Scattering of Surface Gravity Waves by Islands, Reefs, and Barriers
This chapter focuses on the scattering of surface gravity waves by islands, reefs, and barriers. Surface gravity waves that propagate from the deep ocean to coastal regions may be strongly amplified by reflection, refraction, diffraction, and shoaling due to variation in water depth. Analytical solutions provide an attractive approach to studies on wave scattering, but they are obtainable for only special topographies and simple governing equations. The chapter considers long surface gravity waves (linear shallow water waves) such that the depth of the water is much greater than the vertical free surface displacement and the wavelength is much larger than the depth. The fluid equations are derived directly for the present context. The discussion covers trapped waves, the scattering or S-matrix, submerged circular islands, edge waves on a sloping beach, one-dimensional edge waves on a constant slope, and wave amplication by a sloping beach.