Wave induced oscillations in harbors with connected basins

Abstract

A linear, inviscid theory, termed the coupled basins theory, has been developed to analyze the response to periodic incident waves of an arbitrary shape harbor containing several interconnected basins. The region of consideration is divided into an open-sea region and several inner-basin regions (the number depending on the harbor geometry). The solution in each region is formulated as an integral equation in terms of the normal velocity at the entrance and/or at the common boundaries between regions. An approximate method is used to solve the integral equation by converting it to a matrix equation. The initially unknown boundary condition at the entrance is determined by matching the wave amplitudes and their normal derivatives at the harbor entrance and at all the common boundaries. The solution for the response and the amplitude distribution within the complete harbor can then be obtained. It has been found that the coupled-basins theory gives results which agree well with experiments both for an irregular shape harbor as well as for a harbor composed of two connected circular basins. Various aspects of the response of harbors composed of several types of circular connected basins as well as circular harbors with rectangular entrance channels have been investigated. It is found that to a first approximation the response of a coupled harbor system can be constructed by superposing the response of the individual harbors Certain aspects of the effect of viscous dissipation on harbor resonance are discussed. Some attention is given to problems of scaling model results to the prototype harbor.