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A note on waveless subcritical flow past symmetric bottom topography

Published online by Cambridge University Press:  26 October 2016

R. J. HOLMES  and
G. C. HOCKING
R. J. HOLMES
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Western Australia, Australia email: rachel.holmes.22@gmail.com, G.Hocking@murdoch.edu.au
G. C. HOCKING
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Western Australia, Australia email: rachel.holmes.22@gmail.com, G.Hocking@murdoch.edu.au
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Abstract

This paper re-examines the problem of the flow of a fluid of finite depth over two Gaussian-shaped obstructions on the stream bed. A weakly nonlinear analysis in the form of the Korteweg–de Vries equation is used to compare with the results of the fully nonlinear problem. The main focus is to find waveless subcritical solutions, and contours showing the obstruction height and separation values that result in waveless solutions are found for different Froude numbers and different obstruction widths.

Keywords

Stream flowfree-surface flowwater wavespotential flow
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 4 , August 2017 , pp. 562 - 575
Copyright
Copyright © Cambridge University Press 2016 

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References

[1] Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. (2005) Forced solitary waves and fronts past submerged obstacles. Chaos 15, 037106-1–037106-13.CrossRefGoogle ScholarPubMed
[2] Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. (2008) Influence of rapid changes on free surface flows. IMA J. Appl. Math. 73, 254–273.CrossRefGoogle Scholar
[3] Choi, J. W., An, D., Lim, C. & Park, S. (2003) Symmetric surface waves over a bump. J. Korean Math. Soc. 40, 1051–1060.CrossRefGoogle Scholar
[4] Dias, F. & Vanden-Broeck, J.-M. (1989) Open channel flows with submerged obstructions. J. Fluid Mech. 206, 155–170.CrossRefGoogle Scholar
[5] Dias, F. & Vanden-Broeck, J.-M. (2002) Generalised critical free surface flows. J. Eng. Math. 42, 291–301.CrossRefGoogle Scholar
[6] Dias, F. & Vanden-Broeck, J.-M. (2002) Steady two-layer flows over an obstacle. Phil. Trans. R. Soc. Lond. A 360, 2137–2154.CrossRefGoogle ScholarPubMed
[7] Dias, F. & Vanden-Broeck, J.-M. (2004) Trapped waves between submerged obstacles. J. Fluid Mech. 509, 93–102.CrossRefGoogle Scholar
[8] Forbes, L. K. (1982) Non-linear, drag-free flow over a submerged semi-elliptical body. J. Eng. Math. 16, 171–180.CrossRefGoogle Scholar
[9] Forbes, L. K. (1988) Critical free-surface flow over a semi-circular obstruction. J. Eng. Math. 22, 3–13.CrossRefGoogle Scholar
[10] Forbes, L. K. & Hocking, G. C. (2007) An intrusion layer in stationary incompressible fluids: Part 2: A solitary wave. Eur. J. Appl. Math. 17, 577–595.CrossRefGoogle Scholar
[11] Hocking, G. C., Holmes, R. J. & Forbes, L. K. (2013) A note on waveless subcritical flow past a submerged semi-ellipse. J. Eng. Math. 81 1–8.CrossRefGoogle Scholar
[12] Holmes, R. J., Hocking, G.C., Forbes, L. K. & Baillard, N. Y. (2013) Waveless subcritical flow past symmetric bottom topography. Eur. J. Appl. Math. 24, 213–230.CrossRefGoogle Scholar
[13] Lamb, H. (1932) Hydrodynamics, 6th ed., Cambridge University Press, Cambridge.Google Scholar
[14] Lustri, C. J., McCue, S. W. & Binder, B. J. (2012) Free surface flow past topography: a beyond-all-orders approach. Eur. J. Appl. Math. 23, 441–467.CrossRefGoogle Scholar
[15] Pratt, L. J. (1984) On nonlinear flow with multiple obstructions. J. Atmos. Sci. 41, 1214–1225.2.0.CO;2>CrossRefGoogle Scholar
[16] 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. Math. 53, 701–719.CrossRefGoogle Scholar
[17] Sivakumaran, N. S., Tingsanchali, T. & Hosking, R. J. (1983) Steady shallow flow over curved beds. J. Fluid Mech. 128, 469–487.CrossRefGoogle Scholar