Abstract
New free-surface flows past a semi-infinite ‘step’ in the bottom of a channel are considered. Surface tension is neglected but gravity is included in the dynamic boundary condition. Fully nonlinear solutions are computed by boundary integral equation methods. Additional weakly nonlinear solutions are derived analytically. A thorough analysis of the weakly nonlinear problem provides a systematic approach to identify all the possible types of solutions and the number of independent parameters.
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Binder B.J., Vanden-Broeck J.-M. (2005). Free surface flows past surfboards and sluice gates. Eur. J. Appl. Math. 16:601–619
Binder B.J., Vanden-Broeck, J.-M., Dias, F.: Forced solitary waves and fronts past submerged obstacles. Chaos 15, 037106-1–13 (2005)
Dias F., Vanden-Broeck J.-M. (1989). Open channel flows with submerged obstructions. J. Fluid Mech. 206:155–170
Dias F., Vanden-Broeck J.-M. (2002). Generalised critical free-surface flows. J. Eng. Math. 42:291–301
Dias F., Vanden-Broeck J.-M. (2004). Trapped waves between submerged obstacles. J. Fluid Mech. 509:93–102
Forbes L.-K. (1988). Critical free-surface flow over a semi-circular obstruction. J. Eng. Math. 22:3–13
Grimshaw R.H.J., Smyth N. (1986). Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169:429–464
King A.C., Bloor M.I.G. (1987). Free-surface flow over a step. J. Fluid Mech. 182:193–208
King A.C., Bloor M.I.G. (1990). Free-surface flow of a stream obstructed by an arbitrary bed topography. Q. J. Mech. Appl. Math. 43:87–106
Lee S.-J., Yates G.T., Wu T.Y. (1989). Experiments and analysis of upstream-advancing solitary waves generated by moving disturbances. J. Fluid Mech. 199:569–593
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
Shen S.S., Gong L. (1993). Solitary waves on a shelf. Phys. Fluids A 5:1071–1073
Smyth N.F. (1987). Modulation theory solution for resonant flow over topography. Proc. R. Soc. Lond. A 409:79–97
Vanden-Broeck J.-M. (1996). Numerical calculations of the free-surface flow under a sluice gate. J. Fluid Mech. 330:339–347
Yasuda T., Mutsuda H., Mizutani N. (1997). Kinematics of overturning solitary waves and their relations to breaker types. Coast. Eng. 29:317–346
Zhang Y., Zhu S. (1997). Subcritical, transcritical and supercritical flows over a step. J. Fluid Mech. 333:257–271
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Binder, B.J., Dias, F. & Vanden-Broeck, J.M. Steady Free-surface Flow Past an Uneven Channel Bottom. Theoret. Comput. Fluid Dynamics 20, 125–144 (2006). https://doi.org/10.1007/s00162-006-0017-y
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DOI: https://doi.org/10.1007/s00162-006-0017-y