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Steady free-surface flow over spatially periodic topography

Published online by Cambridge University Press:  16 September 2015

B. J. Binder ,
M. G. Blyth  and
S. Balasuriya
B. J. Binder*
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
M. G. Blyth
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
S. Balasuriya
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
*
†Email address for correspondence: benjamin.binder@adelaide.edu.au
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Abstract

Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg–de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Waves/Free-surface Flows: Waves/Free-surface Flows

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Type
Rapids
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , R3
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Copyright
© 2015 Cambridge University Press 

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