Generation and Propagation of Water Waves in a Two-Dimensional Numerical Viscous Wave Flume

Abstract

This study investigated the generation and propagation of water waves in a numerical viscous wave flume. The numerical scheme developed by Huang and collaborators for solving the unsteady two-dimensional Navier–Stokes equations for wavemaking problems was employed to generate different incident waves, including small- and finite-amplitude waves and solitary waves. The accuracy of the numerical results for the wave and velocity profiles was verified by comparison with the analytical solutions. The wave propagation in a numerical wave flume was also investigated. For periodic gravity waves on finite water depth, the results showed that waves with larger Ursell numbers are more stable than those with smaller Ursell numbers. The propagation of solitary waves in the channel is stable. For stable waves, the wave height attenuation caused by the energy dissipation in the wave motion was shown to be consistent with the theoretical results.