Reflection and transmission of nonlinear water waves at a semi-submerged dock

Abstract

A theoretical approach is applied to predict reflection and transmission of nonlinear water waves at a semi-submerged dock. The solution was achieved analytically and by the method of matched eigenfunction expansions. The results show that the dock geometry has a significant effect on the nonlinear components of wave reflection and transmission. The reflection and transmission of nonlinear waves simultaneously increase with increasing dock width for shallow water waves and decrease with increasing dock width for intermediate- and deep-water waves, which is an interesting outcome. A similar simultaneous increase or decrease of nonlinear wave reflection and transmission was observed for the changes of the dock draft. Moreover, the solution reveals that nonlinear wave components may provide a significant contribution to the wave field for a wide range of wave parameters. The nonlinear components of wave reflection and transmission may exceed many times the amplitudes of the corresponding second-order Stokes waves as well as the amplitudes of the corresponding linear components. This phenomenon occurs within the commonly accepted range of the applicability of the second-order wave theory and implies a need to include scattered nonlinear wave components in the analysis of many problems of practical importance, including sediment transport, for which second-order waves have been shown to be the main driving force. Laboratory experiments were conducted to verify nonlinear wave field components. Theoretical results are in reasonable agreement with experimental data.