MATHEMATICAL MODEL FOR INVESTIGATING AMPLITUDE REDUCTION BY A TRAPEZOIDAL BREAKWATER - DWI PUTRI (NIM: 10114078), ANANDA
In this final project, a mathematical model in the form of 1-D half linear shallow water equation was developed to study the reduction of wave amplitude by trapezoidal breakwater. Analytically, we derived a reflection and transmission coefficients that are Bessel functions and explicitly depend on the breakwater characteristics, such as width of two slopes (in front and at the rear) and the top of the breakwater as well as the depth in front, above and behind the breakwater. The results of this analytical solution show that the reflection coefficient increases, and the transmission coefficient decreases when the slope width both in front and at the rear of the breakwater becomes narrower. From the present analytical solution, it is also found that the periodicity of the wave reflection and transmission coefficients as the function of the breakwater width. The analytical solutions obtained in this study shows a good agreement with the analytical solutions that given by other researchers, which include the wave reflection and transmission from a rectangular breakwater, an infinite step, an infinite step behind a linear slope, and an orthogonal triangular breakwater. On the other hand, when the water depth behind the breakwater is smaller than the depth in front of the breakwater, the shoaling wave phenomenon will occur. Numerically, the shallow water equation is solved using staggered grid finite volume method. Furthermore, the validation of numerical results with analytical solution shows a good agreement.