Nonlinear computation for focused wave groups on abrupt depth transitions

Abstract

Focused wave groups in intermediate water depth propagating over varying abrupt depth transitions are studied numerically and experimentally. The experiments well validate the fully nonlinear model by a conformal mapping method. The generation of second-order and third-order harmonics is observed near the top of the submerged step, as well as the decrease of the main (first-order) components propagating along with the step. In addition, an enhancement of kurtosis occurs just after the step with a high-trailed profile, revealing a considerable asymmetry of the surface elevations. In addition, a wave group passing two or three steps is also investigated numerically. More submerged obstacles effectively strengthen the reflection capability in terms of the reflection coefficients computed with the amplitude of wave envelopes. Although the harmonics manifest a higher risk of extreme waves on abrupt depth transitions, the increase of water depth changes might not further enhance the maximum skewness and kurtosis over the varying bottom.