Scattering of Tidal Frequency Waves around a Cylindrical Island

Abstract

The scattering solution around a small cylindrical island in a shelf sea of uniform depth is derived for Sverdrup, right-bounded Poincare, and Kelvin waves, which includes linear bottom friction, and the solution is extended to the subinertial frequency range. Effects of scattering on the amplitude and phase vary, depending on the type of incident waves. A Sverdrup wave scattering near the inertial frequency produces large amplitude and phase differences around the island due to singularity effect. However, the singularity effect does not happen for Poincare and Kelvin waves, even though the amplitude and phase variation depends on bottom friction and wave frequency. For an observer looking down the direction of wave propagation around the island, the maximum amplitude due to Sverdrup wave scattering occurs on the left-hand side, and the phase difference increases more than twice that by incident wave propagation. Scattering of Poincare waves at a superinertial frequency for an island located at a fixed distance from the straight coast produces its maximum amplitude on the right-hand side and at a subinertial frequency on the leeward coast. In the case of Kelvin wave scattering, the amplitude attenuates by frictional damping along the direction of wave propagation around the island and phase difference increases as much as twice that by incident wave propagation. Application of these theoretical results to tides around Cheju Island, off the south coast of Korea, suggests that the amplitude and phase variations of the M2 and O1 tides are due to the scattering of those tides comprised of Sverdrup and Kelvin waves having superinertial and subinertial frequencies.