Shoaling of Finite-Amplitude Rogue Waves

Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow water. Current theories and experiments describe the rogue wave amplification near shallow water regimes, but only for small-amplitude waves, and thus, not accounting for wave-breaking processes. To address this gap, we perform experiments to probe inhomogeneous wave fields nearing the wave-breaking regime. We also show that by increasing the significant wave height towards the breaking limit, the kinetic energy grows faster than the variance of the surface elevation due to nonlinearity, providing a physical explanation why the occurrence of rogue wave first increases in shallower waters and suddenly decreases further shorewards.