The effect of blocking resonance and current on wave scattering due to finite flexible plate with permeable ocean bottom

Abstract This study explores the effect of wave blocking caused by ocean currents on the oblique wave scattering by a finite flexible plate floating horizontally over a permeable ocean bottom. The velocity potential for finite water depth is calculated using the method of eigenfunction expansions associated with the continuity of velocity and pressure along with the boundary condition of the clamped edge. Due to incident waves, the study also examines the free surface elevations, the deflection of a floating plate, and the wave reflection and transmission coefficients under ocean current and permeable bottom circumstances. Furthermore, the study investigates the influence of flexural rigidity, compressive force, Froude number, wave incidence angle, and porosity parameter on the wave reflection and transmission coefficients. Notably, the wave energy propagation in the form of reflection coefficients decreases with higher Froude numbers. The amplitude of plate deflection increases with the increase in the Froude number. The study shows that zero reflection and full transmission are possible when there is a rigid bottom and a permeable bottom with a real porosity parameter under particular wave and structural characteristics combinations. However, these ideal conditions do not hold for a complex porosity parameter. Furthermore, wave transmission decreases significantly with an increase in the length of the floating plate due to energy dissipation by the permeable ocean bottom, especially for a complex porous-effect parameter. Additionally, the impact of the porosity parameter on wave blocking has been studied. Wave blocking occurs for specific physical conditions but ceases as porosity parameter values increase. The study also emphasizes the significant influence of different wave propagation modes on the reflection coefficients in open water and plate-covered regions. Overall, this research provides valuable insights into the impact of ocean currents, bottom permeability, wave propagation modes, and structural parameters on wave scattering by a floating finite flexible plate over a porous ocean bottom.