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Interactions of currents and weakly nonlinear water waves in shallow water

Published online by Cambridge University Press:  26 April 2006

Sung B. Yoon  and
Philip L.-F. Liu
Sung B. Yoon
Affiliation:
Joseph DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853 USA Present address: Korea Power Engineering Co. Inc., P.O. Box 631, Youngdong, Seoul, Korea.
Philip L.-F. Liu
Affiliation:
Joseph DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853 USA
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Abstract

Two-dimensional Boussinesq-type depth-averaged equations are derived for describing the interactions of weakly nonlinear shallow-water waves with slowly varying topography and currents. The current velocity varies appreciably within a characteristic wavelength. The effects of vorticity in the current field are considered. The wave field is decomposed into Fourier time harmonics. A set of evolution equations for the wave amplitude functions of different harmonics is derived by adopting the parabolic approximation. Numerical solutions are obtained for shallow-water waves propagating over rip currents on a plane beach and an isolated vortex ring. Numerical results show that the wave diffraction and nonlinearity are important in the examples considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 205 , August 1989 , pp. 397 - 419
Copyright
© 1989 Cambridge University Press

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