). “High-resolution method for modeling hydraulic regime changes at canal gate structures.” J. Irrig. Drain. Eng., 795–808.
Lawrence, G. A. (1987). “Steady flow over an obstacle.” J. Hydraul. Eng., 981–991.
Long, D., Rajaratnam, N., Steffler, P. M., and Smy, P. R. (1991). “Structure of flow in hydraulic jumps.” J. Hydraul. Res., 29(2), 207–218.
Mehrotra, S. C. (1974). “Hysteresis effect in one- and two-fluid systems.” Proc., V Australian Conf. on Hydraulics and Fluid Mechanics, Univ. of Canterbury, Christchurch, New Zealand, 452–461.
Mossa, M. (1999). “On the oscillating characteristics of hydraulic jumps.” J. Hydraul. Res., 37(4), 541–558.
Mossa, M., Petrillo, A., and Chanson, H. (2003). “Tailwater level effects on flow conditions at an abrupt drop.” J. Hydraul. Res., 41(1), 39–51.
Muskatirovic, D., and Batinic, D. (1977). “The influence of abrupt change of channel geometry on hydraulic regime characteristics.” Proc., 17th Int. Association for Hydraulic Research Congress, Univ. of Canterbury, Baden-Baden, Germany, 397–404.
Pratt, L. (1983). “A note on nonlinear flow over obstacles.” Geophys. Astrophys. Fluid Dyn., 24(1), 63–68.
Valiani, A., and Caleffi, V. (2008). “Depth-energy and depth-force relationships in open channel flows: Analytical findings.” Adv. Water Resour., 31(3), 447–454.
Viero, D., D’Alpaos, A., Carniello, L., and Defina, A. (2013a). “Mathematical modeling of flooding due to river bank failure.” Adv. Water Resour., 59, 82–94.
Viero, D. P., Susin, F. M., and Defina, A. (2013b). “A note on weak shock wave reflection.” Shock Waves, 23(5), 505–511.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Oct 18, 2016
Accepted: Mar 6, 2017
Published online: Jun 1, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 1, 2017
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.