Wave Forces Exerted on a Submerged Horizontal Plate over an Uneven Bottom

Abstract

Monochromatic wave scattering on a submerged horizontal plate over variable topographies is studied analytically based on the modified matched eigenfunction expansion method. Under the assumption of the shallow flow over a slowly varying bottom, an approximate solution of the flow in the inner region bounded by a submerged plate and a plane slope is presented based on the potential flow theory and perturbation method. The analytical solution is validated by existing analytical results and experimental data on flat bottoms. Parameter analysis is carried out for three types of variable topographies. The effects of the bottom profile on wave reflection and wave loads are investigated. It is found that there are significant influences on wave reflection due to uneven bottoms. Smaller maximum reflection coefficient appears in the following cases: larger relative slope heights for simple slopes, larger relative hump heights for humped bottoms, and larger relative hump heights for combined bottoms. Compared with the change of wave reflection coefficient, the shift of wave loads over the three types of variable topography seem not to be significant.