Shoaling of Finite-Amplitude Rogue Waves

TL;DR

This paper investigates how rogue waves form and intensify in shallow waters, revealing that nonlinear effects cause their occurrence to first increase then decrease as waves approach breaking limits.

Contribution

It provides experimental evidence linking wave energy growth and rogue wave behavior near breaking conditions, addressing gaps in existing theories for large-amplitude waves.

Findings

Kinetic energy increases faster than surface elevation variance near breaking.

Rogue wave occurrence initially rises then drops closer to shore.

Nonlinear effects are key to understanding rogue wave dynamics in shallow water.

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.