Incident wave propagating from deep water to inshore affects not only stability of costal structure but also erosion of coastal beach. In particular, the erosion of costal beach is one of the most interesting subjects concerned by many researchers in Korea. Considering preservation of coastal region from wave attack, investigation into reflection of waves due to various bottom topographies is very important. In this study, wave reflection due to various shapes of trench is calculated by using the eigenfunction expansion method (EFEM). This method has advantage of obtaining solutions with reduced time, labor and cost. The proper numbers of steps and evanescent modes needed for analysis are suggested by applying the eigenfunction expansion method to a bottom topography of which slope or curvature varies. And then, the reflection coefficients are calculated by changing the shape of a bottom topography. To consider real sea state, the Bretschneider- Mitsuyasu frequency and Mitsuyasu type directional spectrum are used. Energy density spectrum is decomposed into individual regular waves. Reflection coefficients of random waves are then calculated by composing the results of eigenfunction expansion method for each regular wave.
Incident waves propagating from deep water to onshore affect not only the stability of costal structures but also erosion of costal beach. In particular, the erosion of costal beach is one of the most interesting subjects concerned by many coastal researchers. Considering the preservation of coastal region from wave attack, investigation of wave reflect ion by varying bottom topographies is very important. The study for wave reflection by changing the water depth has been frequently and widely done through theoretical, experimental and numerical investigations. In the theoretical aspect, the beginning of the study for wave reflection was given by Takano (1960), who studied the wave reflection by an elevated st ill and fixed obstacle at the surface using the eigenfunctions expansion method. Kirby and Dalrymple (1983) calculated the reflection and transmission coefficients of waves propagating over a submerged trench using same method.
