Extreme wave amplification through the interplay of wave nonlinearity and a two-dimensional bathymetry

Wave nonlinearity plays an important role in the formation of extremely large surface waves atop a varying bathymetry, yet much of the understanding has been limited to one-dimensional (1D) bathymetry. Here, we aim to extend this understanding to two-dimensional (2D) bathymetry through numerical simulations using a fully nonlinear potential flow solver for three-dimensional waves experiencing depth changes due to a submerged circular sill. The solver is validated by laboratory experiments and theoretical calculations in limiting cases. The cases chosen for the numerical results are regular waves, with low incident steepness on the deeper side and no wave breaking atop the sill. Conditions are chosen to have high trapping power, and for these cases, we report extreme local amplifications atop the sill, i.e., between 5 and 15 times the linear amplitude of incident waves. The partition of these locally amplified waves into different wave harmonics demonstrates that the first harmonic waves take up <∼ 50%. The remaining components are thus attributed to nonlinear effects, which can take up to 70%. This is considerably more than typically observed, with implications for developing perturbation expansion-based methods in a similar physical setting. How wave amplitudes are considerably amplified by the interplay of wave nonlinearity and a 2D bathymetry has been shown, giving rise to highly localized extremes, which may be hazardous, or exploited for coastal protection, surfing, or energy extraction purposes.