Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-18T18:41:03.703Z Has data issue: false hasContentIssue false
  • English
  • Français

Open channel flows with submerged obstructions

Published online by Cambridge University Press:  26 April 2006

Frrédéric Dias  and
Jean-Marc Vanden-Broeck
Frrédéric Dias
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA
Jean-Marc Vanden-Broeck
Affiliation:
Department of Mathematics and Center for the Mathematical Sciences, University of Wisconsin-Madison, Madison, WI 53705, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Free-surface flows past a submerged triangular obstacle at the bottom of a channel are considered. The flow is assumed to be steady, two-dimensional and irrotational; the fluid is treated as inviseid and incompressible and gravity is taken into account. The problem is solved numerically by series truncation. It is shown that there are solutions for which the flow is suberitical upstream and supercritical downstream and other flows for which the flow is supercritical both upstream and downstream. The latter flows have limiting configurations with a stagnation point on the free surface with a 120° angle at it. It is found that solutions exist for triangular obstacles of arbitrary size. Local solutions are constructed to describe the flow near the apex when the height of the triangular obstacle is infinite.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 206 , September 1989 , pp. 155 - 170
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benjamin, T. B. 1966 J. Fluid Mech. 25, 241.
Binnie, A. M. 1952 Q. J. Mech. Appl. Maths 5, 395.
Birkhoff, G. & Zarantonello, E. H. 1957 Jets, Wakes and Cavities. Academic.
Brodetsky, S. 1923 Proc. R. Soc. Lond. A 102, 542
Dias, F., Keller, J. B. & Vanden-Broeck, J.-M. 1988 Phys. Fluids 31, 2071.
Forbes, L. K. 1981 J. Engng Maths 15, 287.
Forbes, L. K. 1988 J. Engng Maths 22, 3.
Forbes, L. K. & Schwartz, L. W. 1982 J. Fluid Mech. 114, 299.
Havelock, T. H. 1919 Proc. R. Soc. Lond. A 95, 38
Hunter, J. K. & Vanden-Broeck, J.-M. 1983 J. Fluid Mech. 136, 63.
Keller, J. B. 1957 J. Appl. Phys. 28, 859.
Keller, J. B. & Geer, J. 1973 J. Fluid Mech. 59, 417.
Lamb, H. 1945 Hydrodynamics. Dover.
Vanden-Broeck, J.-M. 1984 Phys. Fluids 27, 2604.
Vanden-Broeck, J.-M. 1986 Phys. Fluids 29, 3084.
Vanden-Broeck, J.-M. 1987 Phys. Fluids 30, 2315.
Vanden-Broeck, J.-M. & Keller, J. B. 1986 Phys. Fluids 29, 3958.
Vanden-Broeck, J.-M. & Keller, J. B. 1987 J. Fluid Mech. 176, 283.