Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-15T18:33:33.678Z Has data issue: false hasContentIssue false
  • English
  • Français

Weir flows and waterfalls

Published online by Cambridge University Press:  26 April 2006

Frédéric Dias  and
E. O. Tuck
Frédéric Dias
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA Present address: Université de Nice, INLN, UMR CNRS 129, Parc Valrose, 06034 Nice cedex, France.
E. O. Tuck
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, S.A. 5001, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

Two-dimensional free-surface flows, which are uniform far upstream in a channel of finite depth that ends suddenly, are computed numerically. The ending is in the form of a vertical wall, which may force the flow upward before it falls down forever as a jet under the effect of gravity. Both subcritical and supercritical solutions are presented. The subcritical solutions are a one-parameter family of solutions, the single parameter being the ratio between the height of the wall and the height of the uniform flow far upstream. On the other hand, the supercritical solutions are a two-parameter family of solutions, the second parameter being the Froude number. Moreover, for some combinations of the parameters, it is shown that the solution is not unique.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 525 - 539
Copyright
© 1991 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

Chow, W. L. & Han, T. 1979 Inviscid solution for the problem of free overfall. Trans. ASME E: J. Appl. Mech. 46, 1–5.Google Scholar
Clarke, N. S. 1965 On two-dimensional inviscid flow in a waterfall. J. Fluid Mech. 22, 359–369.Google Scholar
Dias, F. & Christodoulides, P. 1991 Ideal jets falling under gravity. Phys. Fluids A(to appear).Google Scholar
Dias, F., Keller, J. B. & vanden-Broeck, J.-M. 1988 Flow over rectangular weirs. Phys. Fluids.31, 2071–2076.Google Scholar
Dias, F. & vanden-Broeck, J.-M. 1989 Open channel flows with submerged obstructions. J.Fluid Mech. 206, 155–170.Google Scholar
Elcrat, A. R. & Trefethen, L. N. 1986 Classical free-streamline flow over a polygonal obstacle. J. Comput. Appl. Maths 14, 251–265.Google Scholar
Goh, K. M. H. 1986 Numerical solution of quadratically non-linear boundary value problems using integral equation techniques, with application to nozzle and wall flows. Ph.D. dissertation, Dept. of Applied Mathematics, University of Adelaide.
Goh, M. K. & Tuck, E. O. 1985 Thick waterfalls from horizontal slots. J. Engng Maths 19, 341–349.Google Scholar
Smith, A. C. & Abd-El-Malek, M. B. 1983 Hilbert's method for numerical solution of flow from a uniform channel over a shelf. J. Engng Maths 17, 27–39.Google Scholar
Tuck, E. O. 1987 Efflux from a slit in a vertical wall. J. Fluid Mech. 176, 253–264.Google Scholar
Tuck, E. O. 1990 Ship-hydrodynamic free-surface problems without waves. Georg Weinblum Memorial Lecture, Berlin, November 1990.
Tuck, E. O. & vanden-Broeck, J.-M. 1985 Splashless bow flows in two dimensions? In Proc. 15th Symp. Naval Hydrodynamics, Hamburg, 1984, pp. 293–300. Washington, DC: National Academy Press.
vanden-Broeck, J.-M. & Keller, J. B. 1986 Pouring flows. Phys. Fluids 29, 3958–3961.Google Scholar
vanden-Broeck, J.-M. & Keller, J. B. 1987a Free surface flow due to a sink. J. Fluid Mech. 175, 109–117.Google Scholar
vanden-Broeck, J.-M. & Keller, J. B. 1987b Weir flows. J. Fluid Mech. 176, 283–293.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Handbuch der Physik, vol. IX (ed. S. FluUgge). Springer.