摘要：In this paper, a mathematical model is formulated to investigate the effect of a submerged trapezoidal breakwater and its turbulence on reducing wave transmission. The breakwater has a composite slope on the side facing the incident waves, in common with many practical examples. Wave motions obeying modified Linear Shallow Water Equations (LSWE) are considered with the addition of a diffusion term in the momentum equation to represent the energy dissipation due to turbulent motion promoted by the breakwater. The modified equations are solved analytically using the Separation of Variables Method to obtain wave reflection and transmission coefficients. Test cases are presented to validate the analytical solutions against the known solutions for common breakwater structures, such as rectangular breakwaters. For the compositesloped structure, wave shoaling may occur, increasing the incident wave amplitude. After passing over the breakwater, the wave amplitude decreases as it propagates into deeper water. Here, the diffusion effect caused by the breakwater works as a reducer to help reduce the wave amplitude. Applying the model to the real bathymetry of the coast of Aceh, Sumatera, Indonesia, shows that the breakwater can reduce the tsunami wave amplitude slightly. It also shows that the diffusion coefficient reduces the wave amplitude differently depending on the characteristics of the wave itself.
关键词：diffusion term;shallow water equation;submerged trapezoidal breakwater;transmission coefficient;turbulence
