Hostname: page-component-cc8bf7c57-xrnlw Total loading time: 0 Render date: 2024-12-10T18:34:55.870Z Has data issue: false hasContentIssue false

Fully nonlinear flow over successive obstacles: hydraulic fall and supercritical flows

Published online by Cambridge University Press:  17 February 2009

Shaun R. Belward
Affiliation:
Department of Mathematics and Statistics, James Cook University of North Queensland, Townsville, Queensland 4811, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the flow of an incompressible, inviscid and homogeneous fluid over two obstacles in succession. The flow is assumed irrotational and solutions are sought in which a hydraulic fall occurs over the first obstacle with supercritical flow over the second. The method used to solve the problem is capable of calculating flows over topography of any shape.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Belward, S. R. and Forbes, L. K., “Fully nonlinear two-layer flow over arbitrary topography”, J. Eng. Math. 27 (1993) 419432.CrossRefGoogle Scholar
[2]Belward, S. R. and Forbes, L. K., “Interfacial waves and hydraulic falls: some applications to atmospheric flows in the lee of mountains”, J. Eng. Math. 29 (1995) 161179.CrossRefGoogle Scholar
[3]Dias, F. and Vanden-Broeck, J.-M., “Open channel flow with submerged obstructions”, J. Fluid Mech. 206 (1989) 155170.CrossRefGoogle Scholar
[4]Forbes, L. K., “Non-linear, drag-free flow over a submerged semi-elliptical body”, J. Eng. Math. 16 (1982) 171180.CrossRefGoogle Scholar
[5]Forbes, L. K., “Critical free-surface flow over a semi-circular obstruction”, J. Eng. Math. 22 (1988) 313.CrossRefGoogle Scholar
[6]Forbes, L. K. and Belward, S. R., “Atmospheric solitary waves: some applications to the Morning Glory of the Gulf of Carpenteria”, J. Fluid Mech. 321 (1996) 137155.CrossRefGoogle Scholar
[7]Forbes, L. K. and Schwartz, L. W., “Free-surface flow over a semi-circular obstruction”, J. Fluid Mech. 114 (1982) 299314.CrossRefGoogle Scholar
[8]King, A. C. and Bloor, M. I. G., “Free surface flow of a stream obstructed by an arbitrary bed topography”, Quart. J. Mech. Appl. Math. 43 (1990) 87106.CrossRefGoogle Scholar
[9]Pratt, L. J., “On nonlinear flow with multiple obstructions”, J. Atmos. Sci. 41 (1984) 12141225.2.0.CO;2>CrossRefGoogle Scholar
[10]Read, W. W., Belward, S. R. and Higgins, P. J., “Iterative schemes for series solutions to Laplacian free boundary problems”, in Computational techniques and applications: CTAC95 (eds. May, R. L. and Easton, A. K.), (World Scientific, Singapore, 1996) 669676.Google Scholar