A numerical study of solitary wave interaction with rectangular obstacles

Abstract

A well-validated numerical model is employed to study solitary wave interaction with rectangular obstacles. The characteristics of wave transformation in terms of wave reflection, transmission, and dissipation (RTD) coefficients are investigated for various combination of obstacle length a and height b. Considering that a solitary wave will go through the fission process over a long obstacle or step, during which the wave profile continuously evolves that makes it difficult to define the transmission coefficient based on wave heights, we propose the integration of energy flux for the calculation of wave coefficients. A general integral energy equation is derived that serves as the basis of calculating RTD coefficients. This method is applied in this study for the obstacles with 0< b/ h<1+2 H/ h and 0< a/ h<∞ (where H is the wave height and h is the deep water depth), which cover the full range of structural type from a submerged obstacle to an emerged obstacle and from a thin plate to a step. For waves on steps, the present numerical results agree excellently with Lamb's [Lamb, H., 1932. Hydrodynamics, 6th Ed. Dover, New York] theory based on the long wave approximations and Seabra-Santos et al.'s [J. Fluid Mech. 176 (1987) 117] experimental data for both weakly nonlinear and fully nonlinear waves. The “edge-layer” theory developed by Sugimoto et al. [J. Phys. Soc. Jpn. 56 (1987) 1717], however, underestimates wave reflection significantly. For waves over obstacles, only the weakly nonlinear waves H/ h=0.1 are considered. The RTD coefficients for different a/ h and b/ h are calculated and tabulated for the purpose of engineering application. The major differences between waves on a step and on a long obstacle are highlighted. The role of energy dissipation is explored and it is found that it can consume up to 60% of the total energy. The energy dissipation is mainly caused by vortex shedding and wave breaking that reduces wave transmission but has little impact on wave reflection.