Model study of long-wave amplification by circular islands

Abstract

The amplification of periodic gravity waves around circular cylinders and around model islands composed of a circular seamount base and a cylindrical cap was studied in a ripple tank. Five different seamount bases were used: one concave, two conical, and two convex. Three cylindrical caps were used with the parabolic convex seamount base, and five others were used with each of the other four seamount bases. The “islands” were positioned in the ripple tank with the water depth adjusted to equal the height of the seamount base. The circular cylinders were tested in water depths which varied from one to six inches. Water surface fluctuations at several azimuth angles around the “coastline” of the cylindrical cap and around the circular cylinders were recorded for a periodic wave input, and amplification factors were computed. The experimentally determined amplification factors for the cylinders agree with the predicted values of Havelock (1940) and are independent of the ratio of wavelength to water depth. The theory of Webster and Perry (1966) for the model islands proved valid for long waves of length approximately equal to or longer than the island base diameter for an azimuth angle of 0°. Homma's theory (1950) for the parabolic convex island was verified for long waves of length two-thirds the base diameter of the island for all azimuth angles.