Scattering of Water Waves by Vertical Cylinders

The scattering of small amplitude water waves by an array of vertical cylinders is studied theoretically and experimentally. In the theoretical study, a method of matched asymptotic expansions is first developed to find the reflection and the transmission coefficients without considering real fluid effects. Energy loss due to the flow separation near the cylinders is modeled by adopting a linearized form of the quadratic resistance law. It is shown that this is equivalent to introduce a complex blockage coefficient. The energy loss coefficients for square cylinders and circular cylinders are determined by comparing theoretical results with experimental data.