Zaibin Lin

Predicting the load of a focused wave group on a cylinder in a vertically sheared current requires the incident field to reproduce the focal crest, the current-dependent propagation, and the subsurface kinematics together. Existing wave-on-current focusing relies on four-phase harmonic decomposition, which needs a linearized target spectrum and four realizations per correction. We develop a direct spectral-inversion iteration for reduced-data cases with only an event-centred free-surface segment at one gauge. The target and simulated segments are projected onto a common complex spectrum, and inlet amplitude and phase are corrected using the amplitude ratio and wrapped phase error, with one numerical realization per iteration. A four-step procedure assesses current maintenance, focal-event reconstruction, unfitted subsurface velocities with two- to three-dimensional transfer, and the inertia-dominated cylinder load under no, adverse, and following currents. In the no-current example, five iterations reduce the focus-point root mean square error from 6.4599×10−3 to 4.2769×10−3 m and raise the correlation from 0.9679 to 0.9857. Peak-load errors remain within 8.79%, with focus-window root mean square errors of 1.82–3.19 N. The inlet phase corrections follow the shear-modified dispersion, with opposite signs for adverse and following currents. The only substantial discrepancy, the following-current post-focus force, is associated with an amplitude-dominated residual in the primary and sum-frequency bands that this current carries into the post-focus window, where it acts through pressure; viscous and difference-frequency contributions are negligible. Additional no-current Joint-North-Sea-Wave-Project and Pierson–Moskowitz cases indicate portability to other unimodal spectra. Control of post-focus higher-harmonic content still requires phase decomposition.

Wave overtopping over coastal structures involves highly transient shallow flows characterized by strong free-surface deformation and intense turbulence generation. Although considerable research has focused on overtopping discharge and volume, the detailed kinematics and turbulence characteristics of overtopping flows remain insufficiently understood. In the present study, a two-phase wall-modeled large-eddy simulation approach implemented in OpenFOAM is applied to investigate wave overtopping flow over a seawall under regular wave conditions. The numerical model is rigorously validated against laboratory measurements, including overtopping layer thickness and high-speed particle image velocimetry velocity fields, demonstrating good agreement in terms of free-surface evolution and overtopping flow kinematics. The results reveal that the overtopping flow is strongly phase-dependent and dominated by the streamwise velocity component, with pronounced turbulent fluctuations concentrated near the free surface and the bed. The overtopping flow remains supercritical (Fr>1.5) near the leading edge of the seawall crest, while the Froude number gradually decreases downstream due to bed friction and turbulent energy dissipation. The bed shear stress is highly transient, with instantaneous peak values exceeding the time-averaged values by a factor of 3–7. The subgrid-scale turbulent kinetic energy (TKE) accounts for only 6.05% of the total TKE within the resolved flow domain, confirming that the dominant turbulent structures are well captured by the present mesh resolution. The TKE budget further reveals that production and turbulent transport are the dominant terms during the active overtopping phase, with peak production concentrated near the leading edge and within the bottom boundary layer.