Hostname: page-component-76c49bb84f-lvrpm Total loading time: 0 Render date: 2025-07-12T12:49:36.298Z Has data issue: false hasContentIssue false
  • English
  • Français

On satisfying the radiation condition in free-surface flows

Published online by Cambridge University Press:  10 April 2009

B. J. BINDER ,
J.-M. VANDEN-BROECK  and
F. DIAS
B. J. BINDER
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, South Australia, 5005, Australia
J.-M. VANDEN-BROECK*
Affiliation:
Department of Mathematics, University College London, London WC1E 6BT, UK
F. DIAS
Affiliation:
CMLA, ENS Cachan, CNRS, PRES UniverSud, 61 Av. President Wilson, F-94230 Cachan, France
*
†Email address for correspondence: broeck@math.ucl.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Binder & Vanden-Broeck (2005) showed there are no subcritical or critical solutions satisfying the radiation condition for steady flows past a flat plate. By using a weakly nonlinear analysis, it is shown that such flows exist for a curved plate. Fully nonlinear solutions are computed by a boundary integral equation method, and new nonlinear solutions for supercritical and generalized critical flows past a curved plate are presented.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 624 , 10 April 2009 , pp. 179 - 189
Copyright
Copyright © Cambridge University Press 2009

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Asavanant, J. & Vanden-Broeck, J.-M. 1994 Free-surface flows past a surface-piercing object of finite length. J. Fluid Mech. 273, 109–124.CrossRefGoogle Scholar
Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. 2005 Forced solitary waves and fronts past submerged obstacles. Chaos 15, 037106.Google ScholarPubMed
Binder, B. J., Dias, F. & Vanden-Broeck, J.-M. 2006 Steady free-surface flow past an uneven channel bottom. Theor. Comp. Fluid Dyn. 20, 125–144.CrossRefGoogle Scholar
Binder, B. J. & Vanden-Broeck, J.-M. 2005 Free surface flows past surfboards and sluice gates. Eur. J. Appl. Math. 16, 601–619.CrossRefGoogle Scholar
Binder, B. J. & Vanden-Broeck, J.-M. 2007 The effect of disturbances on the flow under a sluice gate and past an inclined plate. J. Fluid Mech. 576, 475–490.CrossRefGoogle Scholar
Budden, P. J. & Norbury, J. 1977 Sluice-gate problems with gravity. Math. Proc. Camb. Phil. Soc. 81, 157–177.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 2002 Generalized critical free-surface flows. J. Engng Math. 42, 291–301.CrossRefGoogle Scholar
Dias, F. & Vanden-Broeck, J.-M. 2004 Trapped waves between submerged obstacles. J. Fluid Mech. 509, 93–102.CrossRefGoogle Scholar
Fridman, G. M. & Tuck, E. O. 2006 Two-dimensional finite-depth planing hydrofoil under gravity. Proc. Third International Summer Scientific School, “High Speed Hydrodynamics and Numerical Simulation”, Kemerovo, Russia.Google Scholar
Forbes, L.-K. 1988 Critical free-surface flow over a semi-circular obstruction. J. Engng Math. 22, 3–13.CrossRefGoogle Scholar
King, A. C. & Bloor, M. I. G. 1987 Free-surface flow over a step. J. Fluid Mech. 182, 193–208.CrossRefGoogle 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. Math. 53, 701–719.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. 1997 Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 330, 339–347.CrossRefGoogle Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1989 Surfing on solitary waves. J. Fluid Mech. 198, 115–125.CrossRefGoogle Scholar