@article{ref1,
title="Interactions of currents and weakly nonlinear water waves in shallow water",
journal="Journal of fluid mechanics",
year="1989",
author="Yoon, Sung B. and Liu, Philip L.-F.",
volume="205",
number="-1",
pages="397-397",
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.<p />",
language="",
issn="0022-1120",
doi="10.1017/S0022112089002089",
url="http://dx.doi.org/10.1017/S0022112089002089"
}