Direct spectral-inversion reconstruction of focused waves on sheared currents for cylinder-load prediction

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.