Hydrodynamic interaction among multiple columns in front of a vertical wall

Abstract

The berthing or mooring facilities in ports and/or harbors are usually in the form of a group of vertical columns. These structures are arranged in close proximity to the long vertical harbor wall. Accurate prediction of wave force on such structures is of importance, yet, challenging, as both interferences among cylinders as well as between cylinders and the wall must be correct. In this work, a novel analytical model has been developed to investigate the hydrodynamic characteristics of such structures within the framework of linear wave theory. The original problem is considered to be equivalent to that of two symmetrical arrays of cylinders in open water; both are exposed to the ambient incident waves. The original array of cylinders is labelled as real cylinders hereafter, and the second array as image cylinders. The assumption of full wave reflection on the wall is essential by using this treatment. Due to the symmetry, simple relationships between the diffracted waves from the real and image cylinders are found, which reduces the number of unknowns associated with the velocity potential by half. After solving the velocity potential, the wave forces as well as the surface elevation are evaluated. Two different solutions have been developed for the calculation of mean drift wave force. One is based on the direct pressure integration and the other is based on the application of momentum conservation theorem in a limited fluid volume surrounding a certain cylinder in the array. Then, the systematic analysis is performed for a line array of equally-spaced cylinders parallel to a vertical wall. Largely amplified wave forces are found at specific wave frequencies, which occur with the appearance of pronounced wave runup around the cylinders. Furthermore, the relative contribution of the first-order and the mean drift wave forces to the total wave force is examined.