Linear free-surface effects on a horizontally submerged and perforated 2D thin plate in finite and infinite water depths

Abstract

The wave diffraction, as well as the forced heave and roll oscillations, of a horizontally submerged two-dimensional plate of zero thickness are studied by a semi-analytical solution for both finite and infinite water depths. The flow caused by the plate is represented by a distribution of vortices along the plate that satisfy the linear free-surface, radiation and sea-bottom conditions in the frequency domain. The vortex density is expressed as the sum of a Fourier series and terms that account for the flow singularities at the plate edges. When the plate is perforated, a quadratic (nonlinear) pressure loss condition, which relates the pressure loss/difference to the square of the transverse velocity, is assumed in our detailed studies. A time-efficient iterative solution technique is applied, and less than 10 Fourier series terms are needed to obtain high accuracy. The added mass and damping, wave loads, wave transmission and reflection depend on a perforation-effect Keulegan–Carpenter (KC) number that combines the effects of the perforation ratio, discharge coefficient and KC number. The presented method is verified by comparing it with published results based on other solution methods. The influence of the wave number, submergence, water depth and perforation-effect KC-number is illustrated. Techniques to minimize wave transmission are discussed.