Abstract
The interaction of a current-free plane surface wave train of fixed frequency and a uniform wave-free current normal to the wave crests in the same or opposite direction to wave propagation is described. Neglecting dissipation, the combined field after the encounter is assumed stable, uniform, steady and irrotational. The parameters describing the wave-current field generated by the interaction, namely the wave height, wave length, stream current and water depth are calculated numerically by solving a set of nonlinear equations. These equations are obtained on satisfying, to second order, conservation of mean mass, momentum and energy flux, as well as a dispersion relation on the free surface of the after-encounter field. Possible solutions are identified a posteriori. Contrary to other approaches the additional contribution to the change in the mean value of the current and mean water depth is not neglected in this work. Numerical results are presented which illustrate the changes in the wave length, wave height, current speed and water depth. A comparison with the numerical and experimental results reported by G.P. Thomas [ J. Fluid Mech. 110, 457–474)] is also provided.
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