Variation of Wave Force on Submerged Object at Shallow Water: Fourier Series Technique

This paper is presented a solution of shallow water wave force, using Fourier series approximation method on two dimensional vertically submerged rectangular thin plates under two different configurations: (1) a surface-piercing rectangular thin plate, and (2) a bottom-standing rectangular thin plate. A propagating wave of different amplitude and at different time period is made to impose normal wave force on submerged object. Bernoulli's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore under different depth of water. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force with respect to the wave amplitude is obtained at different depth of water and at different wave period. The wave force is measured at four different depths on the submerged object. It is observed that the forces are converging with the increase of wave period and the gradients of forces with respect to the wave amplitude are extremely high for lower wave period. Wave forces are maximums on the surface of water and it decreases gradually towards the bottom of water. The purpose of this study is based on to made an innovative design of a low cost wave energy converter (WEC) where the kinetic energy obtainable from the ocean surface wave is converted in the form of potential energy.