A numerical study of nonlinear periodic waves generated by bottom wavemakers using a high-order spectral method and a linear analytical solution

This study numerically investigates characteristics of nonlinear periodic waves generated by a moving bottom wavemaker. A high-order spectral (HOS) method incorporating the moving bottom boundary condition was adopted for simulations of waves initiated by triangular- and rectangular-shaped bottom wavemakers in both two- and three-dimensional settings, and a linear analytical solution was also derived. Results indicate that larger oscillation amplitudes intensify nonlinear effects, producing sharper crests, flatter troughs, and significantly higher harmonics. In three dimensions, snake-type oscillations successfully reproduced obliquely propagating waves. Shadow zones formed perpendicular to the propagation direction, accompanied by diffraction-induced energy transfer and oscillations along crests and troughs. The HOS model closely matched the analytical solution at weak forcing, but under strong nonlinearity, it captured harmonic generation and waveform deformation beyond the linear prediction. This work extends the application of bottom wavemakers from impulsive tsunami-type motions to periodic oscillations, providing new theoretical insights into nonlinear wave dynamics.