Interaction of Incoming Waves With a Steady Intake-Pipe Flow

A linear ray theory is developed to study the interaction of water waves with a steady intake-pipe flow in deep water. The wave-current interaction model is based on the assumption that the current field is slowly varying in comparison with the wave field. With the use of the dispersion relation, an equation is derived for the wave number that also depends on the current velocity field. Imposing the condition of irrotationality of wave number, a nonlinear set of characteristic equations of oblique waves is obtained and solved numerically to determine the rays. The current field is generated by solving the 3-D potential problem of specified intake normal-velocity at the entrance of a horizontal, circular pipe of semi-infinite length, situated on the still-water level, by using the axisymmetric Rankine source method. It appears that the velocity-potential solution of the intake-pipe flow problem presented here does not exist in the literature. Finally, the local wave amplitudes are calculated through the conservation of wave-action equation to predict the focusing of wave energy.