Shoaling of Finite-Amplitude Rogue Waves

Abstract

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.

32 pages, 21 figures; Previously this version appeared as arXiv:2607.12941 which was submitted as a new work by accident

References in corpus (7)

• Saturation of Rogue Wave Amplification over Steep Shoals
• Non-homogeneous approximation for the kurtosis evolution of shoaling rogue waves
• Effect of shoaling length on rogue wave occurrence
• Symmetric influence of forward and opposing tidal currents on rogue wave statistics
• A Continuous Non-ergodic Theory for the Wave Set-up
• Coastal wave refraction in variable currents over a varying bathymetry
• Direction Symmetry of Wave Field Modulation by Tidal Current