Interaction of large amplitude regular waves with linear shear current

Wave–current interaction plays a critical role in ocean and coastal dynamics and affects offshore platform design and ship navigation safety, particularly under large amplitude conditions. This study analyzes the interaction between regular waves of large amplitude and linear shear currents using the stream function theory. The numerical solutions are obtained with the Newton–Raphson method, and the wave profiles, velocity fields, streamlines, and particle trajectories under various wave–current interaction conditions are investigated. The numerical results are first validated against existing experimental and numerical data. The coupled wave–current characteristics are then analyzed under following shear current conditions by considering waves of largest possible amplitude before breaking. Subsequently, a corresponding analysis of the wave characteristics is carried out under opposing linear shear current conditions. The results demonstrate that the presence of shear current alters the encounter periods of fluid particle trajectories at different vertical positions. Finally, the study investigates the effects of linear shear currents with varying velocity gradients (representing different vorticity intensities) on the profiles and associated characteristics of waves at maximum wave height. It is observed that increasing vorticity enhances streamline curvature near the bed under the wave crest. It also changes particle trajectories from extended following curves to opposing spirals.