Higher-harmonic contributions to surface elevation, kinematics, and wave loads in wave packets across an abrupt depth transition

Abstract

The evolution of narrow-banded wave packets across an abrupt depth transition is examined using both laboratory experiments and a fully nonlinear potential-flow model. Whereas available theoretical studies focus up to the second harmonic, here we focus on higher harmonics (i.e., third–fifth) leading to nonlinearity and thereby amplified wave steepness, wave kinematics, and wave force. Surface elevations obtained from laboratory experiments are used to verify the model, with good agreement up to and including the fifth harmonic. Horizontal velocity and acceleration from the model simulations are used to calculate the horizontal force on a cylinder using the Morison equation. The first to fifth harmonics are extracted from the profiles of wave characteristics (e.g., surface elevations, kinematics, wave force) using a Fast Fourier Transform-based bandpass filter to assess their contributions. Higher harmonics accounted for up to 25% of the total surface elevation, up to 30% of horizontal acceleration, and up to 33% in wave force. Thus, higher harmonics should be accounted for in the evolution of waves in coastal waters to ensure loads are not under-estimated.