Citation

Yoon SB, Liu PLF. Journal of Fluid Mechanics 1989; 205(-1): 397.

Copyright

(Copyright © 1989, Cambridge University Press)

DOI

10.1017/S0022112089002089

PMID

unavailable

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.