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The effect of disturbances on the flows under a sluice gate and past an inclined plate

Published online by Cambridge University Press:  28 March 2007

School of Mathematical Sciences, University of Adelaide, Adelaide 5005, South Australia
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK


Free surface potential flows past disturbances in a channel are considered. Three different types of disturbance are studied: (i) a submerged obstacle on the bottom of a channel; (ii) a pressure distribution on the free surface; and (iii) an obstruction in the free surface (e.g. a sluice gate or a flat plate). Surface tension is neglected, but gravity is included in the dynamic boundary condition. Fully nonlinear solutions are computed by boundary integral equation methods. In addition, weakly nonlinear solutions are derived. New solutions are found when several disturbances are present simultaneously. They are discovered through the weakly nonlinear analysis and confirmed by numerical computations for the fully nonlinear problem.

Copyright © Cambridge University Press 2007

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Asavanant, J. & Vanden-Broeck, J.-M. 1994 Free-surface flows past a surface-piercing object of finite length. J. Fluid. Mech. 273, 109124.CrossRefGoogle Scholar
Asavanant, J. & Vanden-Broeck, J.-M. 1996 Nonlinear free-surface flows emerging from vessels and flows under a sluice gate. J. Austcal. Math. Soc. 38, 6386.CrossRefGoogle Scholar
Benjamin, T. B. 1956 On the flow in channels when rigid obstacles are placed in the stream. J. Fluid Mech. 1, 227248.CrossRefGoogle Scholar
Binder, B. J. & Vanden-Broeck, J.-M. 2005 Free surface flows past surfboards and sluice gates. Eur. J. Appl. Maths 16, 601619.CrossRefGoogle Scholar
Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. 2005 Forced solitary waves and fronts past submerged obstacles. Chaos 15, 037106.CrossRefGoogle ScholarPubMed
Binnie, A. M. 1952 The flow of water under a sluice gate.Google Scholar
Chung, Y. K. 1972 Solution of flow under a sluice gates. ASCE J. Engng Mech. Div. 98, 121140.Google Scholar
Dias, F. & Vanden-Broeck, J.-M. 1989 Open channel flows with submerged obstructions. J. Fluid Mech. 206, 155170.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 2002 Generalized critical free-surface flows. J. Engng Maths 42, 291301.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 2004 Trapped waves between submerged obstacles. J. Fluid Mech. 509, 93102.CrossRefGoogle Scholar
Forbes, L.-K. 1981 On the resistance of a submerged semi-elliptical body. J. Engng Maths 15, 287298.CrossRefGoogle Scholar
Forbes, L.-K. 1988 Critical free-surface flow over a semi-circular obstruction. J. Engng Maths 22, 313.CrossRefGoogle Scholar
Forbes, L.-K. & Schwartz, L. W. 1982 Free-surface flow over a semicircular obstruction. J. Fluid Mech. 114, 299314.CrossRefGoogle Scholar
Frangmeier, D. D. & Strelkoff, T. S. 1968 Solution for gravity flow under a sluice gate. ASCE J. Engng Mech. Div. 94, 153176.Google Scholar
Lamb, H. 1945 Hydrodynamics, 6th edn, chap. 9. Dover.Google Scholar
Larock, B. E. 1969 Gravity-affected flow from planar sluice gate. ASCE J. Engng Mech. Div. 96, 12111226.Google Scholar
Shen, S. S.-P. 1995 On the accuracy of the stationary forced Korteweg–de Vries equation as a model equation for flows over a bump. Q. Appl. Maths 53, 701719.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. 1987 Free-surface flow over an obstruction in a channel. Phys. Fluids 30, 23152317.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. 1996 Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 330, 339347.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1989 Surfing on solitary waves. J. Fluid Mech. 198, 115125.CrossRefGoogle Scholar